Doubling Your Money at the Casino

The amount of money you put on a single bet compared to the size of your bankroll can be considered your boldness.

For example, if you have a $1000 bankroll, and you’ve found a casino that allows you to play blackjack for a dollar per hand, you’re not being very bold at all. You’re risking 0.1% of your bankroll on each hand.

Take that same $1000 bankroll and bet it all on red on a roulette wheel, and you’re making the boldest bet you possibly could. (That boldness isn’t related to betting on roulette, though—it’s maximum boldness because of the amount, not the game.)

If you want to know what your best chance of doubling your money when gambling is, it depends on whether you’re playing a game where you have the edge or where the casino has the edge.

Most of the time in most casino games, the casino has the mathematical edge. In that case, a maximum boldness strategy offers you the best chance of doubling your money.

Rare gamblers with advantage strategies, like card counters, have an edge over the casino. In this case, a minimum boldness strategy is the approach that will be most likely to provide you with a shot at doubling your money.

Here’s why:

With a negative expectation game, the more bets you make, the closer you get to the long run. And since the negative expectation is a long-term result, the closer you get to the long-term, the more likely you are to lose money. The short run is your friend when it comes to gambling on negative expectation games.

With a positive expectation game, though, the worse the short run is for you. In the short run, the results are unpredictable. This means you could go broke in the short run even if you’re playing with a mathematical edge over the casino.

Unless you’re a biased wheel specialist—which is beyond the scope of this post—roulette is a game where the house has a clear edge against the player. You have 38 numbers on a standard roulette wheel. The even money bets all have 18 opportunities to win versus 20 opportunities to lose.

Here’s how that works:

The even-money bets on a roulette wheel are as follows:

• Even or odd
• High or low
• Red or black

The numbers on the roulette wheel are 0, 00, and 1 through 36. If you bet on even, there are 18 numbers which can win for you: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, and 36.

Any odd number or any 0 or 00 is a loser for you with that bet.

The high numbers on the roulette wheel are 19 through 36, while the low numbers are 1 through 18. If you bet on high, you have 18 ways to win and 20 ways to lose.

2 of the numbers on the roulette wheel, the 0 and the 00, are green. Half of the rest of the numbers are red, and the other half are black. That’s 18 ways to win if you bet on red.

The probability of something happening is the number of ways it can happen divided by the number of total possible outcomes. So the probability of winning any of these even money bets is 18 divided by 38. (18 ways to win, and 38 total possibilities.)

18/38 = 47.37%

You can express that probability in multiple ways, but most people understand percentages in a reasonably intuitive way. Most people know that 47.37% is a close to 50% shot, which is roughly half the time.

A 47.37% chance of doubling your money isn’t bad, though. Now let’s see what happens to the probability of doubling your money if you divided your bankroll in half and made 2 bet. You’d have to win both bets, right?

The probability of winning 2 bets in a row is the probability of winning each of them multiplied by each other. That’s 47.37% X 47.37%, or 22.44%. That’s a little more than 1 in 5 but not as good as 1 in 4. It’s a far cry from 1 in 2.

Here’s why:

When you place 2 bets on an even-money bet at the roulette table, you have to win both of them. But you have roughly equal probabilities of seeing the following results:

1. You’ll win both bets. (22.44%)
2. You’ll lose both bets. (27.70%)
3. You’ll win the 1st bet but lose the 2nd bet. (24.93%)
4. You’ll win the 2nd bet but lose the 1st bet. (24.93%)

Your probability of losing is always slightly greater in these situations, but there are 4 possible outcomes instead of just 2.

Most gamblers do want to do more than double their money on a single bet, though. They want to gamble a lot. And some of them even want to make a living doing it.

These people are called “advantage gamblers.” They’re card counters, pro poker players, and sharp sports bettors. The thing about all these advantage gamblers is that they all operate with a small edge over the house (or the other players).

Remember how the casino has a small mathematical edge over the player?

This is what gives the player a reasonable chance to double his money if he makes a single bet. You’re taking advantage of how unpredictable the results are in the short run.

If you have a small advantage over the casino, though, your goal becomes getting into the long run. By getting into the long run, you’re able to compound that small edge repeatedly. You just have to avoid going broke in the short run.

Let’s assume you’re hosting a roulette game in your home, but your start-up costs are limited. (Think of the Will Ferrell movie The House.) You have $10,000.

A high roller finds out about your game and comes to your house wanting to bet $10,000 on a spin of the roulette wheel. You’re more likely to win that bet than he is, sure. Your probability of winning, since you’re the house, is 52.63%.

But do you really want to take a 47.37% probability of going out of business because of a single bet?

The risk level is too high. This leads to an important principle—when you have an edge, a minimum boldness strategy is correct. When the house has an edge, a maximum boldness strategy is best.

This is why casinos have betting minimums at their casino games. At many casinos, the most you can wager on a single spin of the roulette wheel is $500.

Let’s look a real example of an advantage gambler in action, since most people don’t host roulette games in their homes. Let’s assume you’re a card counter.

Most card counters have an edge of maybe 1% over the house, give or take. But they still have a less than 50% probability of winning a specific hand, even when the count is positive. They get their edge from the greater probability of getting a natural and the corresponding 3 to 2 payout.

But if a card counter bet all or most of his bankroll on a single hand of blackjack, his risk of going broke would be enormous. He’d be out of business until he put together a new bankroll.

Most card counters will limit the size of their bets to 1% of their bankroll or less. As their bankroll grows, the size of their bets grows.

This is true for professional poker players and sharp sports bettors, too. Few poker players sit down with their entire bankroll in front of them. The pros never do that. With sports bettors, you’re likelier to see a bettors limit his wagers to 1% or 2% of his total bankroll.

The risk of ruin drops as the size of your bets compared to your bankroll decreases. It’s not impossible to go broke in those situations; it’s just less likely.

To maximize your probability of doubling your money, you need to choose the bet in the casino which offers the highest probability of winning even money. Any bet that pays off at more than even money is off limits to begin with, because it’s going to have a much lower probability of winning.

You won’t find a casino bet that has a greater than 50% probability of paying off at even money, either. That’s not how casino games work.

We’ve already established that the probability of winning an even-money roulette bet is 47.37%.

But you can find some casinos which have single-zero wheels. The probability of winning an even-money bet on one of these roulette tables is better, because you now have 18 ways to win out of 37 possible outcomes. That improves your chances to 48.65%.

Believe it or not, that’s probably your best bet, too. You’d be forgiven for thinking that blackjack would be better because it has a lower house edge, but the probability of winning a single bet on a blackjack hand is actually lower—it’s more like 42.20%.

How is that possible?

It’s because a certain percentage of those wins will be naturals, 2-card hands which total 21, and those pay off at higher odds: 3 to 2. This compensates for your lower win rate. Also, a percentage of your blackjack hands will also result in a “push,” which is a tie result where you neither win nor lose any money.

But believe it or not, there’s a game with a house edge between that of roulette and blackjack where your probability of winning is actually a little higher than 50%. It’s casino war.

If you’ve never played casino war, it’s basically a gambling version of the game you played as a kid. You each flip over a single card, and the person with the higher-ranked card wins.

In casino war, though, you must put up a 2nd bet if you go to war. If you win after going to war, you only get a one-unit payout. If you lose, you’ve lost 2 bets.

So even though you have a slightly better than even money chance of doubling your money, the game has a built-in mathematical advantage. You just lose that much more when you lose. That’s where the house gets its edge.

You won’t be able to bet your entire bankroll on a hand of casino war, though, or your probability will differ greatly. That’s because if you go to war, you must put up another bet the same size as your initial bet.

The best way to double your money when gambling in a casino—if you’re playing a game where the house has an edge—is to make the maximum boldness move. Bet your entire bankroll on an even-money bet.

The best bets for this purpose are roulette and casino war, but roulette is actually superior. With casino war, you can’t place a bet of your entire bankroll, because if you do, you won’t have the money to bet when you have to go to war.

On the other hand, if you’re an advantage gambler, you should manage your bankroll carefully. You don’t want to go broke before your long-term edge starts to become realized.