# The Mathematics of Craps

Craps can look like a very complicated game, but there’s actually a beautiful and sophisticated simplicity to it. The more you play it the more you will see that for yourself, and the better your understanding of how the numbers work and what kind of bets you want to place will be.

Personal style always develops over time, and will continue to develop over the whole of your craps career, but you need to understand a few basics first. In addition to the rules of the game, there are some mathematical principles that are important here.

## Mathematics Important to Gambling

It’s not just craps where you’ll find that maths can help you in the casino. You’re actually using it and applying it in many situations that you might not even realise entail maths – as is the case in so much of life. When you’re choosing which bonuses to take because of how much you’ll be able to reap the rewards or how particularly they apply to you, that’s maths. Deciding on a slots machine based on the theoretical return to player rate? Maths again. Anything that requires any kind of numerical application is based in maths – to the extent that it’s safe to say that any successful gambler needs to have a good grasp of the fundamentals.

Aside from what could almost be looked at as basic common sense, mathematical principles apply mostly in table games, where the odds of the outcomes can be accurately detailed. If you know how likely an outcome is, you can decide what your best move in any situation is. This applies to blackjack, video poker, baccarat, roulette and every other table game just as much as it applies to craps. It all comes down to a branch of mathematics that was actually created as a direct result of gambling: Probability Theory.

## Probability Theory

Probability Theory is exactly what its name implies – the study of the likelihood of every potential outcome. A coin that is tossed, for example, has a 50% chance of landing heads and a 50% chance of it landing tails. It was originally developed by French mathematician Pascal, in response to requests and desires to master the seductive art of gambling. Its essence remains the same as in the coin example, but there are almost always many more outcomes to consider and measure for. This is certainly the case with a game of craps.

## Probabilities in Craps

Since craps is a game that is rolled with 2 dice, there are 36 possible final combinations. Each of these has a 1 in 36 chance of being seen on each roll, but some dice totals are a lot more probable than others. There are 6 potential combinations for the number 7, which is the most in the game, and is the reason why so much of craps is based on 7 and its relation to other numbers.

If you consider the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12, which are all the possible totals that a pair of dice can display, 7 is the midpoint. Moving out on either side we have 6 and 8, and each of these have 1 less possible dice pair combination – they can show up in 5 ways on a pair of dice. The same rule of 1 less possible combination applies all the way up and down the number line, so 5 and 9 allow for 4 combinations, 4 and 10 for 3, 3 and 11 for 2 and 2 and 12 for 1.

When you bet on pass line bets in craps you bet with or against the dice, and are either paid out if the set point number is rolled first or if a 7 is rolled first. The 7 always has the greatest probability of being rolled, but the different odds on the other number totals give them different payout rates. You can choose how much risk you want to take for how much reward – the greater the odds, the greater the payout. As you keep playing and getting comfortable with the game of craps and the way the numbers behave, you will intuitively know what works and will be able to move on to more complex bets.

## Practice Makes Perfect

As mentioned above, craps is a game that can feel very complicated and can feel very mentally challenging. However, if you persevere with it, all will suddenly become clear and you’ll be able to place shrewd bets in the blink of an eye. Also, the more you are actually playing the game in a hands-on way, the easier it will be to grasp the different concepts and principle. And the only way to do that is to start, so get going now!