# Casino Craps: The Mathematics

Craps is a popular casino game involving two dice. Understanding the probabilities and the house edge for different bets is essential for maximizing your chances of winning. Here’s an overview of the mathematics behind craps:

## Basic Probabilities

When rolling two six-sided dice, there are 36 possible outcomes (6 faces on each die). The probability of any specific outcome occurring is 1 in 36. However, the sum of the dice has varying probabilities:

• 2 and 12: 1/36 (2.78%)
• 3 and 11: 2/36 (5.56%)
• 4 and 10: 3/36 (8.33%)
• 5 and 9: 4/36 (11.11%)
• 6 and 8: 5/36 (13.89%)
• 7: 6/36 (16.67%)

As you can see, the number 7 has the highest probability of occurring.

## House Edge

The house edge is the casino’s advantage over the player, expressed as a percentage. In craps, the house edge varies depending on the type of bet:

• Pass Line/Come: 1.41%
• Don’t Pass/Don’t Come: 1.36%
• Place Bets (6 and 8): 1.52%
• Place Bets (5 and 9): 4.00%
• Place Bets (4 and 10): 6.67%
• Field Bets: 5.56% (depending on the payouts)
• Hardways (6 and 8): 9.09%
• Hardways (4 and 10): 11.11%
• Proposition Bets: up to 16.67%

## Best Bets

To maximize your chances of winning, you should focus on bets with the lowest house edge. In craps, these are Pass Line, Don’t Pass, Come, and Don’t Come bets, as well as Place bets on 6 and 8.

Focusing on bets with the lowest house edge can help you maximize your chances of winning in craps. Here’s a brief overview of the best bets you can make:

### Pass Line

A Pass Line bet is made before the come-out roll, and you win if the shooter rolls a 7 or 11. If the shooter rolls a 2, 3, or 12, you lose. If any other number is rolled, it becomes the point, and you win if the point is rolled again before a 7. The house edge on Pass Line bets is 1.41%.

### Don’t Pass

The Don’t Pass bet is the opposite of the Pass Line bet. You win if the shooter rolls a 2 or 3 on the come-out roll, and you lose if they roll a 7 or 11. If the shooter rolls a 12, it’s a push (tie). If any other number is rolled, it becomes the point, and you win if a 7 is rolled before the point is rolled again. The house edge on Don’t Pass bets is 1.36%.

### Come

A Come bet is similar to a Pass Line bet, but it can be made after a point has been established. You win if the shooter rolls a 7 or 11 on the next roll and lose if they roll a 2, 3, or 12. If any other number is rolled, it becomes the new come point, and you win if the come point is rolled again before a 7. The house edge on Come bets is 1.41%.

### Don’t Come

The Don’t Come bet is the opposite of the Come bet. You win if the shooter rolls a 2 or 3 on the next roll and lose if they roll a 7 or 11. If the shooter rolls a 12, it’s a push. If any other number is rolled, it becomes the new come point, and you win if a 7 is rolled before the come point is rolled again. The house edge on Don’t Come bets is 1.36%.

### Place Bets (6 and 8)

A Place bet on 6 or 8 is a bet that the selected number will be rolled before a 7. These bets can be made at any time after the point is established. The house edge on Place bets on 6 and 8 is 1.52%.

By focusing on these bets, you can improve your chances of winning at craps and enjoy a more profitable gaming experience. Keep in mind, however, that the house still has an edge, and there’s no guarantee of winning on any given roll.

## Betting Strategies

There are various betting strategies that can be employed in craps, such as the Martingale system, the Iron Cross system, and the Paroli system. However, it’s important to remember that no betting system can overcome the house edge in the long run.

Here is a brief overview of some popular betting strategies used in craps:

### Martingale System

The Martingale system is a negative progression system where you double your bet after every loss. The idea is that, eventually, you will win and recover all your losses plus make a profit equal to your original bet. However, this strategy has its limitations, as it requires a large bankroll and there’s a risk of reaching the table’s maximum bet limit before recouping your losses.

### Iron Cross System

The Iron Cross system involves placing bets on the Field, as well as Place bets on the 5, 6, and 8. This covers a wide range of possible outcomes, and the bettor wins on all rolls except for a 7. The downside is that the house edge on the Field bet is relatively high, and a single 7 can wipe out your winnings.

### Paroli System

The Paroli system is a positive progression system where you double your bet after every win, aiming to take advantage of winning streaks. You start with your base bet and increase it after a win, then return to your base bet after a predetermined number of consecutive wins (typically 3). This strategy limits your losses during losing streaks but can result in significant gains during winning streaks. However, it doesn’t change the overall house edge.

### Press and Collect

This strategy involves increasing your Place bets on 6 and 8 after a win (“pressing”) and collecting your winnings after another win. The goal is to take advantage of winning streaks and maximize your profits while minimizing your losses during losing streaks.

While these betting strategies can make the game more exciting and potentially lead to short-term gains, it’s crucial to remember that no betting system can consistently beat the house edge in the long run. It’s essential to set a budget, play responsibly, and view craps as a form of entertainment rather than a guaranteed way to make money.

## Where to Play

When choosing a casino to play craps, look for one that offers favorable odds, lower minimum bets, and a friendly atmosphere. Online casinos also offer craps games, allowing you to practice and develop your skills before playing at a physical casino.

In summary, understanding the mathematics behind craps can help you make informed decisions about the bets you place and improve your overall gaming experience.