Dice probability: the 36 combinations behind every bet
Every craps number rests on one small sum. Each die has six faces, so a pair lands 36 ways, all equally likely. Dice probability in craps is just counting: how many of the 36 make the total you want. The seven wins that count with six combinations, the 2 and 12 lose it with one each.
Odds against are the same count turned around. A 7 comes up six ways and misses thirty, so it is 5 to 1 against on any roll. A 6 comes up five ways and misses 31, which is why the chart writes it as 31 to 5 against. The table below lists all eleven totals from exact counting.
| Total | Ways out of 36 | Probability | Odds against |
|---|---|---|---|
| 2 | 1 | 2.78% | 35 to 1 |
| 3 | 2 | 5.56% | 17 to 1 |
| 4 | 3 | 8.33% | 11 to 1 |
| 5 | 4 | 11.11% | 8 to 1 |
| 6 | 5 | 13.89% | 31 to 5 |
| 7 | 6 | 16.67% | 5 to 1 |
| 8 | 5 | 13.89% | 31 to 5 |
| 9 | 4 | 11.11% | 8 to 1 |
| 10 | 3 | 8.33% | 11 to 1 |
| 11 | 2 | 5.56% | 17 to 1 |
| 12 | 1 | 2.78% | 35 to 1 |
The same counting answers the side questions people ask. Doubles show up six ways out of 36, a 16.67% chance, as often as a seven. A hard 6 is just the 3-3. Pick any total in the explorer below and it lights up every combination that makes it, which is the fastest way to feel the dice probability.
The craps odds chart for the main bets
The craps odds chart below does for bets what the first table did for totals. For each wager it shows what the casino pays and how much of each bet the house keeps over time. Read the two columns together: a big payout on a rare result is not generous if it falls short of the true odds.
| Bet | Pays | House edge | Per roll |
|---|---|---|---|
| Pass Line | 1 to 1 | 1.41% | 0.42% |
| Don't Pass | 1 to 1 | 1.36% | 0.40% |
| Come | 1 to 1 | 1.41% | 0.42% |
| Place 6 | 7 to 6 | 1.52% | 0.46% |
| Place 5 | 7 to 5 | 4.00% | 1.11% |
| Place 4 | 9 to 5 | 6.67% | 1.67% |
| Buy 4 | 2 to 1 less 5% | 1.67% | 0.42% |
| Field | 1 to 1; 2 pays 2 to 1; 12 pays 2 to 1 | 5.56% | 5.56% |
| Big 6 | 1 to 1 | 9.09% | 2.78% |
| Hard 8 | 9 to 1 | 9.09% | 2.78% |
| Hard 4 | 7 to 1 | 11.11% | 2.78% |
| Any Seven | 4 to 1 | 16.67% | 16.67% |
| Any Craps | 7 to 1 | 11.11% | 11.11% |
| Yo (11) | 15 to 1 | 11.11% | 11.11% |
| Horn | 30 to 1 on 2 or 12, 15 to 1 on 3 or 11 (one unit each) | 12.50% | 12.50% |
Look for the rows where a payout nearly matches the real chance. Place 6 pays 7 to 6 against a true 6 to 5, close enough for a 1.52% edge. Any Seven pays 4 to 1 against a true 5 to 1, a gap that costs 16.67%. For a payout-by-payout view, see our craps payouts guide.
Probability on the come-out roll and the point
The pass line runs in two stages, and each has its own probability. On the come-out roll 8 of the 36 outcomes are naturals, a 22.22% chance of an instant win. Four outcomes are craps, an 11.11% chance of losing straight away. The other 24, two thirds of all rolls, set a point.
Once a point is on, your chance depends on how many ways it rolls against the seven’s six. A 6 or 8 is made 45.45% of the time, a 5 or 9 exactly 40%, and a 4 or 10 one time in three. Combine both stages and the pass line wins 49.29% of decisions, which leaves a 1.41% edge.
Those numbers explain the one bet with no edge at all. The point is already set when you add odds, so the price can match the probability exactly, and it does. A $10 odds bet on the 6 pays $12, on the 5 it pays $15, and on the 4 it pays $20, true odds every time.
House edge: what each bet costs you
The house edge is the share of each bet the casino expects to keep across many decisions. It is not a fee on each bet, and one session can run far from it. Over thousands of bets, though, it is almost exactly what you pay, and craps odds vary more across one table than across most whole casinos.
The cheap end of the list is short: pass and don’t pass, come and don’t come, the odds behind them, and place bets on the 6 and 8. Buy bets on the 4 and 10 cost 1.67% when the commission is taken only on wins. The field bet sits at 5.56%, and after that the house edge climbs quickly.
One trap is comparing edges on bets that last different lengths of time. A pass line bet takes about 3.4 rolls to decide, so it costs roughly 0.42% per roll. Any Seven is settled every roll and costs its full 16.67% each time. At a fast table that single difference decides how long a bankroll lasts.
Combined house edge with odds behind the line
Because the odds bet is free, adding it lowers the average edge on everything you have wagered. The more odds a casino allows, the lower that combined figure goes. The chart below uses exact figures for the pass and don’t pass sides at the odds limits you are likely to see in casinos.
| Odds allowed | Pass + odds | Don’t Pass + odds |
|---|---|---|
| None | 1.414% | 1.364% |
| 1x | 0.848% | 0.682% |
| 2x | 0.606% | 0.455% |
| 3-4-5x | 0.374% | 0.273% |
| 10x | 0.184% | 0.124% |
| 100x | 0.021% | 0.014% |
The catch is variance. At 10x odds most of your money sits on one point, and a seven-out takes it all at once. The edge is lower, but the swings are far larger. Many players settle on 2x or 3-4-5x and keep the flat bet small, which is the approach used in our odds calculator.
The best odds in craps, and the bets to skip
If the question is simply where the best odds in craps sit, the answer is don’t pass with laid odds, at 0.27% with 3-4-5x. Pass with odds is a hair behind at 0.37%. Most players choose the pass side anyway, because betting with the shooter keeps the table friendly, and five hundredths of a percent is a small price.
The bets to skip sit in the middle of the felt. The proposition bets and the hardways cost between 9% and nearly 17%, and a crapless craps table lifts even the pass line to 5.38%. None of them is unfair; each is simply priced for the house, and the craps odds chart above shows by how much.
Checking the numbers before you bet
Every figure on this page comes from counting the 36 combinations, so you can check it by hand or against published tables such as Michael Shackleford’s Wizard of Odds site, which lists the same house edges. Where two sources disagree, the difference is almost always a table rule, such as what the field pays on 12.
Check that rule first at a new table. Look at the 12 in the field box: a circled 2 to 1 means 5.56%, a 3 to 1 means 2.78%. On licensed online tables in New Jersey, Pennsylvania, Michigan and West Virginia, the same payouts sit in the game’s help screen, so open it before your first roll.