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Why You Can’t Beat these Casino Games in the Long Run

I recently wrote a couple of blog posts about how to become a professional gambler. In those 2 posts, I listed several gambling activities where you could get a theoretical long-term mathematical edge. That’s what you’d need to be able to play those games for a living.

Those activities include blackjack, horse betting, poker, progressive slots, sports betting, and video poker. (And progressive slots are debatable—a serious professional gambler would probably avoid most of those games because of the high chance of never hitting the progressive at all.)

Most casino games, though, are completely impossible to beat in the long run. This post explains why in general in the section about probability and the house edge. I look at specific games and why they have an edge in separate sections devoted to each game.

Probability and the House Edge

To understand how the casino makes money, you need at least a rudimentary understanding of probability. Luckily, probability is pretty easy to understand. It’s just a mathematical way of expressing how likely an event is to occur.

The probability of something is just a number between 0 and 1. Something that’s impossible has a probability of 0. Something that’s a sure thing has a probability of 1. Anything else has a probability of between 0 and 1.

This number can be expressed as a fraction, as odds, a decimal, or as a percentage. To calculate the probability of something, divide the number of successful outcomes by the number of total possible outcomes. It’s that simple.

Here’s an example using a coin toss. You guess heads, and you want to know the probability of achieving that result. There’s one way to get heads when tossing a normal coin. But there are 2 possible outcomes, both of which are equally likely—heads or tails. This means the probability is 1 out of 2, or 1/2. You can also express that as 50%, or as 1 to 1 in odds format. Or you could even say that the probability is 0.5. They all mean the same thing.

Let’s take another example—you’re rolling a 6-sided die and want to know the probability of rolling a 1. There are 6 possible outcomes, and only 1 of them constitutes a success. That’s a probability of 1/6, or 16.67%, or 0.167, or 5 to 1.

The house edge comes in when you compare the payoff for a winning bet to the probability of winning. Many casino game bets, like a bet on red or black in roulette, are even-money propositions. This means the payoff odds are 1 to 1. You risk a unit, and if you win, you win a single unit.

If the probability of winning were 50%, you’d have a theoretically break even game in the long run. You wouldn’t win, and neither would the casino.

But the probability of winning that bet on an American roulette wheel is only 47.37%, which means you’ll win a single unit 47.37% of the time, and the casino will win a single unit 52.63% of the time. The difference between the 2 is the house edge: 52.63% – 47.37% = 5.26%

Other games have different payoffs, but those payoffs are always lower than the odds of winning. For example, in craps, if you bet that the next roll of the dice will result in a 7, you have a 5 to 1 probability of winning. But that bet only pays off at 4 to 1 odds.

The difference is the house edge for that bet. Over 6 bets, you’ll win once and lose 5 times on average. If you’re betting $100 each time, you’ll see a net loss of $500 – $400, or $100. That’s an average loss of $16.67 per roll. (You lose $100 total on 6 rolls, so you divide one into the other to get the average.) The house edge for that bet is a whopping 16.67%.

Of course, in the short run, you’ll rarely see results that mirror your long-term expectation. But in the long run, your results will get closer to the expectation. This is called the Law of Large Numbers.

Now let’s look at betting systems, then I’ll follow that up with a discussion of some specific casino games.

Why Betting Systems Can’t Overcome the House Edge in the Long Run

Lots of people think you can beat a game with a house edge by using betting systems. In this context, a betting system is just a way of raising and lowering your bets based on what happened on the previous bet or bets. Depending on the system, you might raise the size of your bets when you’re winning. Or you might raise the size of your bets when you’re losing. It depends on the system.

Either way, it doesn’t matter. Every bet you place on a casino game is a separate event, independent of the previous bet. If the individual bet has you at a mathematical disadvantage, the sum of all those bets will also have a mathematical disadvantage. Think of it as adding up a series of negative numbers. No matter how you do it, if those numbers are all negative, the sum of those numbers will also be negative.

Here’s an example: You’re using a betting system where you raise the size of your bets when you’re losing. Your goal is to recover your losses from the previous bets. (The Martingale System is a good example of this kind of system.)

The problem is that no matter what kind of casino game you’re playing, you’re eventually going to hit a big losing streak. That’s the nature of random chance. The longer you play, the likelier it is that you’ll hit that losing streak, too. When you do, it will wipe out any small winnings you gained from your betting system.

If you really were able to beat a casino game with one of these betting systems, the casinos would go out of business. None of these systems are complicated. The Martingale System just involves doubling the size of your bet after each loss. That’s not hard to figure out. If it worked, everyone would know, everyone would do it, and the casinos would have to shut down after losing all their money.

But no matter what anyone says, no one is winning at any of these negative expectation games using a betting system. There are no professional baccarat players, no professional craps players, and no professional roulette players.

You might find some people who claim to be able to affect the odds of a craps roll with controlled throwing, but I’m skeptical of that. And sure, you might be able to find a biased roulette wheel, but that’s unlikely and impractical. Neither of those techniques uses a betting system, either.

You should still understand how such negative expectation games work, though. For one thing, you might want to play them recreationally. If so, you should learn to minimize your losses. Also, sometimes casinos put together promotions where they give the player the best of it. You can’t recognize such opportunities unless you understand the math behind the games to begin with.

Why You Can’t Beat Craps

You can find some good bets at the craps table, as long as you define “good” as meaning bets with a house edge lower than average. If you define “good” as meaning you have an edge over the house, you won’t find any bets at the craps table that qualify.

You can also find a whole lot of bad bets at the craps table. These are bets where the house edge is so much higher than average that it’s scary. No matter which category of bet you choose at the craps table, you’ll eventually lose all your money if you keep playing.

The worst bets at the craps table are the proposition bets. An example would be a bet on 12 on the next roll. (This isn’t a “hard way” bet, by the way, because there’s no “easy way” to roll a 12. Getting a 6 on each die is the ONLY way to roll a 12.) This bet pays off at 30 to 1 odds, but the odds of winning the bet are 35 to 1. What’s the house edge on a bet like this? Assume $100 bets and 36 statistically perfect rolls. You’ll win $3000 once, but you’ll lose $3500 total on the other bets. That’s a net loss of $500 over 36 bets, which is an average loss per bet of $13.89.

A mathematical edge of 13.89% is way higher than you’ll see at most casino games, or, in fact, most bets at the craps table. If you’re the kind of person who makes a bet when the house edge is that high, you’re probably never going to be a professional gambler.

What about an actual hardway bet? A hardway bet is one in which you get an even total by rolling doubles. For example, you can bet on “10 the hard way” or on a “hard 10.” This is a bet that a roll will come up with a 5 on each die, for a total of 10.

This is a multi-roll bet. It stays in action until you either win, or until the shooter rolls a 7, or until the shooter rolls a 10 the easy way–in either of the latter 2 cases, you lose. The payoff for this bet is 7 to 1. The odds of winning this bet are 8 to 1, though.

It’s easy to calculate the edge here, too. You’ll lose an average of $100 over the course of 9 bets, for an average loss of 11.11% per bet. That’s still a huge house edge. But even the best bets at the craps table have a house edge of over 1%. The pass line bet is the most basic bet at the craps table, and it has a house edge of 1.41%. The come bet also has that same edge.

One bet at the craps table has a house edge of 0%–the free odds bet. It’s not even labeled on the table, but it pays off at true odds. The problem is that you must make a pass or don’t pass bet before being allowed to place an odds bet. (You can also take or lay odds on a come or don’t come bet.)

Some people contend that you can get an edge at craps by influencing how the dice land through controlled shooting. I’m skeptical of this in the extreme. But I’ve seen better-known and better-respected gambling writers than myself who believe that it’s possible.

The idea is that the house edge in craps is low enough that you don’t need to be super-accurate with your controlled shooting to flip that edge. You only need to be able to change the odds enough to overcome the house edge and get the odds into your favor.

You can find any number of videos and books explaining how to set the dice. I can’t guarantee that you’ll succeed, but if you’re going to try it, prepare to spend a LOT of time practicing.

Why You Can’t Beat Roulette

The house has an edge over the player in roulette because of the green 0 and the green 00 on the wheel. You might find a tournament or a promotion that will help tilt the odds in your favor, though.

Here’s why the zeroes make such a big difference:

It’s not because you always lose when the ball lands on a 0 or 00. It’s because those 0s increase the number of possible outcomes from 36 to 38. All the payouts at the roulette table would be break-even payouts if there were 36 numbers on the wheel.

For example, a single number bet has a payoff of 35 to 1. If you had a 35 to 1 probability of hitting a single number, that would be a break-even (or “fair”) bet. But the actual probability of hitting that single number is 37 to 1. If you bet on 2 numbers (a 2-number bet), the payoff is 17 to 1, but the probability of hitting one of those 2 numbers is 18 to 1.

Of course, a roulette wheel with a 0 and a 00 is only one kind of roulette wheel—an American roulette wheel. You can also find roulette wheels that have only a single zero. These are called European roulette wheels. This reduces the house edge from 5.26% to 2.70%. That’s a big difference, but it’s still a bet that the house will win on in the long run.

You can cut that edge in half again if you can find a casino using European rules. These roulette tables put your bet in prison if you lose an even-money bet. If the bet loses a 2nd time, it loses, but if it wins the 2nd time, you get your bet back with no winnings. This reduces the house edge to 1.35%.

One way to think about such a game is that it has only half a zero instead of one or 2 zeroes. You still can’t win such a game in the long run, though. Your money should just last longer.

But let’s say you find a casino that offers you $100 in free chips just for showing up, but you can only bet those free chips on even-money bets. Let’s say that once you’ve wagered those chips, they’re taken away by the casino.

If you gambled those chips on an even-money bet in roulette, you’d have a positive expectation, because the $100 in free chips didn’t cost you anything. You should, on a standard roulette wheel, win an even-money bet 47.37% of the time, so the expected value of that promotion is positive: $47.37.

Or suppose you find a casino that’s holding a promotion where they’re paying 39 to 1 for single number bets on the roulette wheel between the hours of 7pm and 9pm. Since the probability of winning is 37 to 1, you now have a positive expectation situation.

That sounds ludicrous, but casinos do offer some ludicrous promotions once in a while. Something like this is simple enough to understand that you’d have a hard time getting a seat at the roulette table because of all the advantage gamblers who’d be sitting there.

Theoretically, there’s one other way to beat roulette—find a wheel that isn’t working entirely right. This is called a “biased wheel.” The idea is that a mechanical imperfection in the roulette wheel causes it to land on some numbers more often than others.

If a wheel is so biased that some numbers come up 1/34 of the time, for example, and you knew which numbers they were, you’d have an edge over the casino as long as you stuck with those numbers. You’d have an edge, because now you’d win $3500 once while losing $3300, for a net win of $200 over 35 spins. That’s an average win of $5.71 per spin, meaning YOU’D have an edge of 5.71%.

To succeed at this, you’d need to record how often each number comes up over a huge number of spins. You’d need a huge sample size, though, because with a small sample size, some numbers are naturally going to come up more often than others.

On top of that difficulty, not all wheels have a bias. You could spend hours clocking a wheel’s results only to find that it’s perfectly accurate or so close to accurate that you can’t get an edge.

Finally, modern casinos spend money on good equipment. When you read about roulette legends who won loads of money by finding biased wheels, you’re reading about players who played at older casinos in a time gone by. Even if you could find such a wheel, the casinos pay close attention now, too. They’re likely to move or replace the wheel once they realize that you’re taking advantage of its bias.

This makes finding a biased roulette wheel as an advantage play impractical, to say the least. I’m not even going to get into the idea of using a laser pointer and a computer to predict where the ball is going to fall. This would be illegal anyway, but I mention it for the sake of completeness. Anyway, that’s why you can’t beat roulette.

Other Casino Games You Can’t Beat

Baccarat is fun, but it’s also absurd. You go through a lot of rigmarole for what is basically a coin toss with no skill involved. It’s a card game where you compare your score with the banker’s. You can bet on the banker or the player, but either way, the house has an edge of at least 1%. Card counting is of no help in baccarat, either.

Other casino card games, like Casino Holdem, Let It Ride, and Three Card Poker sometimes involve a skill element and sometimes don’t. Either way, it doesn’t matter—you can’t get an edge at those games under normal conditions. If there’s a progressive jackpot attached to the game, it could theoretically get high enough to change your expectation, but it would have to be high indeed.

Keno is still popular, but not only is it impossible to beat, the house edge is crazy high. On average, the house edge in keno is 30% or so. It’s basically a casino-run lottery game. I’m not a fan of lotteries because the payback percentage is always too low.

Pai gow poker is worth playing, but it can’t really be beaten. You’ll have so many hands that push that it turns out to be a much slower game than most other casino games. With proper strategy, the house edge is lower than average, too, so you’ll lose less money gambling recreationally at pai gow poker than you would at most other casino card games.

Most slot machines are unbeatable. The only slot machines where you can sometimes get an edge are the ones with progressive jackpots and the ones that “bank” money as you play. The trouble is that you’re never sure about the odds involved. It’s impossible to know when the game switches from negative to positive expectation. And with slots that don’t have progressive jackpots or banking functionality, forget about it. They just have a high house edge, and that’s it.

Conclusion

Most casino games are impossible to beat regardless of your skill level. That doesn’t mean you should avoid playing them. If you enjoy shooting craps or betting on the roulette wheel, feel free to indulge. Just don’t convince yourself that you can ever beat these games in the long run.

Sometimes you’ll see an otherwise successful poker player or sports bettor waste a lot of money playing games where they can never get an edge. If you’re going to play these games that can’t be beaten, do so for fun, and don’t risk amounts of money that have any consequence.

Joey Richardson