Craps Dice Probability: The Math of Two Dice
Last reviewed: June 2026
Two dice produce exactly 36 equally likely outcomes, and that 6×6 grid is the engine behind every craps decision. Seven appears six ways — more than any other total — giving it a 16.67% probability that shapes the Pass Line, the odds bets, and every prop on the layout.
The full probability table
Each die face (1–6) can pair with each of the other die’s six faces, producing 36 combinations. The table below lists every possible total, the number of ways to roll it, and its exact probability.
| Total | Ways | Probability | Sample combinations |
|---|---|---|---|
| 2 | 1 | 2.78% | 1+1 |
| 3 | 2 | 5.56% | 1+2, 2+1 |
| 4 | 3 | 8.33% | 1+3, 2+2, 3+1 |
| 5 | 4 | 11.11% | 1+4, 2+3, 3+2, 4+1 |
| 6 | 5 | 13.89% | 1+5, 2+4, 3+3, 4+2, 5+1 |
| 7 | 6 | 16.67% | 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 |
| 8 | 5 | 13.89% | 2+6, 3+5, 4+4, 5+3, 6+2 |
| 9 | 4 | 11.11% | 3+6, 4+5, 5+4, 6+3 |
| 10 | 3 | 8.33% | 4+6, 5+5, 6+4 |
| 11 | 2 | 5.56% | 5+6, 6+5 |
| 12 | 1 | 2.78% | 6+6 |
Notice the symmetry: the distribution is a perfect bell curve centered on 7. Totals equidistant from 7 (6 and 8, 5 and 9, 4 and 10) always share the same number of ways.
Why 7 is central to craps
The 7’s dominance flows directly from its six combinations — one more than 6 or 8, two more than 5 or 9. This plays out differently depending on the phase of the hand:
On the come-out roll (no point established), rolling 7 or 11 wins the Pass Line immediately. Rolling 2, 3, or 12 loses it. Rolling any of the point numbers — 4, 5, 6, 8, 9, or 10 — sets the point and begins the second phase.
After a point is set, the shooter tries to repeat the point before rolling a 7. A 7 at this stage is the 7-out: it ends the hand and loses all Pass Line and Come bets. Because 7 has six ways and any given point number has at most five ways (6 or 8), the casino always holds a mathematical edge. That edge works out to 1.41% on the Pass Line — or precisely 7/495 of each dollar wagered.
Don’t Pass bets flip this logic: you win on a 7-out and lose if the point repeats, which slightly narrows the edge to 1.36% (the bar-12 push is what keeps it from being a pure player advantage).
Point numbers: hierarchy by probability
Not all points are equally hard to repeat. The three tiers map directly to the dice table above:
| Point | Ways to make it | Ways to 7-out | Odds against repeating |
|---|---|---|---|
| 6 or 8 | 5 | 6 | 6-to-5 against |
| 5 or 9 | 4 | 6 | 6-to-4 (3-to-2) against |
| 4 or 10 | 3 | 6 | 6-to-3 (2-to-1) against |
Free Odds bets (taken behind the Pass or Come line) pay exactly these true probabilities — 6:5 on a 6/8 point, 3:2 on 5/9, 2:1 on 4/10 — with a 0% house edge. That is the only bet in a casino with no built-in disadvantage. The more odds you take relative to your flat bet, the closer your overall combined edge gets to zero: roughly 0.85% combined at 1× odds, 0.61% at 2×, and the widely available 3-4-5× multiplier brings it to about 0.37% on total action. A full breakdown is in Craps Odds Bets.
The Any Craps and Any 7 props
The craps layout fills the center with high-payout one-roll propositions. The math exposes them quickly.
Any 7 can be rolled 6 ways, giving a 6/36 (16.67%) probability. The bet pays 4:1, but true odds are 5:1 — a 16.67% house edge.
Any Craps covers the totals 2, 3, and 12. Counting the ways: 1 (for 2) + 2 (for 3) + 1 (for 12) = 4 ways out of 36, for a probability of 4/36 = 11.11%. The bet pays 7:1. True odds are 8:1 (there are 32 non-craps outcomes versus 4 craps outcomes). That gap produces an 11.1% house edge. The true odds are 8:1 — not 3:1, which is a figure you may see misquoted elsewhere.
For comparison, the Pass Line’s 1.41% edge makes these center-table bets a poor substitute for basic strategy. See Craps Trap Bets for a full rundown of which wagers to avoid.
Place bets and their edges
If you want action on a specific number without going through the Come line, Place bets let you bet directly. Payouts are slightly below true odds, which is where the edge lives:
| Place bet | Payout | True odds | House edge |
|---|---|---|---|
| 6 or 8 | 7:6 | 6:5 | 1.52% |
| 5 or 9 | 7:5 | 3:2 | 4.00% |
| 4 or 10 | 9:5 | 2:1 | 6.67% |
Place 6 and 8 at 1.52% are close to the Pass Line in quality. Place 5 and 9 at 4.00% are acceptable for recreational play. Place 4 and 10 at 6.67% are poor value — far better to lay odds through the Pass or Come line instead. Full detail in Craps Place Bets.
Putting it together
The dice table is not a strategy in itself — it is the raw math that makes strategy possible. The numbers that appear most often (6, 7, 8) logically anchor the lowest-edge bets. The numbers that appear rarely (2 and 12) are the foundations of the highest-edge props. Once you see that relationship clearly, the layout stops looking random and starts looking like a structured set of tradeoffs.
For a guided walkthrough of the table and how the phases work, visit How to Play Craps or start with the Craps overview. If you already know the basics and want optimal strategy, see Craps Optimal Strategy.
Frequently asked
Why does 7 appear more than any other number? Six distinct die-face pairs sum to 7 (1+6, 2+5, 3+4, and their reverses). No other total has more than five pairs. Since each of the 36 combinations is equally likely, 7 wins by sheer combinatorial count.
Can I use dice probabilities to predict the next roll? No. Each roll is an independent event — the dice have no memory. A shooter who just made three points in a row has exactly the same 16.67% chance of rolling 7 on the next throw as they did on the first. The probabilities describe long-run frequency, not individual outcomes.
What is the safest bet in craps? The Pass Line (1.41% edge) combined with maximum free odds is the lowest-edge combination on the table. With a common 3-4-5× odds multiplier, the combined edge on total action drops to roughly 0.37%. See Craps: What Is the Safest Bet? for a direct comparison.
Sources & further reading
- Wizard of Odds — Craps — comprehensive craps probability tables and house-edge calculations
- Wizard of Odds — House Edge — cross-game edge reference
- /learn/house-edge/ — how the house edge concept works across all casino games
Educational explanation only. No real-money gambling happens on LearnTheOdds.
Responsible gambling: Play for entertainment, not income — the math favors the house over time. Set limits, never chase losses, and if it stops being fun, take a break. 21+. Need help? Call 1-800-MY-RESET (1800myreset.org).