The short answer
In Craps, there are exactly 36 possible combinations of two six-sided dice, and the number 7 is the most probable outcome, occurring 1 out of every 6 rolls (16.67%).
The full calculation
To understand Craps math, you must view the 36-combination grid:
- 7: 6 combinations (1-6, 2-5, 3-4, 4-3, 5-2, 6-1). $P = 16.67%$
- 6 and 8: 5 combinations each. $P = 13.89%$
- 5 and 9: 4 combinations each. $P = 11.11%$
- 4 and 10: 3 combinations each. $P = 8.33%$
- 3 and 11: 2 combinations each. $P = 5.56%$
- 2 and 12: 1 combination each. $P = 2.78%$
The “Point” phase of Craps is simply a race between the Point number and the 7. If the point is 4, you have 3 ways to win and 6 ways to lose (the 7). Your probability of winning that specific point is exactly 33.3%.
What this means at the table
The “Seven” is the gravity of the game. It is the most likely number on every single roll. This is why “Place” bets on the 6 and 8 are popular; they are the only numbers with a probability (13.89%) close to that of the 7. If you are betting on the 2 or 12, you are chasing a 1-in-36 longshot. On average, a shooter will roll a 7 once every 6 tosses. If a shooter has rolled 20 times without a 7, they aren’t “due”—the probability of a 7 on the next roll remains exactly 16.67%.
Common mistakes around this number
The “Gambler’s Fallacy” is the number one killer at the Craps table. Players see a shooter roll four 6s in a row and think another one is “likely,” or they see no 7s for ten minutes and bet heavily on “Any Seven.” The dice have no memory. Each roll of two fair dice is an independent event governed by these fixed 1-through-36 probabilities.
See also
Check how these probabilities dictate the Craps Odds Chart payouts, or read about the foundational Craps Rules.
In Detail
Craps probabilities are the skeleton under the party shirt. Once you see the 36 dice combinations, the game becomes random in a measurable way, not a magical one.
This page is about the probability grid behind every roll. On the surface, that may sound like one small corner of craps, but in a real casino it touches the three things that decide whether a player survives the table: the written rule, the payout, and the way the bet feels when chips are already in action. Craps is dangerous for beginners because a bet can feel smart, social, or lucky while still being badly priced.
The math that matters: Two dice create 36 equally likely ordered combinations. The shape of the game comes from that grid: 7 has 6 combinations, 6 and 8 have 5 each, 5 and 9 have 4 each, 4 and 10 have 3 each, 3 and 11 have 2 each, and 2 and 12 have only 1 each. The master formula is $P(\text{total})=\frac{\text{combinations}}{36}$. So $P(7)=6/36=16.67%$, $P(6)=P(8)=5/36=13.89%$, and $P(2)=P(12)=1/36=2.78%$. Expected value is the grown-up way to price a bet: $EV=\sum(P_i\times W_i)-\sum(P_j\times L_j)$. If the payout is smaller than the true probability deserves, the difference is the house edge.
What it means on the felt: That grid explains why 6 and 8 are popular, why 7 is deadly after a point, and why long-shot bets underpay. A player who understands this subject does not need to act like a robot. You can still enjoy the noise, the shooter, the stick calls, and the little rush when the dice leave the hand. The point is to know when you are paying for entertainment and when you are making a lower-cost decision.
Casino-floor truth: Craps is built to move. The table crew wants clear bets, fast decisions, and clean payouts. The layout also nudges attention toward action. The safest-looking move is not always the cheapest move, and the loudest bet is almost never the best one. Good craps play is not about predicting the next roll. It is about refusing to overpay for it.
The mistake to avoid: Do not say a number is due. Dice are not keeping a diary. Also, never judge this topic by one lucky hit or one ugly loss. Short sessions are noisy. The math only shows its face over repeated decisions, which is exactly why casinos are patient and players are usually not.