Any savvy gambler is aware of the “house edge”—the advantage a casino has in every available bet, including slot games, table games and keno lounges. Sometimes the edge is challenging to understand, such as the odds of winning a grand jackpot on a slot machine. But the house edges for basic Craps bets are simpler to grasp, if you understand that two 6-sided dice yield 36 combinations.
Connecting the (Combinations of) Dots
At a full Craps table, when I say that two dice make 36 combinations, invariably another player (a drunk one) retorts that there are 11 combinations: the numbers 2 through 12.
The misconception is that two dice make 11 sums.
So let’s make it simple. Just take one 6-sided die and replace 1 through 6 with A through F. Rolling the numerical die and the alphabetical die will yield one of the combinations below:
| 1-A | 1-B | 1-C | 1-D | 1-E | 1-F |
| 2-A | 2-B | 2-C | 2-D | 2-E | 2-F |
| 3-A | 3-B | 3-C | 3-D | 3-E | 3-F |
| 4-A | 4-B | 4-C | 4-D | 4-E | 4-F |
| 5-A | 5-B | 5-C | 5-D | 5-E | 5-F |
| 6-A | 6-B | 6-C | 6-D | 6-E | 6-F |
As you can see, taking the alphabetical die in Craps and replacing A through F with 1 through 6 will yield the traditional 11 sums, but the 36 combinations that generate them should be clearer to observe:
| 1-1 | 1-2 | 1-3 | 1-4 | 1-5 | 1-6 |
| 2-1 | 2-2 | 2-3 | 2-4 | 2-5 | 2-6 |
| 3-1 | 3-2 | 3-3 | 3-4 | 3-5 | 3-6 |
| 4-1 | 4-2 | 4-3 | 4-4 | 4-5 | 4-6 |
| 5-1 | 5-2 | 5-3 | 5-4 | 5-5 | 5-6 |
| 6-1 | 6-2 | 6-3 | 6-4 | 6-5 | 6-6 |
Craps: Adding It Up
With these 36 combinations:
- There are 6 ways to roll a sum of 7. The odds of rolling a 7 on a single roll in Craps are 5:1 (roughly a 16.6% chance).
- There are 5 ways to roll a sum of 6, and there are 5 ways to roll a sum of 8. The odds of rolling one of these specific numbers is 31:5 (roughly a 13.8% chance).
- You have 4 ways to roll a sum of 5, and 4 ways to roll a sum of 9. The odds of rolling one of these specific numbers is 8:1 (roughly a 12.5% chance).
- There are 3 ways to roll a sum of 4 in Craps, and there are 3 ways to roll a sum of 10. The odds of rolling one of these specific numbers is 11:1 (roughly an 8.3% chance).
- There are 2 ways to roll a sum of 3, and there are 2 ways to roll a sum of 11. The odds of rolling one of these specific numbers is 17:1 (roughly a 5.5% chance).
- But there’s only 1 way to roll a sum of 2, and only 1 way to roll a sum of 12. The odds of rolling one of these specific numbers is 35:1 (roughly a 2.7% chance).
- Each “hard way”—a pair of twos, a pair of threes, a pair of fours, and a pair of fives—also has one combination, making the odds of rolling a “hard way” the same as the odds of rolling a 2 or 12.
High Risk, Proportionally-Low Rewards
Many statisticians and gambling pros say the bets in the center of a Craps table are sucker bets. To prove this, let’s look at two of the highest-paying center bets:
- Aces/Two: a one-roll bet that pays 30 to 1 when the next roll is a 2. Any other combination loses.
- Boxcars/Twelve: a one-roll bet that pays 30 to 1 when the next roll is a 12. Any other combination loses.
In Craps, betting $1 for a chance to win $30 sounds like a great proposition at first. But the odds of rolling any specific pair is 35:1. Players who consistently make either bet will lose money in the long run; a $30 win is offset by 35 $1 losses. Losing an average of $5 over the course of 36 rolls may not sound terrible, but there are other bets with a far lower house edge.
A brief analysis of other center-table bets yields the following data:
- Hard 4 or Hard 10: You’re an 8:1 underdog to win 7:1.
- Hard 6 or Hard 8: You’re a 10:1 underdog to win 9:1.
- Any 3 or Any 11: You’re a 17:1 underdog to win 15:1.
- With any Craps: You’re an 8:1 underdog to win 7:1.
- Any 7: You’re a 5:1 underdog to win 4:1.
The Craps table has no safe bets. However, some quick mental calculations can help you avoid blatant sucker bets and focus on bets that reduce the house edge. So when the Craps action gets intense, consider taking a deep breath and counting to 36.
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