Craps Odds Explained
What this guide covers
Every payout, house edge figure, and strategic decision in craps traces back to one foundational fact: some dice totals are simply more probable than others. This guide covers exactly why, and how that probability translates into the odds behind every bet on the table. For how this connects to the house's advantage specifically, see craps house edge explained; for the zero-edge bet built directly on this math, see how craps odds bets work.
Two dice, 36 possible combinations
Rolling two six-sided dice produces 36 equally likely combinations (6 possibilities for the first die × 6 for the second). Every probability figure in craps derives from counting how many of these 36 combinations produce a given total, since each individual combination is equally likely regardless of the total it produces.
The full combination count by total
| Total | Combinations | Count | Probability |
|---|---|---|---|
| 2 | 1-1 | 1 | 2.78% |
| 3 | 1-2, 2-1 | 2 | 5.56% |
| 4 | 1-3, 3-1, 2-2 | 3 | 8.33% |
| 5 | 1-4, 4-1, 2-3, 3-2 | 4 | 11.11% |
| 6 | 1-5, 5-1, 2-4, 4-2, 3-3 | 5 | 13.89% |
| 7 | 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 | 6 | 16.67% |
| 8 | 2-6, 6-2, 3-5, 5-3, 4-4 | 5 | 13.89% |
| 9 | 3-6, 6-3, 4-5, 5-4 | 4 | 11.11% |
| 10 | 4-6, 6-4, 5-5 | 3 | 8.33% |
| 11 | 5-6, 6-5 | 2 | 5.56% |
| 12 | 6-6 | 1 | 2.78% |
This table is the single most important reference in craps mathematics — every payout ratio at the table exists in relationship to these figures.
Why 7 is the most probable total
Seven has six different combinations that produce it — more than any other total — which is exactly why it's structurally central to craps: it's both the most common come-out winner (alongside 11) and the most common point-phase ending (as the number that beats every point). This single fact explains why 7 gets so much attention in craps terminology and strategy.
Why the distribution is symmetric around 7
Notice that 6 and 8 share the same probability (13.89% each), as do 5 and 9 (11.11%), and 4 and 10 (8.33%), and 3 and 11 (5.56%), and 2 and 12 (2.78%). This symmetry exists because of simple arithmetic: any combination summing to 7-plus-N has a mirror combination summing to 7-minus-N, and both are equally likely given fair dice. This symmetry is exactly why point-related bets (place, buy, lay, odds) use matched payout structures for each pair.
From probability to true odds
"True odds" express the same information as probability, but as a ratio of losing outcomes to winning outcomes rather than a percentage. A point of 4 has 3 ways to win (rolling a 4) against 6 ways to lose (rolling a 7) before any other roll matters — true odds of 6:3, simplified to 2:1. This is exactly why pass line odds on a point of 4 pay 2:1: the payout matches the true underlying probability precisely, which is what gives odds bets their unique zero house edge.
True odds for every point number
| Point | Ways to win (repeat) | Ways to lose (roll 7) | True odds |
|---|---|---|---|
| 4 or 10 | 3 | 6 | 2:1 |
| 5 or 9 | 4 | 6 | 3:2 |
| 6 or 8 | 5 | 6 | 6:5 |
Compare this table directly to the odds bet payout table in how craps odds bets work — they're identical, which is the entire point: odds bets pay exactly true odds, with nothing shaved off for the house.
Why every other bet's payout sits below true odds
Every bet besides odds pays slightly less than its true odds would suggest — this gap is precisely where house edge comes from. A place bet on 4, for example, pays 9:5 rather than the true 2:1 (equivalent to 10:5) — that small difference between 9:5 and 10:5 is the house's structural advantage on that specific bet, expressed in payout terms rather than percentage terms.
Calculating probability for combined outcomes
Some situations require combining probabilities — for instance, the probability that a shooter rolls at least one 7 within their next three rolls isn't simply three times the single-roll probability, since that would overcount. The correct calculation uses the complement: the probability of avoiding 7 entirely across three rolls is (30/36)³ ≈ 57.9%, meaning the probability of at least one 7 appearing is roughly 42.1%. This kind of compound calculation is genuinely useful for understanding how likely a shooter is to "seven out" within a given stretch of rolls.
Why the field bet's math is more complex than it looks
The field bet covers seven different numbers (2, 3, 4, 9, 10, 11, 12), which sounds like better-than-even odds at first glance — but summing their individual probabilities (2.78% + 5.56% + 8.33% + 11.11% + 8.33% + 5.56% + 2.78% = 44.45%) reveals the covered numbers are actually less collectively probable than the five excluded numbers (5, 6, 7, 8, at 55.55% combined). The boosted 2:1 or 3:1 payout on 2 and 12 exists specifically to partially compensate for this imbalance, though not enough to eliminate the house's edge.
Why proposition bet odds feel counterintuitive
A bet like "any seven" pays 4:1 despite 7 being the single most probable total — this can feel backward until you remember that payout ratios reflect probability inversely: the more likely an outcome, the lower its "fair" payout should be, and 4:1 is already below the true 5:1 odds that a 6-in-36 probability would suggest, which is exactly the source of that bet's notably high house edge.
Using this math to evaluate any new or unfamiliar bet
With the combination table and the true-odds derivation method covered in this guide, you can evaluate the fairness of any craps bet you encounter — including niche hop bets or variant-specific wagers not explicitly covered elsewhere on this site — by counting winning combinations out of 36, converting to true odds, and comparing against the bet's actual advertised payout. The gap between the two is always the house edge, expressed in payout terms.
Frequently asked questions
Why does 7 come up more often than any other total? Because it has six different two-dice combinations that produce it — more than any other total — making it the single most probable result on any given roll.
Why do 6 and 8 have the same probability? Both have five combinations producing them, a direct result of the symmetry in how two-dice totals distribute around 7.
How do I calculate true odds for a specific point number? Divide the number of ways to roll a 7 (always 6) by the number of ways to roll that specific point number, then simplify the ratio.
Why do odds bets pay exactly true odds while other bets don't? Odds bets are a deliberate exception built with zero house edge; every other bet's payout is set slightly below true odds, which is where the house's structural advantage comes from.
Does the field bet actually cover more than half the possible outcomes? It covers seven numbers out of eleven possible totals, but those seven numbers are collectively less probable (44.45%) than the four excluded numbers (55.55%), despite the field's numeric majority.
Can this probability math be applied to variants like crapless craps? The same combination-counting method applies, but the underlying probabilities and resulting bet structures differ since crapless craps changes which totals function as points — see crapless craps explained for those specifics.
