Throw the dice at a full craps table, then see the exact house edge of every bet — from 0% on the odds to 16.7% on Any Seven.
Two dice give 36 equally likely combinations, so every probability here is an exact fraction. House edge is the average loss per unit bet, per decision (pushes count as decisions).
7 is the most common total (6 ways) — which is why it ends every point.
| Bet | Pays | Win chance | House edge | Rolls per decision |
|---|---|---|---|---|
| Pass odds | true odds | 40.61% | 0.000%0 | 3.56 |
| Lay odds | true odds | 59.39% | 0.000%0 | 3.56 |
| Don't Pass | 1:1 | 47.93% | 1.364%3/220 | 3.38 |
| Pass Line | 1:1 | 49.29% | 1.414%7/495 | 3.38 |
| Place 6 | 7:6 | 45.45% | 1.515%1/66 | 3.27 |
| Place 8 | 7:6 | 45.45% | 1.515%1/66 | 3.27 |
| Field | 1:1 (2 → 2:1, 12 → 3:1) | 44.44% | 2.778%1/36 | 1.00 |
| Place 5 | 7:5 | 40.00% | 4.000%1/25 | 3.60 |
| Place 9 | 7:5 | 40.00% | 4.000%1/25 | 3.60 |
| Place 4 | 9:5 | 33.33% | 6.667%1/15 | 4.00 |
| Place 10 | 9:5 | 33.33% | 6.667%1/15 | 4.00 |
| Hard 6 | 9:1 | 9.09% | 9.091%1/11 | 3.27 |
| Hard 8 | 9:1 | 9.09% | 9.091%1/11 | 3.27 |
| Any Craps | 7:1 | 11.11% | 11.111%1/9 | 1.00 |
| Yo (11) | 15:1 | 5.56% | 11.111%1/9 | 1.00 |
| Hard 4 | 7:1 | 11.11% | 11.111%1/9 | 4.00 |
| Hard 10 | 7:1 | 11.11% | 11.111%1/9 | 4.00 |
| Aces (2) | 30:1 | 2.78% | 13.889%5/36 | 1.00 |
| Twelve (12) | 30:1 | 2.78% | 13.889%5/36 | 1.00 |
| Any Seven | 4:1 | 16.67% | 16.667%1/6 | 1.00 |
Odds bets pay exactly what they are worth, so their edge is zero. The flashier the payout in the center, the bigger the edge.
Pass wins on a come-out 7 or 11, or by making the point before a 7:
| Chance | Makes it | Contributes | |
|---|---|---|---|
| Come-out 7 or 11 | 2/9 | 1 | 2/9 |
| Come-out 2, 3, 12 (lose) | 1/9 | 0 | 0 |
| Point 4, then made | 1/12 | 1/3 | 1/36 |
| Point 5, then made | 1/9 | 2/5 | 2/45 |
| Point 6, then made | 5/36 | 5/11 | 25/396 |
| Point 8, then made | 5/36 | 5/11 | 25/396 |
| Point 9, then made | 1/9 | 2/5 | 2/45 |
| Point 10, then made | 1/12 | 1/3 | 1/36 |
| Pass wins | 244/495 = 49.293% |
The Pass line always costs 7/495 per flat bet, but odds add action at zero edge — so the edge on everything you bet falls as you take more odds.
| Strategy | Edge on total action |
|---|---|
| Pass line only | 1.414%7/495 |
| Pass + 1x odds | 0.848%7/825 |
| Pass + 2x odds | 0.606%1/165 |
| Pass + 3-4-5x odds | 0.374%7/1,870 |
| Pass + 10x odds | 0.184%7/3,795 |
| Pass + 100x odds | 0.021%1/4,785 |
| Don't Pass + 6× lay | 0.273%3/1,100 |
A hand ends only on a seven-out (a come-out 7 is a winner). From a Markov chain over the come-out and the six points:
In 2009 Patricia Demauro rolled 154 times before sevening out. The chance of a hand lasting that long is about 1 in 5,590,264,072.
Six players bet the same way on every roll of the same dice. Each line is the house edge they have actually paid on everything wagered; dashed lines are the exact values. Luck dominates early — the order only settles after tens of thousands of rolls.
Many players sit down with the same bankroll and follow one strategy for a number of rolls (5-unit bets; Place 6 & 8 are 6 each). After the last roll an open line bet is played out and everything else is taken down. How many go home ahead?
Roll until each shooter sevens out and count how long every hand lasted. Bars are the simulation; the line is the exact Markov-chain answer.