The Probability and Statistics Behind Craps

Craps is a popular casino game that involves rolling a pair of dice and making bets on the outcome of the roll. While the game may seem like a game of chance, there is actually a significant amount of probability and statistics involved. In this article, we will delve into the mathematics behind craps and how it affects your chances of winning.

The Basics of Craps

Before we get into the probability and statistics, let’s review the basic rules of craps. The game is played with two dice, and the objective of the game is to predict the outcome of the roll. The player can make a variety of bets, each with different odds of winning. Some of the most common bets include:

• Pass Line
• Don’t Pass Line
• Come Bet
• Don’t Come Bet
• Place Bets
• Field Bets

Each bet has its own set of rules and odds, which we will explore in more detail below.

The Mathematics of Craps

Now let’s dive into the probability and statistics behind craps. The game is based on a combination of the outcomes of the two dice, which can yield a total of 36 possible combinations. Some combinations are more likely than others, which affects the odds of winning each bet.

Pass Line Bet

The Pass Line bet is one of the most popular bets in craps, and it has a relatively low house edge of 1.41%. The bet wins if the shooter rolls a 7 or 11 on the come-out roll, and loses if they roll a 2, 3, or 12. If the shooter rolls any other number, that number becomes the point, and the shooter must roll that number again before rolling a 7 in order to win.

The probability of winning a Pass Line bet is 49.29%, while the probability of losing is 50.71%. This means that for every 100 Pass Line bets placed, the player can expect to win 49.29 bets and lose 50.71 bets.

Don’t Pass Line Bet

The Don’t Pass Line bet is essentially the opposite of the Pass Line bet. The bet wins if the shooter rolls a 2 or 3 on the come-out roll, and loses if they roll a 7 or 11. If the shooter rolls a 12, the bet is a push. If the shooter rolls any other number, that number becomes the point, and the shooter must roll a 7 before rolling the point again in order to win.

Due to the nature of the bet, the Don’t Pass Line has a slightly lower house edge of 1.36%. The probability of winning a Don’t Pass Line bet is 50.78%, while the probability of losing is 49.22%. This means that for every 100 Don’t Pass Line bets placed, the player can expect to win 50.78 bets and lose 49.22 bets.

Come Bet

The Come Bet is similar to the Pass Line bet, but it can be placed at any time during the game. The bet wins if the shooter rolls a 7 or 11 after the bet is placed, and loses if they roll a 2, 3, or 12. If the shooter rolls any other number, that number becomes the point, and the shooter must roll that number again before rolling a 7 in order to win.

The probability of winning a Come Bet is 44.44%, while the probability of losing is 55.56%. This means that for every 100 Come Bets placed, the player can expect to win 44.44 bets and lose 55.56 bets.

Don’t Come Bet

The Don’t Come Bet is the opposite of the Come Bet. The bet wins if the shooter rolls a 2 or 3 after the bet is placed, and loses if they roll a 7 or 11. If the shooter rolls a 12, the bet is a push. If the shooter rolls any other number, that number becomes the point, and the shooter must roll a 7 before rolling the point again in order to win.

The probability of winning a Don’t Come Bet is 55.56%, while the probability of losing is 44.44%. This means that for every 100 Don’t Come Bets placed, the player can expect to win 55.56 bets and lose 44.44 bets.

Place Bets

Place Bets are bets placed on a specific number (4, 5, 6, 8, 9, or 10) after the come-out roll. The bet wins if the shooter rolls the chosen number before rolling a 7, and loses if they roll a 7 before rolling the chosen number.

The odds of winning a Place Bet vary depending on the chosen number. The probability of winning a Place Bet on 4 or 10 is 33.33%, while the probability of winning a Place Bet on 5 or 9 is 40%. The probability of winning a Place Bet on 6 or 8 is 45.45%. The house edge for Place Bets ranges from 1.52% to 6.67%, depending on the chosen number.

Field Bets

Field Bets are bets placed on the outcome of the next roll. The bet wins if the next roll is a 2, 3, 4, 9, 10, 11, or 12, and loses if the next roll is a 5, 6, 7, or 8.

The probability of winning a Field Bet is 44.44%, while the probability of losing is 55.56%. The house edge for Field Bets is 5.56%.

As you can see, there is a significant amount of probability and statistics involved in the game of craps. By understanding the odds of each bet, you can make more informed decisions and increase your chances of winning. So the next time you’re at the craps table, remember the mathematics behind the game and use it to your advantage.