Craps probability starts with 36 possible two-dice combinations. Seven is the most common total because six combinations make 7. Six and 8 each have five combinations. Four and 10 each have only three. Every craps payout, house edge, and “good bet” claim starts with this uneven dice distribution.
Quick Facts
- Two six-sided dice create 36 possible ordered combinations.
- 7 has 6 combinations, more than any other total.
- 6 and 8 each have 5 combinations.
- 5 and 9 each have 4 combinations.
- 4 and 10 each have 3 combinations.
- 2 and 12 each have only 1 combination.
- House edge appears when casino payouts are worse than true probability.
Plain Talk
Craps feels chaotic because chips are everywhere, dealers are calling fast, and players talk about hot shooters. Under the noise, the dice are simple.
There are two dice. Each die has six faces. That creates 6 × 6 = 36 possible ordered combinations. A 1-6 and a 6-1 both total 7, but they are two different combinations.
That is the foundation of craps odds, craps house edge, and every bet breakdown in the craps guide.
The Wizard of Odds craps appendix provides detailed craps probability tables, Wolfram MathWorld’s dice page explains dice-combination concepts, and the Wizard of Odds craps basics connects those probabilities to common bets and house edges.
How It Works
Here is the basic two-dice distribution.
| Total | Combinations | Probability | Plain-English Meaning |
|---|---|---|---|
| 2 | 1 | 2.78% | Rarest total with 12 |
| 3 | 2 | 5.56% | Still uncommon |
| 4 | 3 | 8.33% | Outside box number |
| 5 | 4 | 11.11% | Middle box number |
| 6 | 5 | 13.89% | Strong box number |
| 7 | 6 | 16.67% | Most common total |
| 8 | 5 | 13.89% | Strong box number |
| 9 | 4 | 11.11% | Middle box number |
| 10 | 3 | 8.33% | Outside box number |
| 11 | 2 | 5.56% | Natural on come-out |
| 12 | 1 | 2.78% | Rarest total with 2 |
This table explains why craps is built around 7.
On the come-out roll, 7 helps Pass Line players. After a point is established, 7 ends the hand against most right-side bets. Same number. Different phase. Different meaning.
Probability vs Payout
Probability alone does not tell you whether a bet is good. You also need payout.
If an event should pay 5 to 1 by true odds but the casino pays 4 to 1, the missing unit becomes the casino edge.
That is why a bet can hit often and still be bad. It is also why a bet can hit rarely but still be fair if the payout is true. The odds bet is the cleanest example because it is paid at true odds after a point is set.
Craps Table Example
A player sees the point set to 6 and places $12 on the 6.
Before 7 appears, the 6 has five winning combinations. The 7 has six losing combinations.
| Event | Combinations | Result |
|---|---|---|
| Roll 6 | 5 | Place 6 wins |
| Roll 7 | 6 | Place 6 loses |
| Roll 2, 3, 4, 5, 8, 9, 10, 11, 12 | 25 | No decision for this bet |
A Place 6 usually pays 7 to 6. A $12 Place 6 wins $14.
That payout is close to the true risk, but not exact. The shortfall is why Place 6 has a house edge of about 1.52%.
From the Casino Side:
Casino managers do not need every dealer to recite the full 36-combination table. But the table crew must understand what outcomes are frequent, which payouts are standard, and where mistakes are likely.
The base dealer pays Place 6 and 8 constantly because those numbers appear often. The stickman calls 7 clearly because it usually resolves many bets at once. The boxman watches high-risk payouts, odds, buy bets, lay bets, and proposition bets where a small error can cost real money.
Surveillance also thinks in probability. A strange pattern does not automatically mean cheating. Dice are volatile. But procedures exist because the game has many moving parts and a lot of chip movement.
Common Mistakes
- Thinking every total from 2 to 12 has the same chance.
- Forgetting that 1-6 and 6-1 are separate combinations.
- Judging bets only by how often they hit.
- Thinking a frequent bet is automatically cheap.
- Confusing true odds with casino payout odds.
- Treating short-term streaks as proof the math changed.
- Ignoring no-decision rolls when comparing multi-roll bets.
Hard Truth
Craps does not have eleven equally likely totals. It has 36 dice combinations wearing eleven different costumes.
FAQ
How many dice combinations are there in craps?
There are 36 ordered combinations from two six-sided dice.
Why is 7 the most common number?
Six combinations make 7: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1.
Are 2 and 12 equally likely?
Yes. Each has only one combination, so each appears about 2.78% of rolls.
Why are 6 and 8 popular in craps?
Each has five combinations, making them the most common box numbers after 7.
Does probability guarantee what happens next?
No. Probability describes long-run frequency, not the next roll.
What is true odds in craps?
True odds means the payout matches the real probability relationship between winning and losing outcomes.
Is a high-probability bet always better?
No. The payout matters. A common event can still be overpriced by the casino.
Deeper Insight
Craps math is built from conditional probability. Some bets resolve in one roll. Others ignore many totals until a deciding number appears.
A Field bet resolves immediately. If the next roll is a Field number, it wins. If not, it loses. That is simple one-roll probability.
A Place 6 is different. Rolls of 2, 3, 4, 5, 8, 9, 10, 11, and 12 do not resolve the bet. Only 6 wins and 7 loses. So the key comparison is 5 combinations for 6 versus 6 combinations for 7.
A Pass Line bet is more complex. It has a come-out phase and then a point phase. That is why the Pass Line house edge is not just one line from the dice table. It combines multiple possible point cycles.
This is where players get fooled. They look at one part of the game and ignore the rest.
Formula / Calculation
Total Two-Dice Combinations = 6 × 6 = 36
P(event) = Favorable Dice Combinations / 36
P(7) = 6 / 36 = 16.67%
P(6) = 5 / 36 = 13.89%
True Odds Payout = Losing Combinations / Winning CombinationsFor Place 6 after the point is relevant:
Winning combinations = 5
Losing combinations = 6
True odds against rolling 6 before 7 = 6 to 5Formula Explanation in Plain English
Count how many dice combinations help you and how many hurt you. Divide by 36 for one-roll probability. For multi-roll bets, ignore non-deciding rolls and compare the combinations that actually resolve the wager.
Related Reading
For the visual version, read craps dice combinations. For bet costs, move to craps odds and craps house edge. To test numbers, use the craps odds calculator or expected loss calculator. If you want the practical consequence of the 7, continue with Why 7 Is the Most Important Number.