Craps is a game of chance, but understanding the math behind the dice rolls can significantly improve your betting strategy. The key to becoming a savvy craps player lies in recognizing the probabilities associated with each possible outcome of a dice roll. The number 7 has the highest probability of being rolled, followed by 6 and 8, then 5 and 9, and finally 4 and 10. This distribution of probabilities explains why certain bets are safer and why others, like the high/low bet, are considered sucker bets. Let’s dive into the mathematics of craps and explore these concepts further.
The Probability of Rolling a 7
In craps, players roll two six-sided dice, resulting in 36 possible combinations (6 sides on the first die x 6 sides on the second die). Each combination of dice adds up to a sum ranging from 2 to 12. The number 7 has the most combinations:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
This gives 7 a total of six combinations out of the 36 possible outcomes, resulting in a probability of 1 in 6, or about 16.67%.
The Probabilities of Rolling 6 and 8
The numbers 6 and 8 each have five possible combinations:
- 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
- 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
This results in a probability of 5 in 36, or about 13.89%, for each. Because of their relatively high probability of appearing, bets on 6 and 8 are safer than most other bets on the craps table.
The Probabilities of Rolling 5 and 9, and 4 and 10
The numbers 5 and 9 each have four possible combinations:
- 5: (1, 4), (2, 3), (3, 2), (4, 1)
- 9: (3, 6), (4, 5), (5, 4), (6, 3)
This results in a probability of 4 in 36, or about 11.11%, for each.
The numbers 4 and 10 each have three possible combinations:
- 4: (1, 3), (2, 2), (3, 1)
- 10: (4, 6), (5, 5), (6, 4)
This results in a probability of 3 in 36, or about 8.33%, for each.
Betting Strategy: Why 6 and 8 are Safer
Given the higher probabilities of rolling a 6 or 8 compared to other numbers (except 7), betting on 6 and 8 is safer and more likely to yield consistent wins. Players often expand their bets outward from these numbers to include 5 and 9, and then 4 and 10, as they feel more comfortable and seek higher payouts. This strategy leverages the probabilities, maximizing the chances of winning while managing risk.
High/Low Bets: Sucker Bets
High/low bets involve betting on the numbers 2 and 12. Each of these numbers has only one possible combination:
- 2: (1, 1)
- 12: (6, 6)
This gives them a probability of 1 in 36, or about 2.78%. Because these bets are so unlikely to win, they are known as sucker bets. They offer high payouts, but the chances of winning are very slim. In the context of the All Tall Small (ATS) bonus, these are typically the last numbers shooters attempt to hit, as they are the hardest to roll.
The ATS Bonus and Shooting Strategy
The All Tall Small (ATS) bonus is a side bet where players wager on the shooter’s ability to hit a sequence of numbers. The goal is to roll every number from 2 to 12, excluding 7. Since the probabilities of hitting 2 and 12 are the lowest, they are usually the last numbers to be hit. Players often focus on hitting the more probable numbers (6 and 8, then 5 and 9, then 4 and 10) first to build up to the ATS bonus.
Conclusion
Understanding the math behind craps is crucial for making informed betting decisions. By focusing on the numbers with the highest probabilities, such as 6 and 8, you can increase your chances of winning and enjoy a more strategic game. Avoiding sucker bets like high/low can save you money in the long run. Whether you’re a novice or an experienced player, keeping these probabilities in mind will help you play smarter and have more fun at the craps table.
Another related topic that you may be interested in Differences in Betting Strategies.
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