Casino game statistics

Online casino sites to play on real money

As a site that teaches profitable betting strategies, and we’ve taught thousands of people via our free beginner course and on-site lessons, it’s saddening to see what appears to be genuine delusion throughout punters in the country. Fans of horse racing were most likely to believe they were profitable bettors, whereas fans of formula 1 were least likely.

Alarming UK gambling statistics, sports betting data & research 2020

We asked people in the UK aged 18-54 about their interest in watching sports, betting on sports, and playing casino games. Some of the results were expected, but other findings were alarming.

It’s worth noting that we screened anyone that did matched betting or arbitrage betting to ensure our dataset was not skewed by those that know how to beat the system.

This data was compiled & published in september 2018.

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Our thoughts

They’re harsh words, but arguably more than fair.

It’s not unusual for people to think they are profitable bettors when in fact they are not; psychologically you remember your wins more than you remember your losses.

However, it’s the sheer number of people that think they are profitable — a massively unrealistic quantity — that no doubt spurs bookmakers and casinos, and broadcasters and the media as a byproduct, to shove gambling adverts in the faces of spectators anywhere they turn.

The fact that over half of 18-24 that place sports bets think they are profitable is a sure sign, to us, that there’s a serious lack of education in the betting world — probably made worse by aggressive marketing from bookmakers in the industry.

It’s hard to judge exactly how much marketing affects our data because those that watch sports are obviously more likely to bet on it than those that don’t watch sports. However, the fact that those who watch football on TV are 33% more likely to gamble on casino games compared to those that don’t watch football on TV suggests that football fans have a subconscious desire to gamble, which must surely be influenced by how often they’re subject to betting and gambling-related adverts.

Another telling statistic is that 35.3% of all sports bettors believe they are profitable — this number rises to 41.24% for those that bet regularly — but only 7.8% of these people have ever been restricted or banned by a bookmaker. As a site with years of experience in the industry, we can assure you that almost all profitable bettors (long-term) are banned or restricted in terms of stakes and access to promotions. Large bookmakers like skybet claim to have only restricted 2-3% of their customer base — nowhere near this 35.3% supposed ‘winner’ percentage.

Only just over half of these ‘profitable’ bettors knew what a betting exchange was; a type of site that will give higher odds (and therefore more value) on almost all markets, almost all of the time.

One of the most disturbing findings is that 29.55% of all people that play casino games believe they are profitable players.

We already know, due to the pre-survey screening, that none of these people know how to beat casinos. Without them knowing how to exploit casinos, we can confidently say that 0% of these people play casino games profitably long-term.

A very small number of people may have hit a big win, combined with playing infrequently, which would lead to them thinking they were profitable. But there is no way that ‘very small number’ could be anywhere close to 29.55% of people, which means there are likely millions of uneducated people in the UK that think they can actually beat casinos using some form of strategy or system.

You can’t ‘beat’ casinos without exploiting them: even playing the perfect blackjack game loses you around 50p on every £100 staked in expected value.

The findings

Viewers of horse racing were by far the most likely to place bets out of all TV sports audiences, with only 2.6% of horse racing fans saying they never bet.

Percentage of TV audiences that do bet on sports:

97.4% horse racing

86.4% boxing

81.1% tennis

81.1% golf

76.8% football

74.9% formula 1

73.1% cricket

43.9% other

…although they’re not necessarily betting on the sport in question.

Fans of horse racing were most likely to believe they were profitable bettors, whereas fans of formula 1 were least likely.

People that bet online were more likely to bet more money each month compared to those that prefer to bet in bookmakers on the high street:

38.7% of online bettors bet £10 – £100 each month (vs 29%)

8.6% bet £100 – £500 each month (vs 5%)

1.2% bet £500+ each month (vs 1%)

35.3% of sports bettors consider themselves to be ‘profitable’.

…but only 52.6% of these know what a betting exchange is.

…and only 7.8% have ever been banned or restricted (stake limits or removed promotional access) by a bookmaker before.

Of people that believe they aren’t profitable…

20.9% say they have lost ‘hundreds’

8.5% say they have lost ‘thousands’

0.7% say they have lost ‘tens of thousands’

Those that bet in-play (45.4% of bettors surveyed) were 2.2 times more likely to say they believed they make a profit than those that don’t bet in-play.

Men that watch sport are more likely to bet on sports than women that watch sport:

Men: 55.1% sometimes, 19% regularly, 25.9% never

Women: 50.7% sometimes, 17.4% regularly, 31.9% never

Men are also around 22% more likely to believe they were profitable sports bettors than women are.

Those aged 18-24 were significantly more likely to believe they were profitable sports bettors, with 58.5% of this age bracket saying they turned a profit by betting. This number is 36.4% for those aged 25-34, 27.7% for those aged 35-44 and 29.7% for those aged 45-54.

Those aged 18-24 are also betting in bigger quantities than any other age category. 52.3% of bettors in this category are risking more than £10 a month, with this figure being 48.1% for 25-34, 42.5% for 35-44 and 41.5% for 45-54.

12.2% of those in the 18-24 category are risking more than £100 a month on sports bets. This figure is 9.3% for 25.34, 7.8% for 35-44 and 7.9% for 45-54.

Those in middle income brackets were 21% more likely to bet on sports than those in low income brackets and 12% more likely than those in high income brackets.

Of those that never bet on sports, 81.2% also never play games such as blackjack, roulette, slots or bingo.

In comparison, those that bet on sports sometimes were 3.2 times more likely to gamble on casino games, and those that bet regularly on sports were 3.9 times more likely.

29.6% of casino game players considered themselves profitable players.

Those that played casino games regularly were also over 2 times more likely to believe they turned a profit versus those that only played sometimes (25.4% vs 50.9%).

Men are more likely to play casino games than women are:

Men: 8% regularly, 39% sometimes, 53% never

Women: 7% regularly, 35% sometimes, 58% never

Men are more likely to believe they are profitable players than women. 31.4% of men that play casino games believe they are profitable, compared to 24.4% of women.

Those aged 18-24 are most likely to think they are profitable casino players, with 54.5% in this category judging themselves as profitable. This figure is 30.7% for the 25-34 category, 20.8% for 35-44 and 16.4% for 45-54.

Those in low income brackets were 8% more likely to believe they were profitable casino game players than those in higher income brackets.

Fans of watching football on TV were 33% more likely to play casino games than those that do not like watching.

You are welcome to use any of our data with source link credit to beating betting.

Full data set can be found publicly at beatingbetting.Co.Uk/dataset. Matched bettors and arbitrage bettors were screened beforehand and were not included in the survey to eliminate unreliable or skewed data.

About the author

This post was written by luke jordan. Luke founded beating betting at the start of 2016 and ran the site until february 2020. He is passionate about entrepreneurship, marketing and video creation.

Casino game statistics

Gamers and gaming behavior
in 2015, 49 percent of american consumers said they had played a video game at least once in their life. Men are still the dominant gender among gamers, and while there was a time when the proportion of female gamers had seen an increase, it seems that men are reclaiming their majority as gamers. The average american gamer spent nearly 29 hours with a game console each month. On a weekly basis, 27 percent of console users spent an average of three to five hours playing games on this device. Despite the fact that 2012 saw rapid decrease in consumer expenditures to 20.77 billion U.S. Dollars, from 24.82 billion in 2011 or 25.13 billion in 2010, recent data on consumer spending on gaming shows that the industry might be picking up again, as 2016 was to see the figure grow to 30.4 billion U.S. Dollars.

Statista’s exclusive global consumer survey holds further information on the video gaming behavior of adult internet users in the united states. The comprehensive catalog of consumer research provides detailed figures on device preferences, gamer spending habits, commonly used streaming platforms as well as gaming intensity and weekly hours devoted to the activity. For more in-depth insights each data point is broken down by various target groups to better portray specific gaming habits. All this and much more can be explored in the global consumer survey.

This text provides general information. Statista assumes no liability for the information given being complete or correct. Due to varying update cycles, statistics can display more up-to-date data than referenced in the text.

Interesting statistics

In the following 5 chapters, you will quickly find the 34 most important statistics relating to "gaming".

7 statistics about gambling you need to become familiar with

As a blogger, I have goals. One of them is to write data-driven posts. What better way to provide informative content to my readers?

Statistics about gambling provide a perfect opportunity to write just this kind of post. I came up with the idea for this post a couple of days ago. A friend of mine (also a blogger) asked for feedback on his latest post.

The first three paragraphs—your introduction—are boring. Much of what you’ve written is bland to the point of being meaningless. For example, one of your sentences is “gambling games are part of our culture”.

You want to include specific data about HOW those gambling games are woven into our culture. The best way to do this—especially in your introduction—is by sharing specific statistics and data points to catch your readers’ interest from the start.

King richard outlawed dice among his soldiers in 1190. Cervantes was writing about blackjack as early as the early 17 th century. The word lottery is derived from the biblical concept of “casting lots”.

That’s a data-driven approach to explaining that gambling games are a part of our history.

Of course, that’s a little bit of a digression. You want to read a post with gambling statistics that you NEED. I offer 7 of these statistics below, along with some commentary and analysis related to each of them.

1. On any given day, a casino gambler will walk away a winner 30% of the time

This statistic is from the wall street journal. It’s encouraging, but it doesn’t tell the whole story, either.

The data comes from a 2 year period and looks at results of casino players on the internet. Over the entire period, 11% of those gamblers ended profitably. Most of them had a net win of less than $150.

A more important detail is how those results change for heavy gamblers. The top bettors are the ones who placed the most wagers over the 2 year period. Only 5% of the top-tier gamblers walked away a winner.

Here’s another telling detail:

2% of the gamblers made up 50% of the casinos’ revenue. And 10.7% of the gamblers made up 80% of the casinos’ revenue.

What about the gamblers who spent less time gambling? How did they fare?

The 10% of the gamblers who placed the fewest wagers had the highest winning percentage. 17% of them walked away winners.

The study looked at a total of 4222 gamblers. Of them, only 7 won more than $5000, but 217 lost more than $5000.

What do specific individuals look like?

One example is a swiss customer who played an average of 3 days per week. He made 1000 wagers per day at an average of $9 per bet. He won 16% of the days he gambled.

What was his net loss over 2 years?

Another example is a slovenian gambler who only placed a few small wagers each day. He had 2 big winning days within the same 2 week period. On each of those days, he won a little over $14,000. He played for a little longer, but he still quit while he was ahead. His net profit was $22,000, making him the biggest winner in the study.

Why do you need to know and understand this data?

It keeps your expectations realistic. You shouldn’t gamble at a casino, online or otherwise, with the idea that you’re going to get rich.

It also should inform your strategy and playing tendencies. If you want to be a winner, you should use the slovenian gambler as your role model. Only place a few small wagers. Once you’ve had a couple of big winning days, quit.

Quitting while you’re ahead is the most difficult gambling strategy to adapt.

It’s also the most effective.

What does this data NOT indicate?

It’s not a condemnation of the industry. It doesn’t mean you shouldn’t gamble or play casino games. It just means you need to take a reasonable approach.

Casino gambling is like eating sweets. It’s best done in moderation, but who’d want to live their entire life without sweets?

2. Less than 2% of americans have a gambling addiction or compulsive gambling problem

This data comes from the national council on problem gambling. The number sounds small because it is.

Of course, the united states is a big country, so that tiny percentage actually equates to over 5.77 million people. By comparison, americans with a substance abuse problem number around 7%, or 20 million people.

Unfortunately, the united states does a lousy job of addressing compulsive gambling. The amount of public money spent on compulsive gambling treatment is only 1/281 of the amount provided to substance abuse treatment.

Why do you need to know this?

For one thing, it should reassure you that you’re probably not a problem gambler. Don’t assume that just because you’ve had a losing session or two that you’re a gambling addict. By all means, seek help if you need it, but gambling moderately isn’t impossible for most people.

I like to think of gambling as being like alcohol. It’s probably not good for people in general, but it’s also not something we should outlaw. Some people can handle this kind of fun. Others can’t.

Know which camp you fall into. Behave accordingly.

3. Only 0.5% of gamblers fall into the category of “professional”

This statistic is 18 years old. But I can’t imagine it’s more than double or tripled over the last couple of decades. I found it in a 1997 new york times article about a professional sports bettor. They, in turn, got the statistic from the council on compulsive gambling of new jersey.

Many of these professionals are involved in sports betting. To break even in that niche, you need to win 53% of the time. To make a living, you need to win 55% to 58% of the time. Winning more than 58% of the time is almost impossible.

But before 1987, there was no legal designation for a professional gambler. Robert P groetzinger, an illinois greyhound bettor had a dispute with the IRS, and he had to take it to the supreme court. They ruled that he was, in fact, a professional gambler.

To be considered a professional gambler, you must meet the following criteria:

You must gamble full time.

Your primary motive must be income or profit.

The biggest perk to being considered a professional gambler is that you can deduct business expenses, like newsletter subscriptions.

Why do you need to know this statistic?

It’s going to keep you realistic about your odds of becoming a professional gambler. Gambling for a living is hard work. It involves near-insane levels of self-discipline, meticulous record-keeping, and lots of knowledge.

It’s hard enough to be in the top 20% of your field. Imagine trying to be in the top ½ of 1%.

What’s the other reason for knowing and understanding this statistic?

So you’ll know that even though it’s hard and unlikely, it is POSSIBLE. If you think you’re the type of person who’d make a great professional gambler, know that it is possible.

Give it a try. It might be the lifestyle for you.

4. Electronic gaming machines are the favorite casino game of 61% of gamblers

This statistic is from americangaming.Org. The percentage of revenue generated from gaming machines is also in line with that number. Some states report revenue by game. In the states that do, 62% of their revenue comes from gaming machines.

Iowa and south dakota casinos are outliers, though. They get 91% and 90% of their gambling revenues from machines. Nevada, on the other hand, is the lowest, with 62.5%.

Why does this statistic matter to you?

For one thing, if you’re not playing electronic gaming machines, you might be missing out on some of the most entertaining games in the casino. If these games weren’t fun, people wouldn’t play them.

Slot machines and video poker are sometimes looked down on by serious gamblers. But they shouldn’t be. Many of the better-quality casinos offer slot machines without payout percentages in the 95%+ range.

And video poker has some of the best odds in any casino. Look hard enough and you’ll find video poker games with payback percentages of over 98% or 99%.

And video blackjack and roulette are becoming more popular, too. They’re worth a try if you’ve never played one before.

5. The house edge for the lottery is 50%

In an article on live science, michael shackleford, a gambling math expert, explains that the worst gambling game you can play is the lottery. That’s because the house edge is 50%.

How does that compare to other gambling games?

Even roulette has better odds. If you bet $10 on the lottery, you are mathematically expected to lose $5. Wager that same amount on a spin of the roulette wheel, and your expected lost is only about 53 cents.

Why does this statistic matter?

Once you understand how bad a bet on a lottery ticket is, you’ll probably never play again. In fact, I’d much prefer that you save your gambling money for the casino. I’ve written at length about why I hate the lottery and love casinos, but here’s a quick summary:

The government has no business running a gambling business. That’s not what the united states government is supposed to be about. Imagine if the government decided to start opening bars where they could sell alcohol.

Also, and probably more importantly, they offer a lousy game. No one should play a game with a 50% house edge. No one should offer such a game. The worldwide gambling and casino industry is a living example of how huge profits can be made offering games with much better odds.

Finally, the government doesn’t really spend the money generated by the lottery on education. The reality is that most of those funds subsidize tax cuts for corporations.

6. The best payback percentage for slot machines (96.71%) in las vegas can be found on the boulder strip. The worst (87.15%) can also be found on the boulder strip

The payback percentage for a slot machine is the amount of money a casino expects you to win per spin over the long run.

You’re playing a slot machine with a 96.71% payback percentage. You’re wagering 25 cents per spin, and you make 600 spins per hour. For every 25 cents you bet, the casino expects you to win 24.18 cents. That results in a net loss of 0.82 cents per spin. Over 600 spins, that’s a total expected loss of $4.92.

That’s not a bad deal for an hour’s entertainment. According to american casino guide, that’s the historical rate of return reported for the quarter machines on the boulder strip.

The megabucks machines offer the worst returns in vegas, and they’re especially bad on the boulder strip. Yeah, you have the possibility of winning a huge life-changing jackpot. But most of the time, you’re just going to lose the expected amount.

In this case, you’re looking at betting $1 per spin 600 times per hour. The casino expects you to keep 87.15 cents per spin; they expect to win 13.85 cents per spin. Over an hour, that adds up to $83.10.

There’s a big difference between losing $83/hour and losing $4 or $5 per hour.

Avoid the megabucks slot machine games. They’re better than the lottery, but not by much. What really matters is how they compare to other games.

7. In 2001, macau generated less than $2 million in gaming revenue. In 2012, that number rose to over $35 million

According to the reports at the university of las vegas website, macau is the fastest growing gambling destination in the world. In fact, they generate over 3 times the gambling revenue of the entire state of nevada (home to las vegas).

Why does this statistic matter?

It might matter if you’re looking for a new frontier to explore, gambling-wise. Just be ready to play baccarat. It’s by far the most popular game there. 85% of the gambling revenue generate in macau is generated from action at the baccarat tables.

Compare that with the united states, where 65% of the gambling revenue comes from slot machines. You’ve noticed that slot machines take up most of a casino’s floor nowadays. Imagine all that space covered in baccarat tables instead.

They also play pai gow there, and you’ll find other gambling games you’re familiar with.

Conclusion

Data-driven posts about gambling are hard to come by, but knowing some of the statistics makes the hobby more interesting. Knowing approximately what the odds are that you’ll walk away a winner is a good thing. It’s also good to know exactly how unusual it is for someone to be able to gamble professionally.

Understanding the house edge can help you decide which games to play and where. Stretching your gambling budget is one way to get more entertainment value for your money. The numbers don’t lie about the popularity of gambling in macau, either.

Casino stats: why gamblers rarely win

In a down economy, it's normal to start thinking of alternative ways to generate some extra money, but if you're tempted into thinking gambling is one of those good alternatives, you need to keep reading. Once you step foot into a casino and exchange your money for chips, you've sold away your only advantage, which is staying out of the casino to begin with. Casinos can bring great shows, food and entertainment, but statistically they won't bring you much more than that. (for more, see going all-in: comparing investing and gambling.)
IN PICTURES: 7 forehead-slapping stock blunders

Big business and big profits
to say casino gambling is a lucrative business would be an understatement. Last year, commercial casinos brought in a gross revenue of about $31 billion and indian casinos cashed in for about $26 billion. Although revenue from private casinos was down last year, it was still three-times higher than hollywood's 2009 ticket sales revenue of $10.6 billion, a banner year for the silver screen. It's no surprise where those profits are coming from, but that didn't stop over 36 million visitors from showing up in las vegas last year alone, with some hoping to win more money than they came in with.

Games of no chance
math is the universal language, and it rarely ever lies. Each game you play at a casino has a statistical probability against you winning. Every single time. This house advantage varies for each game, and helps ensure that over time the casino won't lose money against gamblers. For people who are really good at blackjack, the advantage for the casino might only be 0.5%, but certain types of slot machines might have a 35% edge over a player, and other games fall somewhere in between. The slot machine odds are some of the worst, ranging from a one in 5,000 to a one in about 34 million chance of winning the top prize when using the maximum coin play. (read more, in are you investing or gambling?)

The house advantage obviously doesn't mean that you can't win, because people do and sometimes they win substantial amounts, but it does mean that the more you play, the more the math works against you and the better the chances are of you walking out of the casino with less money in your wallet than when you came in.

Everyone's (not) a winner
think of all those profits we mentioned earlier as all of the losses from casino patrons each year. Of course, some of the money may come from other venues within the casino, but the breadwinner for this industry is the games. Now, think of yourself walking into a casino with the feeling that you're going to beat those odds (or profits) because luck, whatever that is, is on your side. Not likely. You can't even bet on winning or losing streaks either. If you'd had a slew of bad hands, the likelihood of that turning into a winning streak simply doesn't exist, it's not in the cards, or math for that matter.

The betting rip current
aside from the entertainment of casinos, some people do get swept into an addiction that far surpasses the entertainment value of the games. Only a small percentage of gamblers, about 5%, reach that point, but unfortunately it's estimated that their losses make up a quarter of the profits for the casinos. This is all the more reason to understand the house advantage and how it works against a player who has lost a significant sum and is spending lots of time in the casino trying to win it back. The more a player struggles to get ahead, the more he gets pulled into additional losses. (read more background info, in sinful investing: is it for you?)

Quit while you're ahead
almost every time, it's in your best financial interest not to walk into that casino and place the bet - the math simply isn't your friend. For those who want to press their luck anyway, make sure to quit while you're ahead, because that winning streak you're on is definitely all in your head. (looking for more action? Check out A quick and dirty look at sports gambling.)

Statistics and data casino mathematics

Soon after their initial discovery, mathematicians started applying the laws of probability to many different parts of life – including casino games.

One of these mathematicians was karl pearson who analysed the results of roulette games published in the french newspaper le monaco.

Roulette consists of a wheel with the numbers from 1 to 36 coloured in red and black, as well as a green 0. A ball rolls around the outside and randomly lands on one of the numbers. Gamblers can bet on a single number, a set of multiple numbers, or just a colour. Their potential winning depends on the likelihood of each of these outcomes.

Here is one of the many hundreds of newspaper extracts which pearson collected and analysed. At first sight, it looks pretty random:

Roulette results on 19 august 1823, table 5:

A roulette wheel has the same number of red and black numbers. If we ignore the green 0 (which means the casino wins) we would expect the number of red and black numbers to be approximately the same exactly equal . Let’s check that this is indeed the case for the set of results above.

This looks pretty evenly distributed – there is a small difference between the number of red and black results, but that is always to be expected in probability.

However, pearson didn’t stop here. He realised that if the results were completely random, then each of the four possible pairs of two consecutive colours should also be equally likely. Again we can count the number of occurrences in our example:

For some reasons, it seems that RR and BB happen much less frequently more frequently than R B and B R, even though they should all have the same probability. Of course, we might have just been unlucky in this particular sequence of results – but pearson tested many thousands of results and always found the same.

It gets even worse if we look at triples of results. Each of the 8 possible triples of colours should be equally likely, but that is clearly not the case here:

It seems that in this particular casino, the colours alternate much more often than one would expect. There are hardly any long sequences of the same colour ( RRR or BBB).

Pearson calculated that the probability of seeing results which were this skewed was less than 1 in 100,000,000! He assumed that the roulette wheels were rigged to create higher profits for the casino – and wrote many angry letters to expose this scam.

When he finally travelled to monte carlo, he discovered that the reason for the skewed results was of a very different nature: the journalists who were supposed to be recording the results were instead just sitting in the bar of the casino, drinking, and making up random colours…

This story shows that we humans tend to be quite bad at coming up with random-looking data: we often underestimate unlikely events (long sequences of the same colour) and overestimate likely ones (alternating colours). This can be used effectively to detect fraud in banking and insurance.

Here you can try for yourself if you are better than the journalists: write down a sequence of rs and bs, and find out how random it really is:

While pearson only analysed previous roulette results, others tried to use mathematics to increase their chances of winning in casinos. One of these was edward thorp , who invented card counting – a technique that allowed him to beat casinos at blackjack .

He later turned his focus to roulette: believing that, if you knew the exact position and speed of the ball in a roulette wheel, you should be able to use physics to approximately predict the outcome. After the dealer sets the roulette wheel spinning, there are just a few seconds when you are still allowed to place new bets. Unfortunately this time is much too short for humans to calculate the outcome in their head.

At the massachusetts institute of technology, thorp discussed his ideas with claude shannon , another mathematician and the father of information theory . Together they decided to build the first ever wearable computer, decades before the likes of google glass or apple watch.

The computer was roughly the size of a pack of cigarettes and strapped around their waist. A set of wires ran down to their shoe, which they tapped whenever the ball crossed a certain marker on the roulette wheel. That allowed the computer to calculate its speed, and predict where it would end up. Another set of wires led from the computer to an earpiece, which produced different tones based on different outcomes.

During the summer of 1961, thorp and shannon successfully tried their computer in las vegas. But while they made some money, the computer – which even contained parts of model airplanes – was not robust enough to be used at a larger scale.

Thorp wrote about their results in a scientific paper, and of course, computers were later forbidden in casinos. Thorp even got banned from all casinos in las vegas, but by then he had already moved on to yet more profitable ventures: using mathematics and computers on the stock market.

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19 astounding casino demographics

Going to a casino means more than just putting cash into a slot machine or playing some table games. The modern casino has high quality restaurants, fun nightclubs, and even concerts for people to enjoy. This gives the casino demographics an interesting twist that other industries don’t usually have.

The demographic profile of a casino visitor is very similar to the profile of the average american in the US population.

It is a misconception to say that the poorest households typically visit casinos the most. Although this may be true in from a localized standpoint at some casinos, the average household income of a casino visitor is above $35k, but below $100k per year.

Here is the typical casino visitor

78% of casino visitors who go to gamble are generally optimistic about their personal financial situation.

57% of gambling casino visitors have saved more money this year when compared to the year before. Only 44% of non-gambling casino visitors can say the same thing.

1 in 5 casino gamblers say that they are approached for their opinion about how people should invest their money.

37% of all casino visitors say that they speak to friends or relatives when they have questions about financial matters.

3 out of 4 gamblers who have not yet retired have plans in place to set aside enough money to meet their retirement goals. 2 out of 5 non-gamblers don’t have any retirement plans in place.

Men are slightly more likely to find themselves visiting a casino when compared to women.

If gamblers do find themselves with an income of less than $35k, then they are more likely to have a gambling addiction when compared to other income groups.

Is the sub-20% of people who are living in poverty in the US going to outspend those not in poverty at a casino? Very doubtful. Someone with $100k in income can spend 3x more gambling and still be reasonably secure financially. The problem is that when people who are poor gamble, they are gambling a larger percentage of their income on a game instead of things they may need. This is why the perception exists that gambling hurts the poor the most. Yet despite this, non-gambling revenues exceed gambling revenues in las vegas.

How connected are casino visitors?

51% of gamblers who visit a casino say that they stay in-touch with people through email on a regular basis.

Gamblers [78%] are more likely than non-gamblers [72%] to be homeowners.

More than 50 million people visit a casino in the average year. Each person makes an average of 7 trips per year, with many using electronic games as their primary source of entertainment.

People in the 36-50 age demographic are more likely to play slot machine games than any other age demographic. They’re also the most likely to be married and enjoy playing bingo-style games.

Younger gamblers prefer to play traditional or electronic versions of blackjack.

People who go to a casino to play craps are the most likely to also gamble online.

Just because electronics and the internet make gambling easier than ever to accomplish, this doesn’t mean that people are actually taking advantage of these mediums. Although casinos are seeing a rise in younger players embracing slot-style machines with electronic versions of roulette, craps, and blackjack available, there is still a preference for table games – especially for players who enjoy poker. Casino visitors are connected, but they don’t necessarily use those connections to actually gamble.

The values of casino visitors

58% of gamblers say that they view their work as a career. 51% of non-gamblers say that they view their work as just a job.

Half of all casino visitors who gamble say that they view owning their own business as their ideal work situation.

44% of gamblers say that their definition of personal success includes being a good spouse and/or parent.

Gamblers are less likely to place an emphasis on what god thinks of them when compared to non-gamblers in every demographic.

Although both gamblers and non-gamblers [4% each] volunteer at equal rates, it is the gamblers who are more likely to donate money to social issues [33%] than non-gamblers [20%].

Values are something that is subjective to the individual. When it comes to the average casino visitor, the notion of not judging a book by its cover seems very applicable. Gamblers especially are full of surprises when it comes to the values that they hold. It isn’t the poor that are in desperate need for a meal, a bath, and fresh clothes that you’ll find at your average casino. The casino demographics show that someone just like you is who you’re going to find.

Casino game statistics

This guide, written by casino math professor robert hannum, contains a brief, non-technical discussion of the basic mathematics governing casino games and shows how casinos make money from these games. The article addresses a variety of topics, including house advantage, confusion about win rates, game volatility, player value and comp policies, casino pricing mistakes, and regulatory issues. Statistical advantages associated with the major games are also provided.

Understanding casino math

Introduction

Why is mathematics important?

The house edge

Probability versus odds

Confusion about win rate

Volatility and risk

Player value and complimentaries

Gaming regulation and mathematics

Summary tables for house advantage

At its core the business of casino gaming is pretty simple. Casinos make money on their games because of the mathematics behind the games. As nico zographos, dealer-extraordinaire for the 'greek syndicate' in deauville, cannes, and monte carlo in the 1920s observed about casino gaming: "there is no such thing as luck. It is all mathematics."

With a few notable exceptions, the house always wins - in the long run - because of the mathematical advantage the casino enjoys over the player. That is what mario puzo was referring to in his famous novel fools die when his fictional casino boss character, gronevelt, commented: "percentages never lie. We built all these hotels on percentages. We stay rich on the percentage. You can lose faith in everything, religion and god, women and love, good and evil, war and peace. You name it. But the percentage will always stand fast."

Puzo is, of course, right on the money about casino gaming. Without the "edge," casinos would not exist. With this edge, and because of a famous mathematical result called the law of large numbers, a casino is guaranteed to win in the long run.

Why is mathematics important?

Critics of the gaming industry have long accused it of creating the name "gaming" and using this as more politically correct than calling itself the "gambling industry." the term "gaming," however, has been around for centuries and more accurately describes the operators' view of the industry because most often casino operators are not gambling. Instead, they rely on mathematical principles to assure that their establishment generates positive gross gaming revenues. The operator, however, must assure the gaming revenues are sufficient to cover deductions like bad debts, expenses, employees, taxes and interest.

Despite the obvious, many casino professionals limit their advancements by failing to understand the basic mathematics of the games and their relationships to casino profitability. One casino owner would often test his pit bosses by asking how a casino could make money on blackjack if the outcome is determined simply by whether the player or the dealer came closest to 21. The answer, typically, was because the casino maintained "a house advantage." this was fair enough, but many could not identify the amount of that advantage or what aspect of the game created the advantage. Given that products offered by casinos are games, managers must understand why the games provide the expected revenues. In the gaming industry, nothing plays a more important role than mathematics.

Mathematics should also overcome the dangers of superstitions. An owner of a major las vegas strip casino once experienced a streak of losing substantial amounts of money to a few "high rollers." he did not attribute this losing streak to normal volatility in the games, but to bad luck. His solution was simple. He spent the evening spreading salt throughout the casino to ward off the bad spirits. Before attributing this example to the idiosyncrasies of one owner, his are atypical only in their extreme. Superstition has long been a part of gambling - from both sides of the table. Superstitions can lead to irrational decisions that may hurt casino profits. For example, believing that a particular dealer is unlucky against a particular (winning) player may lead to a decision to change dealers. As many, if not most, players are superstitious. At best, he may resent that the casino is trying to change his luck. At worst, the player may feel the new dealer is skilled in methods to "cool" the game. Perhaps he is even familiar with stories of old where casinos employed dealers to cheat "lucky" players.

Understanding the mathematics of a game also is important for the casino operator to ensure that the reasonable expectations of the players are met. For most persons, gambling is entertainment. It provides an outlet for adult play. As such, persons have the opportunity for a pleasant diversion from ordinary life and from societal and personal pressures. As an entertainment alternative, however, players may consider the value of the gambling experience. For example, some people may have the option of either spending a hundred dollars during an evening by going to a professional basketball game or at a licensed casino. If the house advantage is too strong and the person loses his money too quickly, he may not value that casino entertainment experience. On the other hand, if a casino can entertain him for an evening, and he enjoys a "complimentary" meal or drinks, he may want to repeat the experience, even over a professional basketball game. Likewise, new casino games themselves may succeed or fail based on player expectations. In recent years, casinos have debuted a variety of new games that attempt to garner player interest and keep their attention. Regardless of whether a game is fun or interesting to play, most often a player will not want to play games where his money is lost too quickly or where he has a exceptionally remote chance of returning home with winnings.

Mathematics also plays an important part in meeting players' expectations as to the possible consequences of his gambling activities. If gambling involves rational decision-making, it would appear irrational to wager money where your opponent has a better chance of winning than you do. Adam smith suggested that all gambling, where the operator has an advantage, is irrational. He wrote "there is not, however, a more certain proposition in mathematics than that the more tickets [in a lottery] you advertise upon, the more likely you are a loser. Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets, the nearer you approach to this certainty."

Even where the house has an advantage, however, a gambler may be justified if the amount lost means little to him, but the potential gain would elevate him to a higher standing of living. For example, a person with an annual income of $30,000 may have $5 in disposable weekly income. He could save or gamble this money. By saving it, at the end of a year, he would have $260. Even if he did this for years, the savings would not elevate his economic status to another level. As an alternative, he could use the $5 to gamble for the chance to win $1 million. While the odds of winning are remote, it may provide the only opportunity to move to a higher economic class.

Since the casino industry is heavily regulated and some of the standards set forth by regulatory bodies involve mathematically related issues, casino managers also should understand the mathematical aspects relating to gaming regulation. Gaming regulation is principally dedicated to assuring that the games offered in the casino are fair, honest, and that players get paid if they win. Fairness is often expressed in the regulations as either requiring a minimum payback to the player or, in more extreme cases, as dictating the actual rules of the games offered. Casino executives should understand the impact that rules changes have on the payback to players to assure they meet regulatory standards. Equally important, casino executives should understand how government mandated rules would impact their gaming revenues.

The player's chances of winning in a casino game and the rate at which he wins or loses money depends on the game, the rules in effect for that game, and for some games his level of skill. The amount of money the player can expect to win or lose in the long run - if the bet is made over and over again - is called the player's wager expected value (EV), or expectation. When the player's wager expectation is negative, he will lose money in the long run. For a $5 bet on the color red in roulette, for example, the expectation is -$0.263. On the average the player will lose just over a quarter for each $5 bet on red.

When the wager expectation is viewed from the casino's perspective (i.E., the negative of the player's expectation) and expressed as a percentage, you have the house advantage. For the roulette example, the house advantage is 5.26% ($0.263 divided by $5). The formal calculation is as follows:

EV = (+5)(18/38) + (-5)(20/38) = -0.263
(house advantage = 0.263/5 = 5.26%)

When this EV calculation is performed for a 1-unit amount, the negative of the resulting value is the house edge. Here are the calculations for bets on a single-number in double-zero and single-zero roulette.

Double-zero roulette (single number bet):
EV = (+35)(1/38) + (-1)(37/38) = -0.053
(house advantage = 5.3%)

Single-zero roulette (single number bet):
EV = (+35)(1/37) + (-1)(36/37) = -0.027
(house advantage = 2.7%)

The house advantage represents the long run percentage of the wagered money that will be retained by the casino. It is also called the house edge, the "odds" (i.E., avoid games with bad odds), or just the "percentage" (as in mario puzo's fools die). Although the house edge can be computed easily for some games - for example, roulette and craps - for others it requires more sophisticated mathematical analysis and/or computer simulations. Regardless of the method used to compute it, the house advantage represents the price to the player of playing the game.

Because this positive house edge exists for virtually all bets in a casino (ignoring the poker room and sports book where a few professionals can make a living), gamblers are faced with an uphill and, in the long run, losing battle. There are some exceptions. The odds bet in craps has zero house edge (although this bet cannot be made without making another negative expectation wager) and there are a few video poker machines that return greater than 100% if played with perfect strategy. Occasionally the casino will even offer a promotion that gives the astute player a positive expectation. These promotions are usually mistakes - sometimes casinos don't check the math - and are terminated once the casino realizes the player has the edge. But by and large the player will lose money in the long run, and the house edge is a measure of how fast the money will be lost. A player betting in a game with a 4% house advantage will tend to lose his money twice as fast as a player making bets with a 2% house edge. The trick to intelligent casino gambling - at least from the mathematical expectation point of view - is to avoid the games and bets with the large house advantages.

Some casino games are pure chance - no amount of skill or strategy can alter the odds. These games include roulette, craps, baccarat, keno, the big-six wheel of fortune, and slot machines. Of these, baccarat and craps offer the best odds, with house advantages of 1.2% and less than 1% (assuming only pass/come with full odds), respectively. Roulette and slots cost the player more - house advantages of 5.3% for double-zero roulette and 5% to 10% for slots - while the wheel of fortune feeds the casino near 20% of the wagers, and keno is a veritable casino cash cow with average house advantage close to 30%.

Games where an element of skill can affect the house advantage include blackjack, video poker, and the four popular poker-based table games: caribbean stud poker, let it ride, three card poker, and pai gow poker. For the poker games, optimal strategy results in a house edge in the 3% to 5% range (CSP has the largest house edge, PGP the lowest, with LIR and TCP in between). For video poker the statistical advantage varies depending on the particular machine, but generally this game can be very player friendly - house edge less than 3% is not uncommon and some are less than 1% - if played with expert strategy.

Blackjack, the most popular of all table games, offers the skilled player some of the best odds in the casino. The house advantage varies slightly depending on the rules and number of decks, but a player using basic strategy faces little or no disadvantage in a single-deck game and only a 0.5% house edge in the common six-deck game. Despite these numbers, the average player ends up giving the casino a 2% edge due to mistakes and deviations from basic strategy. Complete basic strategy tables can be found in many books and many casino-hotel gift shops sell color-coded credit card size versions. Rule variations favorable to the player include fewer decks, dealer stands on soft seventeen (worth 0.2%), doubling after splitting (0.14%), late surrender (worth 0.06%), and early surrender (uncommon, but worth 0.24%). If the dealer hits soft seventeen it will cost you, as will any restrictions on when you can double down.

Probability represents the long run ratio of (# of times an outcome occurs) to (# of times experiment is conducted). Odds represent the long run ratio of (# of times an outcome does not occur) to (# of times an outcome occurs). If a card is randomly selected from a standard deck of 52 playing cards, the probability it is a spade is 1/4; the odds (against spade) are 3 to 1. The true odds of an event represent the payoff that would make the bet on that event fair. For example, a bet on a single number in double-zero roulette has probability of 1/38, so to break even in the long run a player would have to be paid 37 to 1 (the actual payoff is 35 to 1).

There are all kinds of percentages in the world of gaming. Win percentage, theoretical win percentage, hold percentage, and house advantage come to mind. Sometimes casino bosses use these percentages interchangeably, as if they are just different names for the same thing. Admittedly, in some cases this is correct. House advantage is just another name for theoretical win percentage, and for slot machines, hold percentage is (in principle) equivalent to win percentage. But there are fundamental differences among these win rate measurements.

The house advantage - the all-important percentage that explains how casinos make money - is also called the house edge, the theoretical win percentage, and expected win percentage. In double-zero roulette, this figure is 5.3%. In the long run the house will retain 5.3% of the money wagered. In the short term, of course, the actual win percentage will differ from the theoretical win percentage (the magnitude of this deviation can be predicted from statistical theory). The actual win percentage is just the (actual) win divided by the handle. Because of the law of large numbers - or as some prefer to call it, the law of averages - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage.

Because handle can be difficult to measure for table games, performance is often measured by hold percentage (and sometimes erroneously called win percentage). Hold percentage is equal to win divided by drop. In nevada, this figure is about 24% for roulette. The drop and hold percentage are affected by many factors; we won't delve into these nor the associated management issues. Suffice it to say that the casino will not in the long term keep 24% of the money bet on the spins of roulette wheel - well, an honest casino won't.

To summarize: house advantage and theoretical win percentage are the same thing, hold percentage is win over drop, win percentage is win over handle, win percentage approaches the house advantage as the number of plays increases, and hold percentage is equivalent to win percentage for slots but not table games.

· hold % = win/drop
· win % (actual) = win/handle
· H.A. = theoretical win % = limit(actual win %) = limit(win/handle)
· hold percentage ¹ house edge

Furthermore, the house advantage is itself subject to varying interpretations. In let it ride, for example, the casino advantage is either 3.51% or 2.86% depending on whether you express the advantage with respect to the base bet or the average bet. Those familiar with the game know that the player begins with three equal base bets, but may withdraw one or two of these initial units. The final amount put at risk, then, can be one (84.6% of the time assuming proper strategy), two (8.5%), or three units (6.9%), making the average bet size 1.224 units. In the long run, the casino will win 3.51% of the hands, which equates to 2.86% of the money wagered. So what's the house edge for let it ride? Some prefer to say 3.51% per hand, others 2.86% per unit wagered. No matter. Either way, the bottom line is the same either way: assuming three $1 base bets, the casino can expect to earn 3.5¢ per hand (note that 1.224 x 0.0286 = 0.035).

The question of whether to use the base bet or average bet size also arises in caribbean stud poker (5.22% vs. 2.56%), three card poker (3.37% vs. 2.01%), casino war (2.88% vs. 2.68%), and red dog (2.80% vs. 2.37%).

For still other games, the house edge can be stated including or excluding ties. The prime examples here are the player (1.24% vs. 1.37%) and banker (1.06% vs. 1.17%) bets in baccarat, and the don't pass bet (1.36% vs. 1.40%) in craps. Again, these are different views on the casino edge, but the expected revenue will not change.

That the house advantage can appear in different disguises might be unsettling. When properly computed and interpreted, however, regardless of which representation is chosen, the same truth (read: money) emerges: expected win is the same.

Statistical theory can be used to predict the magnitude of the difference between the actual win percentage and the theoretical win percentage for a given number of wagers. When observing the actual win percentage a player (or casino) may experience, how much variation from theoretical win can be expected? What is a normal fluctuation? The basis for the analysis of such volatility questions is a statistical measure called the standard deviation (essentially the average deviation of all possible outcomes from the expected). Together with the central limit theorem (a form of the law of large numbers), the standard deviation (SD) can be used to determine confidence limits with the following volatility guidelines:

Volatility analysis guidelines
· only 5% of the time will outcomes will be more than 2 SD's from expected outcome
· almost never (0.3%) will outcomes be more than 3 SD's from expected outcome

Obviously a key to using these guidelines is the value of the SD. Computing the SD value is beyond the scope of this article, but to get an idea behind confidence limits, consider a series of 1,000 pass line wagers in craps. Since each wager has a 1.4% house advantage, on average the player will be behind by 14 units. It can be shown (calculations omitted) that the wager standard deviation is for a single pass line bet is 1.0, and for 1,000 wagers the SD is 31.6. Applying the volatility guidelines, we can say that there is a 95% chance the player's actual win will be between 49 units ahead and 77 units behind, and almost certainly between 81 units ahead and 109 units behind.

A similar analysis for 1,000 single-number wagers on double-zero roulette (on average the player will be behind 53 units, wager SD = 5.8, 1,000 wager SD = 182.2) will yield 95% confidence limits on the player win of 311 units ahead and 417 units behind, with win almost certainly between 494 units ahead and 600 units behind.

Note that if the volatility analysis is done in terms of the percentage win (rather than the number of units or amount won), the confidence limits will converge to the house advantage as the number of wagers increases. This is the result of the law of large numbers - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage. Risk in the gaming business depends on the house advantage, standard deviation, bet size, and length of play.

Player value and complimentaries

Using the house advantage, bet size, duration of play, and pace of the game, a casino can determine how much it expects to win from a certain player. This player earning potential (also called player value, player worth, or theoretical win) can be calculated by the formula:

Earning potential = average bet ´ hours played ´ decisions per hour ´ house advantage

For example, suppose a baccarat player bets $500 per hand for 12 hours at 60 hands per hour. Using a house advantage of 1.2%, this player's worth to the casino is $4,320 (500 ´ 12 ´ 60 ´ .012). A player who bets $500 per spin for 12 hours in double-zero roulette at 60 spins per hour would be worth about $19,000 (500 ´ 12 ´ 60 ´ .053).

Many casinos set comp (complimentary) policies by giving the player back a set percentage of their earning potential. Although comp and rebate policies based on theoretical loss are the most popular, rebates on actual losses and dead chip programs are also used in some casinos. Some programs involve a mix of systems. The mathematics associated with these programs will not be addressed in this article.

In an effort to entice players and increase business, casinos occasionally offer novel wagers, side bets, increased payoffs, or rule variations. These promotions have the effect of lowering the house advantage and the effective price of the game for the player. This is sound reasoning from a marketing standpoint, but can be disastrous for the casino if care is not taken to ensure the math behind the promotion is sound. One casino offered a baccarat commission on winning banker bets of only 2% instead of the usual 5%, resulting in a 0.32% player advantage. This is easy to see (using the well-known probabilities of winning and losing the banker bet):

EV = (+0.98)(.4462) + (-1)(.4586) = 0.0032
(house advantage = -0.32%)

A casino in biloxi, mississippi gave players a 12.5% edge on sic bo bets of 4 and 17 when they offered 80 to 1 payoffs instead of the usual 60 to 1. Again, this is an easy calculation. Using the fact that the probability of rolling a total of 4 (same calculation applies for a total of 17) with three dice is 1/72 (1/6 x 1/6 x 1/6 x 3), here are the expected values for both the usual and the promotional payoffs:

Usual 60 to 1 payoff: EV = (+60)(1/72) + (-1)(71/72) = -0.153
(house advantage = 15.3%)

Promotional 80 to 1 payoff: EV = (+80)(1/72) + (-1)(71/72) = +0.125
(house advantage = -12.5%)

In other promotional gaffes, an illinois riverboat casino lost a reported $200,000 in one day with their "2 to 1 tuesdays" that paid players 2 to 1 (the usual payoff is 3 to 2) on blackjack naturals, a scheme that gave players a 2% advantage. Not to be outdone, an indian casino in california paid 3 to 1 on naturals during their "happy hour," offered three times a day, two days a week for over two weeks. This promotion gave the player a whopping 6% edge. A small las vegas casino offered a blackjack rule variation called the "free ride" in which players were given a free right-to-surrender token every time they received a natural. Proper use of the token led to a player edge of 1.3%, and the casino lost an estimated $17,000 in eight hours. Another major las vegas casino offered a "50/50 split" blackjack side bet that allowed the player to stand on an initial holding of 12-16, and begin a new hand for equal stakes against the same dealer up card. Although the game marketers claimed the variation was to the advantage of the casino, it turned out that players who exercised the 50/50 split only against dealer 2-6 had a 2% advantage. According to one pit boss, the casino suffered a $230,000 loss in three and a half days.

In the gaming business, it's all about "bad math" or "good math." honest games based on good math with positive house advantage minimize the short-term risk and ensure the casino will make money in the long run. Players will get "lucky" in the short term, but that is all part of the grand design. Fluctuations in both directions will occur. We call these fluctuations good luck or bad luck depending on the direction of the fluctuation. There is no such thing as luck. It is all mathematics.

Gaming regulation and mathematics

Casino gaming is one of the most regulated industries in the world. Most gaming regulatory systems share common objectives: keep the games fair and honest and assure that players are paid if they win. Fairness and honesty are different concepts. A casino can be honest but not fair. Honesty refers to whether the casino offers games whose chance elements are random. Fairness refers to the game advantage - how much of each dollar wagered should the casino be able to keep? A slot machine that holds, on average, 90% of every dollar bet is certainly not fair, but could very well be honest (if the outcomes of each play are not predetermined in the casino's favor). Two major regulatory issues relating to fairness and honesty - ensuring random outcomes and controlling the house advantage - are inextricably tied to mathematics and most regulatory bodies require some type of mathematical analysis to demonstrate game advantage and/or confirm that games outcomes are random. Such evidence can range from straightforward probability analyses to computer simulations and complex statistical studies. Requirements vary across jurisdictions, but it is not uncommon to see technical language in gaming regulations concerning specific statistical tests that must be performed, confidence limits that must be met, and other mathematical specifications and standards relating to game outcomes.

Summary tables for house advantage

The two tables below show the house advantages for many of the popular casino games. The first table is a summary of the popular games and the second gives a more detailed breakdown.

House advantages for popular casino games
*game*	*house advantage*
roulette (double-zero)	5.3%
craps (pass/come)	1.4%
craps (pass/come with double odds)	0.6%
blackjack - average player	2.0%
blackjack - 6 decks, basic strategy*	0.5%
blackjack - single deck, basic strategy*	0.0%
baccarat (no tie bets)	1.2%
caribbean stud*	5.2%
let it ride*	3.5%
three card poker*	3.4%
pai gow poker (ante/play)*	2.5%
slots	5% - 10%
video poker*	0.5% - 3%
keno (average)	27.0%
*optimal strategy

House advantages for major casino wagers
*game*	*bet*	HA*
baccarat	banker (5% commission)	1.06%
baccarat	player	1.24%
big six wheel	average	19.84%
blackjack	card-counting	-1.00%
blackjack	basic strategy	0.50%
blackjack	average player	2.00%
blackjack	poor player	4.00%
caribbean stud	ante	5.22%
casino war	basic bet	2.88%
craps	any craps	11.11%
craps	any seven	16.67%
craps	big 6, big 8	9.09%
craps	buy (any)	4.76%
craps	C&E	11.11%
craps	don't pass/don't come	1.36%
craps	don't pass/don't come w/1X odds	0.68%
craps	don't pass/don't come w/2X odds	0.45%
craps	don't pass/don't come w/3X odds	0.34%
craps	don't pass/don't come w/5X odds	0.23%
craps	don't pass/don't come w/10X odds	0.12%
craps	don't place 4 or 10	3.03%
craps	don't place 5 or 9	2.50%
craps	don't place 6 or 8	1.82%
craps	field (2 and 12 pay double)	5.56%
craps	field (2 or 12 pays triple)	2.78%
craps	hard 4, hard 10	11.11%
craps	hard 6, hard 8	9.09%
craps	hop bet - easy (14-1)	16.67%
craps	hop bet - easy (15-1)	11.11%
craps	hop bet - hard (29-1)	16.67%
craps	hop bet - hard (30-1)	13.89%
craps	horn bet (30-1 & 15-1)	12.50%
craps	horn high - any (29-1 & 14-1)	16.67%
craps	horn high 2, horn high 12 (30-1 & 15-1)	12.78%
craps	horn high 3, horn high 11 (30-1 & 15-1)	12.22%
craps	lay 4 or 10	2.44%
craps	lay 5 or 9	3.23%
craps	lay 6 or 8	4.00%
craps	pass/come	1.41%
craps	pass/come w/1X odds	0.85%
craps	pass/come w/2X odds	0.61%
craps	pass/come w/3X odds	0.47%
craps	pass/come w/5X odds	0.33%
craps	pass/come w/10X odds	0.18%
craps	place 4 or 10	6.67%
craps	place 5 or 9	4.00%
craps	place 6 or 8	1.52%
craps	three, eleven (14-1)	16.67%
craps	three, eleven (15-1)	11.11%
craps	two, twelve (29-1)	16.67%
craps	two, twelve (30-1)	13.89%
keno	typical	27.00%
let it ride	base bet	3.51%
pai gow	poker skilled player (non-banker)	2.54%
pai gow poker	average player (non-banker)	2.84%
red dog	basic bet (six decks)	2.80%
roulette	single-zero	2.70%
roulette	double-zero (except five-number)	5.26%
roulette	double-zero, five-number bet	7.89%
sic bo	big/small	2.78%
sic bo	one of a kind	7.87%
sic bo	7, 14	9.72%
sic bo	8, 13	12.50%
sic bo	10, 11	12.50%
sic bo	any three of a kind	13.89%
sic bo	5, 16	13.89%
sic bo	4, 17	15.28%
sic bo	three of a kind	16.20%
sic bo	two-dice combination	16.67%
sic bo	6, 15	16.67%
sic bo	two of a kind	18.52%
sic bo	9, 12	18.98%
slots	dollar slots (good)	4.00%
slots	quarter slots (good)	5.00%
slots	dollar slots (average)	6.00%
slots	quarter slots (average)	8.00%
sports betting	bet $11 to win $10	4.55%
three card poker	pair plus	2.32%
three card poker	ante	3.37%
video poker	selected machines	-0.50%
*house advantages under typical conditions, expressed "per hand" and including ties, where appropriate. Optimal strategy assumed unless otherwise noted.

Note: this summary is the intellectual property of the author and the university of nevada, las vegas. Do not use or reproduce without proper citation and permission.

Cabot, anthony N., and hannum, robert C. (2002). Gaming regulation and mathematics: A marriage of necessity, john marshall law review, vol. 35, no. 3, pp. 333-358.

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Griffin, peter (1991). Extra stuff: gambling ramblings, huntington press, las vegas, NV.

Hannum, robert C. And cabot, anthony N. (2001). Practical casino math, institute for the study of gambling & commercial gaming, university of nevada, reno.

Humble, lance, and cooper, carl (1980). The world's greatest blackjack book, doubleday, new york, NY.

Kilby, jim and fox, jim (1998). Casino operations management, wiley, new york, NY.

Levinson, horace C. (1963). Chance, luck and statistics, dover publications, mineola, NY.

Millman, martin H. (1983). "A statistical analysis of casino blackjack," american mathematical monthly, 90, pp. 431-436.

Packel, edward (1981). The mathematics of games and gambling, the mathematical association of america, washington, D.C.

Thorp, edward O. (1984). The mathematics of gambling, gambling times, hollywood, CA.

Thorp, edward O. (1966). Beat the dealer, vintage books, new york, NY.

Vancura, olaf, cornelius, judy A., and eadington, william R. (eds.) (2000). Finding the edge: mathematical analysis of casino games. Institute for the study of gambling and commercial gaming, university of nevada, reno, NV.

Vancura, olaf (1996). Smart casino gambling, index publishing group, san diego, CA.

Weaver, warren (1982). Lady luck: the theory of probability, dover publications, new york, NY.

Wilson, allan (1970). The casino gambler's guide, harper and row, new york.

Bob hannum is a professor of risk analysis & gaming at the university of denver where he teaches courses in probability, statistics, risk, and the theory of gambling. His publications includepractical casino math (co-authored with anthony N. Cabot) and numerous articles in scholarly and gaming industry journals. Hannum regularly speaks on casino mathematics to audiences around the globe. (some of this guide has been excerpted from practical casino math.)

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The games industry in numbers

Data and industry statistics are important so we can tell our story. This page brings together the headline statistics that show how our industry has grown.

We've also compiled a huge repository of industry stats and data in our downloadable games industry fact sheet.

UK success stories

The UK has a long history of making world class video games. With the global games audience estimated between 2.2 and 2.6 billion people and the global software market expected to grow from $137.9 billion in 2018 to an estimated $180.1 billion by the end of 2021, the opportunities for the UK games industry have never been greater.

As of june 2018, there are 2,261 active games companies in the UK (UK games map), operating at all sizes and scales, with world-class talent across the full spectrum of games technologies - from mobile, PC and console, to fast-developing sectors such as VR / AR, esports and artificial intelligence.

Recent global UK successes include:

Grand theft auto V by rockstar games, is the most financially successful media product of all time, selling over 95 million units worldwide and over $6bn in global revenue. It is the fastest selling entertainment product ever, grossing $1bn worldwide in just 3 days and the top selling game of all time in the UK, generating over £240m from more than 6 million physical copies sold - or roughly 3.5 sales per minute (ukie / gfk), as well as being the top-selling game in the US in terms of both revenue and units. GTAV still continues to defy expectations, returning to the top of the UK chart in march 2018, 4.5 years after it was first launched.

Batman: arkham knight by rocksteady studios, the fastest-selling game of 2015 and winner of multiple awards, including the 2016 BATFA for best british game.

Monument valley by ustwo, downloaded over 26 million times and winner of 20 international awards, including apple ipad game of the year 2014 and the 2015 batfas for both best mobile & handheld and best british game.

Hellblade: senua’s sacrifice by ninja theory, winner of 5 baftas in 2018, including best british game, as well as numerous other awards and accolades. It was one of the top selling games on steam in 2017 and was the best-selling playstation game in europe the month it was released. The game was widely recognised for its pioneering work depicting the mental health of the main character, based on research partnerships with the university of cambridge, the university of durham and the wellcome trust.

There are plenty more. We support the creative industries website which features more great UK games stories.

UK consumer market

The UK is the 6th largest video game market in 2018 in terms of consumer revenues, after china , USA, japan and germany. Approximately 37.3mpeople in the UK play games.

The UK consumer spend on games was valued at a record £5.7bn in 2018, up 10.0% from 2017 (£5.18bn):

2018 was the biggest ever year for games software, growing +10.3% to a record £4.01bn in sales, driven by record results in both digital and online sales, which eclipsed £2.01bn for the first time, up +20.3%, and mobile games, which grew +8.2% to £1.17bn . Boxed software remains a substantial factor in software sales, experiencing a slight drop of -2.6% to £770m, however pre-owned games dropped significantly -30.8% to £67.9m.

Game hardware continued to be a core driver of spend in 2018, up +10.7% to £1.57bn. Consoles sales grew a solid +6.5% to £702m, despite no new consoles being released. PC game hardware sales saw a strong year, up +18.4% to £445m, and the peripherals and accessories market similarly increase +19.9% to £355m. VR hardware had a more difficult year, dropping -20.9% to £72m, as early adopters await the next generation of headsets.

Consumer spend on wider game culture contributed an additional £109.6m in revenues across game-related toys, merchandise, books, movies and soundtracks, as well as game-based events around the UK, .

More detail on the 2018 valuation is available here.

The 2018 UK games industry consumer spend valuation was made possible thanks to data partnerships with gfk chart-track, IHS markit, kantar worldpanel, NPD, nielsen bookscan, the official charts company, the british film institute and ABC. Contact details for these companies are available via clicking the "read more" button below.

Boxed software, console hardware, perihperals & accessories: gfk chart-track - dorian bloch, business group director, dorian.Bloch@gfk.Com, 020 8600 0547

Digital and online, mobile games, VR hardware: IHS markit - piers harding-rolls

Pre-owned software: kantar worldpanel - james brown, consumer insight director

Magazines: ABC - richard gentle, 01442 870 800, enquiries@abc.Org.Uk

Movies & soundtracks: the official charts company - chris austin, head of operations executive, chris@officialcharts.Com, 020 7620 7450

Books: nielsen bookscan - matthew mansfield, head of business development

Toys: the NPD group, inc. UK - melissa symonds, director UK toys, eurotoys

Looking at an alternative source of software sales data, according to the entertainment retailers association (ERA), combined physical and digital sales UK games sales in 2018 generated a record £3.86bn, increasing 9.1% on the previous year.

This figure is now greater than that of home music and video sales combined, comprising 51.3% of the overall value of the sector, making the UK games market 1.65 times the size of the video market (£2.3bn) and 2.9 times the size of music (£1.3bn).

Digital games sales provided the majority of growth, increasing 9.1% to £3.01bn, while physical game sales declined slightly by -2.1% to £769m, although not as drastically as in physical sales for both music (-16.6%) and video (-17.1%).

ERA entertainment sales 2018

In 2016, electronic art's FIFA 17 was the highest selling entertainment product selling 2.5m units, approximately 9% more sales than star wars: the force awakens, which sold 2.3m units.

UK games map

In september 2016, ukie launched the UK games map, the first interactive, real-time map of the UK games industry.

Built in partnership with nesta, the UK's innovation foundation, the UK games map builds on the methodology established in the 2014 ukie/nesta report 'A map of the UK games industry' to provide the most complete dataset of the geography of the UK games industry ever compiled. A more detailed description of the UK games map can be found here.

The UK games map is constantly being updated with new data from across the industry - since launch in september 2016 there have been more than 1,000 updates to company data on the platform.

Key findings:

There are 2,261 active games companies in the UK (listed in the map, as of june 2018)

2,712 UK games companies have been mapped to date

62% of UK games companies were founded since the beginning of 2010

Only 41% of UK games companies use the right standard industrial classification codes

The map also lists 149 games industry service companies and 231 games-related courses across 95 universities and academic institutions.

As of june 2018, there 21 towns / cities that are home to more than 20 games companies, the top 10 of which are listed below:

top 10 towns by company count (jun 2018)

town / city	no. Companies
london	614
manchester	96
brighton	73
guildford and aldershot	70
slough and heathrow	67
cambridge	53
bristol	50
sheffield	41
glasgow	37
liverpool	37

Economic contribution

In october 2018, the BFI published a report covering the games industry's economic contribution to the UK in 2016, entitled 'screen business'. Both the full and summary versions of the report and can be downloaded in full via the BFI website.

Findings from the BFI's economic contribution report:

Overall in 2016, the UK games industry provided 47,620 FTE jobs and contributed £2.87bn in GVA to the UK economy.

The UK games industry directly employs 20,430 ftes in development, publishing and retail roles, which contribute £1.52bn in direct GVA to the economy.

Direct economic contribution of the UK games industry in 2016

Subsector	employment (ftes)	GVA (£m)
development	13,840	826.0
publishing	2,300	526.6
digital retail	310	31.7
physical retail	3,980	132.0
TOTAL	20,430	1.52

The economic impact of the growing UK esports sector was also assessed for the first time and was shown to have supported 470 FTE jobs and contributed £18.4m in GVA in 2016.

In 2016, the UK games industry spent £1.25bn on game development.

In the period 2015-2017, there was at least £1.75bn of inward investment in the UK games industry.

More detail on the economic impact of the UK games industry can be found here.

Video games tax relief

Video games tax relief (VGTR) has been available for qualifying games companies to claim since april 2014.

The BFI 'screen business' report, released in october 2018, showed the economic impacts of the relief in 2016

The VGTR supports 9,240 FTE jobs across the UK games industry, including 4,320 directly in development roles (31% of the total UK development workforce).

VGTR games represented £389.9m of UK development spend, 31% of the total development spend. Overall, projects supported by the VGTR contibuted £525m in GVA to the UK economy and £158m in tax revenue.

68% of VGTR-supported games would not be made in the UK, or at all, without the relief in place.

For every £1 the government invested into the games sector via VGTR, an additional £4 in GVA was generated for the UK economy.

Of all the screen sector tax reliefs, the games sector was shown to have the highest rate of productivity, where each employee generated an average of £83,800 in GVA for the economy, significantly above the national industrial average of £62,100.

According to data released by HMRC in july 2018, VGTR has provided £230m to UK studios across 770 claims since the relief was launched in april 2014. Of that total, £105m was paid out to 345 claims in the financial year 2017-18.

To date, VGTR has been claimed by 480 video game productions, accounting for over £1bn in UK expenditure.

The latest annual figures from the BFI certification unit on how many games passed the cultural test for qualification for VGTR were released in may 2017. The full BFI release is available here.

The latest end-of year figures for games certification numbers are:

VGTR cultural test certification, apr 2014 – mar 2017

certification	number	EEA/UK spend £m	total budget £m	EEA/UK spend as a % of total budget
final	364	423.9	548.4	77.3%
interim	370	1,146.4	1,280.6	89.5%

However, in october 2017 the BFI released further data showing that 161 games received final certification between 1st jan to 30th september 2017, representing £136.8m EEA/UK spend from a total budget of £159.5m. This is a 25% increase in the number of games, but a slight decrease of -3.8% in EEA/UK spend over the same period the previous year. Looking at interim certifcication in the same period, 130 games were interim certified (-9.7%) representing an £296.6m of EEA/UK spend (-2.3%) and a total budget of £319.6m (-11.5%).

Final certification covers games that have been completed and released, and have claimed their tax relief.

Interim certification covers games that are still in development but have been approved for the cultural test.

Some games that have progressed from development to completed and released since the launch of the VGTR may be counted in both interim and final categories.

Since the relief was introduced in apr 2014, the number of games gaining final and interim certification has increased significantly year-on-year. In the financial year 2016/17, 212 games received final certification while 187 received interim certification, an increase of +59.4% and +38.5% on the previous year respectively.

In FY2016/17, the 212 games that received final certification had a total budget of £258m, £220.4m of which was spent in the UK. For the 187 games recieving interim certification, the total budget was £482.2, £412.2m of which was spent in the UK.

Median budget for the projects applying for VGTR has also shown a huge year on year increase, rising from £0.2 million in 2014 to £0.7 million in Q1 2017.

Games qualifying through the 'cultural test' typically receive a return of about 20 per cent of their development costs.

The BFI publish as list of all video games certified as british through the video games cultural test, which can be downloaded here.

UK esports

In 2016, the UK esports audience will grow to 6.5 million people, with 3.1 million watching more than once a month. The audience is expected to grow 7.5% year-on-year to reach 8 million people by 2019.

According to PWC, the UK esports market will see a 27.6% CAGR, reaching £8min consumer ticket sales by 2021. Digital advertising in esports will increase to £12m by 2021, a CAGR of 46.2%.

Esports is popular with milennials in the UK, with the 21-35 age group representing 63% of the market. Women make up 31% of the audience and are most likely to watch when aged between 21-35.

The largest prize pool event held in the UK to date was ESL one birmingham, with a prize pool of $1 million, held at arena birmingham in may 2018.

The UK is the home to some of the world's top esports talent. One of the UK's leading esports teams, team dignitas were acquired by the owners of the US basketball's philadelphia 76ers in september 2016.

Major UK football clubs including manchester city and west ham have signed professional esports players.

The UK's largest gaming retailer, game, acquired multiplay, one of the UK's longest established esports businesses, for £20m.

There is also growing grassroots esports scene in the UK's universities, with 3,000 players in the national university esports league, representing 110 universities.

UK mobile games

There are 1,483 active games companies making mobile games in the UK (as of august 2017). (UK games map)

The UK has the largest mobile games workforce in the EU, with 5,000 full-time employees. This represents nearly a quarter of all 21,000 mobile game jobs across the EU. (deloitte and ISFE)

71% of UK adults (approx 40m) own a smartphone and 59% of UK households (approx 15.9m) own a tablet. (ofcom, Q1 2016)

47% of UK smartphone owners use apps on their phones to play games – more that use apps for online banking (40%) or reading the news (33%).

44% households own an iphone, 46% and android phone and 12% a windows phone.

The free apps with in-app purchase model is king, representing 76% of the revenue share of the UK for apps (distimo/appannie)

In terms of revenue per download, the UK is best positioned in western europe with a potential profit of $0.47 per download. The UK is more profitable than germany, united states and china. (distimo/appannie)

UK player demographics

There are several different estimations for UK player demographics available:

In 2017, 32.4 million people play games in the UK. Spending $4.2 billion this year, they make the UK the 5th largest games market in the world.

The UK mobile market is very evenly represented between the genders, with a 48% female / 52% male split between those who are playing more than once a month.

32% of UK players play mobile, console and PC games.

In 2016, there were 31.6m players in the UK, approximately 50% of the total population. Of those that play games, 59% of them spend money on games, annually spending an average of $206 per player.

There are 23.1m people aged between 6 and 64 playing games in the UK, or 49% of the population in that age group. (2018 Q1)

On average, 11 to 64 year-olds in the UK spend 10.3 hours per week playing games. (2018 Q1)

Across all UK 6-64 year olds, 26% (12.4m) played packaged games, 25% app games (12m) and 29% (13.6m) online games. (2018 Q1)

Similarly, 29% (13.9m) play on consoles, 28% (13.5m) on computers, 25% (12.1m) on smartphones, 19% (9.1m) on tablets and 11% on handhelds (5.2m). (2018 Q1)

54% players in the UK are male and 46% female. The largest single age/gender demographic is 15-24 year-old males, making up 14% of all players, whereas 15-24 year-old females make up 11% of all players. (2018 Q1)

Internet advertising bureau

In 2014, IAB released the below infographic from their 'gaming revolution' study:

Specialised courses and a qualified workforce

UK higher education is a strong supporter of the games industry. 60 universities/colleges provide 215 undergraduate and 40 master video game courses throughout the UK in 2014. (creative skillset)

23% of the courses are in london, 18% in the west midlands and 16% in yorkshire and the humber: these 3 regions cover 57% of all courses provided. (creative skillset)

The top 3 universities in number of courses provided are: staffordshire university (29 courses), university of east london (17 courses) and sheffield hallam university (16 courses). (creative skillset)

The computer games workforce is highly qualified, with 63% having a degree compared to 57% of the wider creative media workforce and 37% of the wider UK economy in 2011. (creative skillset)

Game-ready infrastructure

Mobile phone and broadband penetration are key drivers for the UK games industry. Ofcom's 'communications market report 2017' report contains substantial data and analysis on the UK telecommunications network.

88% of UK households have access to the internet, an increase of 2% on 2016. There are 25.3 million fixed broadband connections, 10.8 million (44%) of which can be classified as super-fast (more than 30mbps).

Games industry fact sheet

The games industry fact sheet is a compilation of hundreds of facts, stats and snippets about all aspects of the UK and global games industry.

It's a big document, but there's a good chance it has what you're looking for! If in doubt, please contact luke.

Must-know: the most popular casino games

Leakage effect

Casinos can impact the society where they’re located. The size of the effect depends on how many visitors the casino draws from outside the area. It also depends on the number of jobs the casino generates within the area.

Casino revenues that support jobs and purchases are generated by casino visitors’ spending. The jobs and purchases generate funds. These funds are diffused into the community. The funds have secondary or multiplier effects in subsequent rounds of spending. There’s a second category of direct and secondary effects. They include the non-casino expenditures generated from visitors outside the area. These non-casino expenditures include purchases in local stores or meals in local restaurants.

A variety of factors impact the degree of the direct and secondary effects experienced outside the local area. This occurs when a casino purchases supplies from an out-of-area vendor. It also occurs when a casino hires a worker who commutes to the casino from outside the community. The individual takes the income they made at the casino and spends it outside the local area. This is a phenomenon known as “leakage.”

Displacement effect

The positive economic impact is offset by other local economic activity. It’s negatively affected by the casino. The casino could cause a loss of a business in the existing local economy. For example, an existing restaurant could lose business to a restaurant that’s located inside the casino. Also, local residents could take money that they would spend for other purposes and redirect the funds to the casino. This is referred to as “displacement.” casino-related spending displaces or substitutes other forms of spending.

Social cost

Social costs impact major players including las vega sands (LVS), MGM resorts, wynn resorts (WYNN), and caesar entertainment (CZR). Social cost includes is the increase in corruption or organized crime. Casinos offer gambling for entertainment. However, they also have financial activities that are similar to financial institutions. These activities put casinos at risk for money laundering. This could be controlled through careful regulations.

Exchange-traded funds (or etfs) like the vaneck vectors gaming (BJK) and the consumer discretionary select sector SPDR fund (XLY) track leisure companies.

To know more about the casino gaming market performance click here.

To access our premium industry primers, company overviews and financial models, please email premium@marketrealist.Com. Specify the industry or company ticker(s) you are interested in and a representative will get in touch with you.

Discretionary consumer spending effect

The casino business is sensitive to reduced consumer spending. Reduced spending can be caused by economic downturns. Consumer demand for hotels, casino resorts, and luxury amenities is also impacted by the state of the economy.

This could impact major casino players like las vegas sands (LVS), MGM resorts (MGM), melco crown entertainment (MPEL), and caesar entertainment (CZR). Exchange-traded funds (or etfs) like the vaneck vectors gaming (or BJK) and the consumer discretionary select sector SPDR fund (XLY) track the performance of leisure companies. The etfs could also be impacted by an economic downturn.

The above chart shows that in 2012, consumers spent more at commercial casinos than they did on movies, craft beer, and outdoor equipment combined. However, consumers spent less on casino gambling than what they spent on full-service restaurants or consumer electronics.

Changes in discretionary consumer spending could be caused by many factors. These factors include:

Weaknesses in the job or housing market

Additional credit market disruptions

High energy costs

Fuel and food costs

Increased travel costs

The potential for bank failures

Recession fears

Changes in consumer confidence in the economy

Fears war and terrorism

These factors could reduce consumer demand for luxury amenities and leisure activities.

Political effect

The casino business is prone to extensive regulations. The compliance costs—or the cost of not complying with regulations—may have a negative impact on the business, financial conditions, operations, or cash flows.

The casino business is sensitive to customers’ willingness to travel. As a result, acts of terrorism, regional political events, and conflicts in other countries could disrupt air travel. This would reduce the number of casino visitors. Fewer visitors could hurt the casino’s financial conditions, operations, or cash flows.

The business is also subject to taxation and regulation by various government agencies—primarily in macao, singapore, and the U.S. The government agencies include the federal, state, and local levels. U.S. Federal, state, local, and foreign governments change tax rules. Changing rules could result in higher taxes than existing tax laws. Changes in tax laws and regulations could have a severe impact on the business’ financial condition and operations.

How does it work?

The right location has to be selected before a casino is built. The local zoning laws have to be checked to make sure they will allow a casino in the area. The casino has to register with the city and state. It also has to get the required licenses and employer identification number (or EIN).

The capital that the casino raises could be invested to get gaming equipment like slot machines, video poker machines, roulette tables, poker tables, blackjack tables, craps tables, baccarat tables, chips, cards, and card shoes.

Advertisement is important for a casino. Television and radio commercials draw attention to the casino. Internet advertisements also increase tourism and recreation.

The above chart shows how an accurate business plan and enough funding make sure that a casino is established correctly. Generated revenue is used to meet business costs—like license fees, capital expenditures, and wages. The revenue is also used to distribute the free cash flow to the shareholders—through dividends and share buybacks. If there’s any remaining free cash flow, the business keeps it. The business uses it to provide for more growth. It can also use it to meet any contingent liability.

Licensing requirements

Three types of licenses are required to run a casino:

Operating license – this is required to run a casino or offer casino games—for example, running a website that offers poker, roulette, and blackjack.

Personal license – there are two kinds of personal licenses—the personal management license (or PML) and personal functional license (or PFL). PML is for individuals who are responsible for specific areas in the organisation. Casino employees would have to apply for PFL if they are involved in gaming or handling gambling money.

Premises license – this is required to run small or large casino. It’s also required to run an existing casino. It’s issued by the local licensing authority.

Key stocks and exchange-traded funds (or etfs)

Key players in the casino industry include las vegas sands (LVS), MGM resorts (MGM), penn national gaming (PENN), and melco crown entertainment (MPEL). Exchange-traded funds (or etfs) like the consumer discretionary select sector SPDR fund (XLY) and the vaneck vectors gaming (or BJK) track leisure companies.

Casino visitors’ demographics

The commercial casino industry plays a vital role in the overall U.S. Travel and tourism industry. Roughly a quarter of the U.S. Adult population visits a casino at least once a year. Casinos attract a substantial number of overseas visitors.

Today’s casinos—including las vegas sands (LVS), MGM resorts (MGM), caesar entertainment (CZR), and pinnacle entertainment (PNK)—provide top-notch entertainment experiences that go beyond gaming. Exchange-traded funds (or etfs) like the vaneck vectors gaming (or BJK) and the consumer discretionary select sector SPDR fund (XLY) track the leisure companies.

Modern casinos have diverse amenities. The amenities attract a variety of tourists. The tourists also visit neighboring attractions. This stimulates the local economy.

The above chart shows that young people aged between 21–35 visit casinos the most. Nearly four out of ten individuals in the age group went to a casino in 2012. However, this visitation rate is only slightly higher than respondents aged between 50–64 at 36% and those aged between 36–49 at 34%. Only a quarter of older americans aged 65 and over visited a casino during 2012.

What’s your total household income?

The above chart shows that casino visitors have similar household incomes compared to national survey respondents. Casino visitor households make slightly more. Nearly 50% of all casino visitors’ households make more than $60,000 per year. Only 34% of households in the overall national sample have the same annual income. Household incomes for young adult casino visitors are almost in line with the broader population of casino visitors.

Casino gambling is an activity that adults aged 21 and over enjoy every day across the U.S. However, there are underlying differences. Young adult casino visitors, as a group, have distinct gambling habits that could shape casinos in the future. Also, young adult casino visitors are more likely to participate in other forms of gambling—like casual betting with friends, playing poker, or gambling on the internet.

It’s the “house edge”

Casino games have a built-in advantage for the operator. It’s known as the “house edge.” the house edge is the difference between the true odds and the odds—or probability—that the casino pays you when you win. This is known as the casino odds. The likelihood of rolling a particular number is known as the true odds.

The more combinations possible, the higher the odds. For example, you’re more likely to roll a seven than a two or a 12. However, since casinos take a portion of the winnings as a result of the house edge, the winner gets true odds less the difference between true odds and the casino odds.

Depending on the game and player, the house edge may be larger than what the above data suggests. As you can see from the chart above, there are different house edges for blackjack. The stats are based on three types of games. The games are played with a particular basic strategy. In those games, the house edge can be lessened by learning advanced strategy. Also, the house edge can grow based on rule changes.

Most casino games have a house edge between 0%–5%. Slot machines have a house edge of 10%. Keno has a house edge of 27%. Playing games with a smaller house edge and learning correct strategy allows your dollars to last longer. This increases your chance of winning.

Estimating the loss

A player can estimate the loss before playing a particular game—if they know the house edge. For example, a player knows the house edge in blackjack is 0.6%. They can assume that for every $10 original wager they make, they would lose $0.06 on average. Most players aren’t going to know how much their average wager would be in games like blackjack—relative to the original wager. As a result, any statistic based on the average wager would be difficult to apply to real life scenarios.

Gambling addiction

With so many people gambling, the casino odds generate substantial profits for the casinos. Unfortunately, a need to keep playing the odds causes many people to develop a gambling addiction.

Major casino players like las vegas sands (LVS), MGM resorts (MGM), caesar entertainment (CZR), and pinnacle entertainment (PNK) attract millions of customers. This is one of the main reasons why casinos are such a profitable business. At times, there are big winners at the gaming tables. However, the only sure winner in a casino is the owner.

Exchange-traded funds (or etfs) like the consumer discretionary select sector SPDR fund (XLY) and the vaneck vectors gaming (or BJK) give investors exposure to the leisure industry.

The most popular casino games

Casinos’ popularity is growing. This suggests that people like to gamble occasionally. Unfortunately, they don’t always win. For most of the people, the real fun is playing the game—not necessarily winning. Here’s a list of the top five most popular casino games.

Slots are machines that play a number of different games. Generally, a player inserts coins into the machine. Then they pull a handle or press a button. This causes the wheels to spin. When the wheels stop, the player gets paid based on the pattern of symbols.

Blackjack is a card game. It’s played between the house—also known as the dealer—and the player. The dealer deals out two cards to each player and keeps two cards. The dealer has one card face up and one down. The players take turns trying to get as close as they can to 21. The player calls “hit” to get a card and end their turn. A player can also call “double.” this doubles their bet. They can only get one card and their turn ends. If a player has two identically numbered cards, they can split.

In roulette, the player places their chips on the table to wager them. The table has numbers 0-36 and 00. It has additional betting for even-odd, red-black, low 18-high 18, low/middle/high 12 and for the first/second/third columns. The dealer spins the wheel clockwise. Then, they roll a ball counter-clockwise. The ball lands in a numbered slot on the wheel. All bets that correspond with the number win.

Poker is a card game. It’s based on a five card hand. Hands are ranked from lowest to highest. The order of hands is high card, pair, two pair, three of a kind, straight, flush, full house, four of a kind, straight flush, and royal flush. The player with the best hand wins.

Craps is a dice game. The players make wagers on the outcome of the roll, or a series of rolls, of a pair of dice. If a seven or 11 turn up on the first roll of the dice, the shooter wins whatever they bet. If the shooter rolls two, three, or 12 on the first roll, they loose the money, but not the dice. When the person rolls a four, five, six, eight, nine, or ten that number becomes their “point.” the shooter keeps rolling until their “point” turns up again for a win or until the person throws a seven and loses the money and the dice.

Major casinos that offer the above mentioned games include las vegas sands (LVS), melco crown entertainment (MPEL), caesar entertainment (CZR), and pinnacle entertainment (PNK). Investors who would like to get exposure to the sector may invest in exchange-traded funds (or etfs) like the vaneck vectors gaming (BJK). It tracks casino companies.

The evolution of casino industry

A banked game is a game of chance. The participating players don’t determine the prizes. A casino offers banked games. The commercial casino industry in the U.S. Has changed over the last two decades. An increased emphasis has been placed on a wide range of entertainment and recreational activities.

The above chart shows different types of casinos in the U.S. It shows that land-based casinos are widespread. Racetrack casinos are popular in the eastern U.S. Tribal casinos are the native american casinos. They’re the gambling operations on indian reservations. Tribal casinos are widespread across the U.S. They aren’t always run by the tribe itself. The casinos can be run by an outside management company. Other commercial gaming venues include excursion—mobile—and dockside—permanently moored—riverboats and card rooms.

Until the recession started at then end of 2007, the U.S. Casino industry was thought to be recession-proof—especially in las vegas. However, the industry experienced a steady decline in revenue during 2008 and 2009.

The casino industry’s expansion depends on voters. It also depends on hosting government jurisdictions. Governments enjoy the potential tax revenues that casinos offer. However, they have concerns about potential social costs and other problems that casinos may bring. The uncertainty has caused extreme volatility in the industry’s stock prices.

Key stocks and exchange-traded funds (or etfs)

Key players in the casino industry include las vegas sands (LVS), MGM resorts (MGM), caesar entertainment (CZR), and melco crown entertainment (MPEL). Exchange-traded funds (or etfs) like the vaneck vectors gaming (or BJK) and the consumer discretionary select sector SPDR fund (XLY) give investors exposure to the leisure industry.

Leverage’s positive impact on share price

The casino business model entails a significant amount of leverage use, in which the effects could be magnified to have a positive impact on equity. Land-based casinos are inherently highly leverage businesses that usually need to build properties, whether they’re tribal casinos in oklahoma or multipurpose complexes in macau. Casinos also have high fixed costs to pay for maintenance, labor, utilities, and licenses.

The above chart shows the share price performance of highly leveraged casino stocks since january 2013. It shows that in the past, boyd gaming’s (BYD) share price has doubled. Boyd gaming has a net debt of over $4.1 billion and a market capitalization of about $1.2 billion.

MGM resorts (MGM) had a 60% leverage in its capital structure but surged over 100%.

Most importantly, caesars entertainment’s (CZR) share price increased in excess of 350%, despite some $24 billion in debt. It’s also important to note that caesars entertainment’s leverage is greater than 100%, signifying that it has negative shareholders’ equity or shareholders’ deficit in its balance sheet.

However, las vegas sands (LVS) and melco crown (MPEL)—with leverage of around 50% and 36%, respectively—have also seen a rise in their share prices.

Investors who’d like to get exposure to the industry can invest in exchange-traded funds (or etfs) like vaneck vectors gaming (BJK) and consumer discretionary select sector SPDR fund (XLY).

Unlocking hidden value

Major casino players have been looking into online gaming as a way to increase their market share and reach consumers who might not be willing to physically come to casinos.

In august 2009, harrah’s interactive entertainment, now known as caesars entertainment (CZR), signed a long-term deal with dragonfish, the business-to-business (or B2B) technology arm of the gaming site 888 holdings, to power harrah’s website.

From the above table, it can be seen that industry consolidation is an important step, as it usually profits the players by unlocking the hidden potential value. Each of these acquisitions in some way expand company offerings horizontally in the gaming space. The consolidation in gaming may actually benefit customers, provided that online gaming is approved nationwide.

The share prices for bally technologies (BYI), scientific games (SGMS), and pinnacle entertainment (PNK) surged immediately after announcing the deal.

Investors can get exposure to the leisure industry through exchange-traded funds (or etfs) like vaneck vectors gaming (BJK) and consumer discretionary select sector SPDR fund (XLY).

Online gaming growth rates have been driving market consolidation, as larger players in the gaming sector are looking to fill out their capabilities or to reach new markets. For example, in 2008, international game technology (IGT) purchased million-2-1, a developer of mobile or cell phone gaming technology.

Million-2-1 also has a consumer-facing internet games portal—kerching—that offers online casino, poker, bingo, and SMS games and cell phone java slots games in legal territories.

In september 2009, bwin purchased one of italy’s largest online poker sites, gioco digitale.

So merger and acquisition activity is likely for traditional gaming companies that are reaching into virtual markets and for existing virtual leaders that are taking over smaller niche competitors.

A look into immediate future performance

Enterprise value (or EV) divided by earnings before interest, tax, depreciation, and amortization (or EBITDA) is a significant financial metric used in valuing comparable companies. This multiple’s capital structure is neutral, meaning it takes both the debt and shareholders perspective, unlike price divided by earnings (or PE) which takes only the shareholders perspective.

Generally, the lower the ratio, the more undervalued the company is believed to be. Since the casino operators are experiencing both organic and inorganic growth, EV divided by the trailing twelve months (or TTM) EBITDA would be less meaningful due to the failure to take into account the consolidated or expanded future performance of the casino operators.

So EV divided by the next twelve month (or NTM) EBITDA is a suitable measure for valuing the companies since it takes into account the immediate future performance of the company, incorporating the organic and inorganic growth factors into EBITDA.

The above chart shows that both genting malaysia and SJM holdings are undervalued relative to its peers since both of these companies have significant net cash positions, which reduce the firms’ EV.

Companies like caesars entertainment (CZR), boyd gaming (BYD), MGM resorts (MGM), and penn national gaming (PENN) have seen a rise in their share prices. A good way to get exposure to these companies is to invest in exchange-traded funds (or etfs) like vaneck vectors gaming (BJK).

Buyer’s perspective

Buyers are more interested in ensuring their purchase price is reasonable against the next twelve months’ performance. It’s the future performance that would ultimately support the price paid by the buyer. In stable or mature industries, the last twelve months’ performance can serve as a good proxy for the next twelve months.

However, for companies in growth industries, like technology, or rapidly growing markets, the last twelve months would be less relevant. So buyers would focus on the reasonability of the NTM EV-to-EBITDA ratio and ensure that the multiple paid is within its tolerance level and industry benchmarks.

To know more about the casino gaming market performance, click here.

It’s more than just a casino

Does the traditional casino company that offers multiple services and products to its customers maximize its shareholder value? Or does a focused casino facility that specializes primarily in casinos maximize shareholder value? Or is it something in-between?

Rapid expansion of casino resorts, rather than casinos alone, suggests that diversifying amenities is profit-maximizing. Modern casinos offer a wide range of activities besides gambling, and adult visitors of all ages take advantage of these amenities.

The above chart shows that eating at a fine dining restaurant and seeing a show or concert are the most popular among all casino-goers, with 69% and 55% participating in such activities respectively. Young adult casino visitors are more likely to participate in all of the activities mentioned in the above chart.

Dominating non-casino activities

The market returns for a casino will be directly related to the casino’s ability to cross-promote its products and services to a diverse customer base. Moreover, the casino’s ability to tailor a variety of new products and services to its existing customers is expected to result in increased sales and shareholder value.

The casino industry has followed this path since non-casino revenues are now contributing significantly to the total revenues at many destination resort casinos, especially in large casino companies like las vegas sands (LVS).

Attract and retain more customers

The above chart shows the diversified revenue streams of a casino operator. This diverse casino management strategy that moves away from casinos and moves towards other sources of revenue significantly impacts the value of casino companies.

With the expansion of casinos into new jurisdictions, competition has increased significantly. This competition gives rise to questioning which casino amenities are most important to offer casino patrons to drive profitability.

Other casino operators like boyd gaming (BYD), melco crown (MPEL), and penn national gaming (PENN) have to find a niche to place themselves in a unique position in the market due to this competition. So amenities other than the casino have started to have a significant impact on the overall performance of the firm.

Exchange-traded funds (or etfs) like vaneck vectors gaming (BJK) and consumer discretionary select sector SPDR fund (XLY) track companies in the leisure industry.

The benefit of a fixed cost business model

Let’s say ABC is a casino operator with revenue and costs of $110 million and $100 million respectively, and its revenue increases by 10% in the following year, which causes modest increase in labor costs, maintenance expenditures, and fixed license fees.

ABC’s overall costs increase by say 5%, and instead of making $10 million in profits, it’s now making $16 million in profits ($121 million in revenue and $105 million in costs.) in other words, a 10% increase in revenue results in a 60% increase in profits. Assuming that the earnings before interest, tax, depreciation, and amortization (or EBITDA) multiple remains unchanged, this results in an increase to the share price.

The above chart shows the firm—which is generating $110 million in revenue, with $100 million in costs—is initially valued at say 10x EBITDA, or $100 million, with $70 million in debt and $30 million in equity. Now since revenue and costs rose by 10% and 5% respectively, owing to the fixed cost nature of the casino business, ABC’s EBITDA will rise to $16 million.

The total value of the firm at the same 10x EBITDA multiple will rise to $160 million. But the debt remains unchanged at $70 million. So equity will rise from $30 million to $90 million, or by 200%, as a result of the 10% increase in revenue.

This shows that when a company with high fixed costs touches breakeven, each additional customer becomes massively profitable. At this point, profit grows exponentially since each additional customer who comes in is at a minimal cost to the operator.

The pessimistic view

Let say ABC’s revenue drops by 5% to $104.5 million, but its costs decrease by say 2.5% to $97.5 million since state governments don’t lower license fees. ABC now experiences EBITDA of $7 million annually. Based on the same 10x EBITDA multiple, the firm is now valued at $70 million.

Remember that its debt is $70 million, which signifies that a 5% decline in revenue has entirely wiped its shareholder value, as shown by the above chart. This is the risk in high-debt casino stocks like MGM resorts (MGM), boyd gaming (BYD), and caesars entertainment (CZR). This also explains why gambling stocks are more volatile than other stocks.

However, to avoid the risk of investing in such stocks individually, investors can invest in exchange-traded funds (or etfs) like vaneck vectors gaming (BJK) and consumer discretionary select sector SPDR fund (XLY) that give exposure to the industry.

Casino game statistics

Understanding casino math

Introduction

Why is mathematics important?

The house edge

Probability versus odds

Confusion about win rate

Volatility and risk

Player value and complimentaries

Gaming regulation and mathematics

Summary tables for house advantage

Why is mathematics important?

EV = (+5)(18/38) + (-5)(20/38) = -0.263
(house advantage = 0.263/5 = 5.26%)

Double-zero roulette (single number bet):
EV = (+35)(1/38) + (-1)(37/38) = -0.053
(house advantage = 5.3%)

Single-zero roulette (single number bet):
EV = (+35)(1/37) + (-1)(36/37) = -0.027
(house advantage = 2.7%)

· hold % = win/drop
· win % (actual) = win/handle
· H.A. = theoretical win % = limit(actual win %) = limit(win/handle)
· hold percentage ¹ house edge

Volatility analysis guidelines
· only 5% of the time will outcomes will be more than 2 SD's from expected outcome
· almost never (0.3%) will outcomes be more than 3 SD's from expected outcome

Player value and complimentaries

Earning potential = average bet ´ hours played ´ decisions per hour ´ house advantage

EV = (+0.98)(.4462) + (-1)(.4586) = 0.0032
(house advantage = -0.32%)

Usual 60 to 1 payoff: EV = (+60)(1/72) + (-1)(71/72) = -0.153
(house advantage = 15.3%)

Promotional 80 to 1 payoff: EV = (+80)(1/72) + (-1)(71/72) = +0.125
(house advantage = -12.5%)

Gaming regulation and mathematics

Summary tables for house advantage

The two tables below show the house advantages for many of the popular casino games. The first table is a summary of the popular games and the second gives a more detailed breakdown.

House advantages for popular casino games
*game*	*house advantage*
roulette (double-zero)	5.3%
craps (pass/come)	1.4%
craps (pass/come with double odds)	0.6%
blackjack - average player	2.0%
blackjack - 6 decks, basic strategy*	0.5%
blackjack - single deck, basic strategy*	0.0%
baccarat (no tie bets)	1.2%
caribbean stud*	5.2%
let it ride*	3.5%
three card poker*	3.4%
pai gow poker (ante/play)*	2.5%
slots	5% - 10%
video poker*	0.5% - 3%
keno (average)	27.0%
*optimal strategy

House advantages for major casino wagers
*game*	*bet*	HA*
baccarat	banker (5% commission)	1.06%
baccarat	player	1.24%
big six wheel	average	19.84%
blackjack	card-counting	-1.00%
blackjack	basic strategy	0.50%
blackjack	average player	2.00%
blackjack	poor player	4.00%
caribbean stud	ante	5.22%
casino war	basic bet	2.88%
craps	any craps	11.11%
craps	any seven	16.67%
craps	big 6, big 8	9.09%
craps	buy (any)	4.76%
craps	C&E	11.11%
craps	don't pass/don't come	1.36%
craps	don't pass/don't come w/1X odds	0.68%
craps	don't pass/don't come w/2X odds	0.45%
craps	don't pass/don't come w/3X odds	0.34%
craps	don't pass/don't come w/5X odds	0.23%
craps	don't pass/don't come w/10X odds	0.12%
craps	don't place 4 or 10	3.03%
craps	don't place 5 or 9	2.50%
craps	don't place 6 or 8	1.82%
craps	field (2 and 12 pay double)	5.56%
craps	field (2 or 12 pays triple)	2.78%
craps	hard 4, hard 10	11.11%
craps	hard 6, hard 8	9.09%
craps	hop bet - easy (14-1)	16.67%
craps	hop bet - easy (15-1)	11.11%
craps	hop bet - hard (29-1)	16.67%
craps	hop bet - hard (30-1)	13.89%
craps	horn bet (30-1 & 15-1)	12.50%
craps	horn high - any (29-1 & 14-1)	16.67%
craps	horn high 2, horn high 12 (30-1 & 15-1)	12.78%
craps	horn high 3, horn high 11 (30-1 & 15-1)	12.22%
craps	lay 4 or 10	2.44%
craps	lay 5 or 9	3.23%
craps	lay 6 or 8	4.00%
craps	pass/come	1.41%
craps	pass/come w/1X odds	0.85%
craps	pass/come w/2X odds	0.61%
craps	pass/come w/3X odds	0.47%
craps	pass/come w/5X odds	0.33%
craps	pass/come w/10X odds	0.18%
craps	place 4 or 10	6.67%
craps	place 5 or 9	4.00%
craps	place 6 or 8	1.52%
craps	three, eleven (14-1)	16.67%
craps	three, eleven (15-1)	11.11%
craps	two, twelve (29-1)	16.67%
craps	two, twelve (30-1)	13.89%
keno	typical	27.00%
let it ride	base bet	3.51%
pai gow	poker skilled player (non-banker)	2.54%
pai gow poker	average player (non-banker)	2.84%
red dog	basic bet (six decks)	2.80%
roulette	single-zero	2.70%
roulette	double-zero (except five-number)	5.26%
roulette	double-zero, five-number bet	7.89%
sic bo	big/small	2.78%
sic bo	one of a kind	7.87%
sic bo	7, 14	9.72%
sic bo	8, 13	12.50%
sic bo	10, 11	12.50%
sic bo	any three of a kind	13.89%
sic bo	5, 16	13.89%
sic bo	4, 17	15.28%
sic bo	three of a kind	16.20%
sic bo	two-dice combination	16.67%
sic bo	6, 15	16.67%
sic bo	two of a kind	18.52%
sic bo	9, 12	18.98%
slots	dollar slots (good)	4.00%
slots	quarter slots (good)	5.00%
slots	dollar slots (average)	6.00%
slots	quarter slots (average)	8.00%
sports betting	bet $11 to win $10	4.55%
three card poker	pair plus	2.32%
three card poker	ante	3.37%
video poker	selected machines	-0.50%
*house advantages under typical conditions, expressed "per hand" and including ties, where appropriate. Optimal strategy assumed unless otherwise noted.