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House Edge for all the Major Craps Bet on Both a Per Bet Made and Per Roll Basis
Introduction
One argument that comes up a lot is how to quantify the house edge in craps. Normally the house edge is defined as the ratio of expected loss to the initial bet. However, how do you treat bets, like the place bet for example, when many rolls may be required to resolve the bet and the player can take it down anytime? Is it a push or should we assume the bet will stay on the table until resolved?
Personally, I prefer to define the house edge in craps on a "per bet resolved" basis. However, for those who disagree, I present this page, which defines the house edge all three ways.
Multi-Roll Bets
The following table shows the house edge of all the bets in craps which may take multiple rolls to resolve. The house edge is shown three ways: per bet made, per bet resolved, and per roll.
Craps House Edge
| Bet | Pays | Expected Rolls | House Edge Per Bet Made |
House Edge Per Bet Resolved |
House Edge Per Roll |
|---|---|---|---|---|---|
| Pass | 1 to 1 | 3.38 | 1.41% | 1.41% | 0.42% |
| Don't Pass | 1 to 1 | 3.47 | 1.36% | 1.40% | 0.40% |
| Taking Odds 6 and 8 | 6 to 5 | 3.27 | 0.00% | 0.00% | 0.00% |
| Taking Odds 5 and 9 | 3 to 2 | 3.60 | 0.00% | 0.00% | 0.00% |
| Taking Odds 4 and 10 | 2 to 1 | 4.00 | 0.00% | 0.00% | 0.00% |
| Laying Odds 6 and 8 | 5 to 6 | 3.27 | 0.00% | 0.00% | 0.00% |
| Laying Odds 5 and 9 | 2 to 3 | 3.60 | 0.00% | 0.00% | 0.00% |
| Laying Odds 4 and 10 | 1 to 2 | 4.00 | 0.00% | 0.00% | 0.00% |
| Place 6 and 8 | 7 to 6 | 3.27 | 0.46% | 1.52% | 0.46% |
| Place 5 and 9 | 7 to 5 | 3.60 | 1.11% | 4.00% | 1.11% |
| Place 4 and 10 | 9 to 5 | 4.00 | 1.67% | 6.67% | 1.67% |
| Big 6 and 8 | 1 to 1 | 3.27 | 2.78% | 9.09% | 2.78% |
| Don't Place 6 and 8 | 4 to 5 | 3.27 | 0.56% | 1.82% | 0.56% |
| Don't Place 5 and 9 | 5 to 8 | 3.60 | 0.69% | 2.50% | 0.69% |
| Don't Place 4 and 10 | 5 to 11 | 4.00 | 0.76% | 3.03% | 0.76% |
| Buy 6 and 8 * | 23 to 21 | 3.27 | 1.46% | 4.76% | 1.46% |
| Buy 5 and 9 * | 29 to 21 | 3.60 | 1.32% | 4.76% | 1.32% |
| Buy 4 and 10 * | 39 to 21 | 4.00 | 1.19% | 4.76% | 1.19% |
| Buy 6 and 8 ** | 23 to 20 | 3.27 | 0.69% | 2.27% | 0.69% |
| Buy 5 and 9 ** | 29 to 20 | 3.60 | 0.56% | 2.00% | 0.56% |
| Buy 4 and 10 ** | 39 to 20 | 4.00 | 0.42% | 1.67% | 0.42% |
| Lay 6 and 8 * | 19 to 25 | 3.27 | 1.22% | 4.00% | 1.22% |
| Lay 5 and 9 * | 19 to 31 | 3.60 | 0.90% | 3.23% | 0.90% |
| Lay 4 and 10 * | 19 to 41 | 4.00 | 0.61% | 2.44% | 0.61% |
| Lay 6 and 8 ** | 19 to 24 | 3.27 | 0.69% | 2.27% | 0.69% |
| Lay 5 and 9 ** | 19 to 30 | 3.60 | 0.56% | 2.00% | 0.56% |
| Lay 4 and 10 ** | 19 to 40 | 4.00 | 0.42% | 1.67% | 0.42% |
| Hard 6 and 8 (US) | 9 to 1 | 3.27 | 2.78% | 9.09% | 2.78% |
| Hard 6 and 8 (AU) | 19 to 2 | 3.60 | 1.39% | 4.55% | 1.26% |
| Hard 4 and 10 (US) | 7 to 1 | 4.00 | 2.78% | 11.11% | 2.78% |
| Hard 4 and 10 (AU) | 15 to 2 | 4.00 | 1.39% | 5.56% | 1.39% |
Footnotes:
* Commission always paid
** Commission on win only
AU Australia rules
US United States rules
Let me add two more things, based on frequent reader comments:
- Some of these bets may not exist anywhere on earth. For example, I've never seen a casino with buy bets on a 5, 6, 8, and 9 where the commission was payable on a win only. Nevertheless, I don't know the rules of every craps table on earth. I also know that if I omit such bets, somebody will write in and take me to task for the omission.
- The table above assumes wins are calculated exactly. In other words, no rounding up or down. Let me make it perfectly clear that you can lower the house edge if the dealers will round a win up or a commission down. A common one is a 5% commission on a $25 bet is $1.25. If the casino rounds that down to $1, then that cuts the commission to 4%. Finding other situations is an exercise left up to the reader.
Single-Roll Bets
The following table shows the house edge of all the bets in craps which are always resolved in a single roll, except the field. Thus, there can be only one way to define the house edge.
Craps House Edge
| Bet | Pays | Probability Win |
House Edge |
|---|---|---|---|
| 2, 12, and all "hard" hop bets | 33 | 2.78% | 5.56% |
| 2, 12, and all "hard" hop bets | 32 | 2.78% | 8.33% |
| 2, 12, and all "hard" hop bets | 31 | 2.78% | 11.11% |
| 2, 12, and all "hard" hop bets | 30 | 2.78% | 13.89% |
| 2, 12, and all "hard" hop bets | 29 | 2.78% | 16.67% |
| 3, 11, and all "easy" hop bets | 16 | 5.56% | 5.56% |
| 3, 11, and all "easy" hop bets | 15 | 5.56% | 11.11% |
| 3, 11, and all "easy" hop bets | 14 | 5.56% | 16.67% |
| Any craps (2, 3, or 12) | 7 | 11.11% | 11.11% |
| Any craps (2, 3, or 12) | 7.5 | 11.11% | 5.56% |
| Any seven (US) | 4 | 16.67% | 16.67% |
| Any seven (AU) | 4.5 | 16.67% | 8.33% |
Field
- If the field bet pays 2 to 1 on both the 2 and 12, then the house edge is 5.56%.
- If the field bet pays 2 to 1 on the 2 and 3 to 1 on the 12, then the house edge is 2.78%.
- If the field bet pays 3 to 1 on the 2 and 2 to 1 on the 12, then the house edge is 2.78%.
- If the field bet pays 3 to 1 on both the 2 and 12, then the house edge is 0.00%.
Internal Links
- How the house edge for each bet is derived, in brief.
- The house edge of all the major bets on both a per-bet made and per-roll basis
- Dice Control Experiments. The results of two experiments on skillful dice throwing.
- Dice Control Advantage. The player advantage, assuming he can influence the dice.
- Craps variants. Alternative rules and bets such as the Fire Bet, Crapless Craps, and Card Craps.
- California craps. How craps is played in California using playing cards.
- Play Craps. Craps game using cards at the Viejas casino in San Diego.
- Number of Rolls Table. Probability of a shooter lasting 1 to 200 rolls before a seven-out.
- Ask the Wizard. See craps questions I've answered about:
- Simple Craps game. My simple Java craps game.