Craps Odds and Probability: Mastering the Math of the Dice
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The Probability of Rolling Each Total
The “Curve of Seven” is the most important concept in craps. Since there are more ways to roll a 7 than any other number, it is the center point of all craps math.
| Total | Combinations | Probability | True Odds |
| 2 | (1+1) | 2.78% | 35 to 1 |
| 3 | (1+2, 2+1) | 5.56% | 17 to 1 |
| 4 | (1+3, 2+2, 3+1) | 8.33% | 11 to 1 |
| 5 | (1+4, 2+3, 3+2, 4+1) | 11.11% | 8 to 1 |
| 6 | (1+5, 2+4, 3+3, 4+2, 5+1) | 13.89% | 6.2 to 1 |
| 7 | (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) | 16.67% | 5 to 1 |
| 8 | (2+6, 3+5, 4+4, 5+3, 6+2) | 13.89% | 6.2 to 1 |
| 9 | (3+6, 4+5, 5+4, 6+3) | 11.11% | 8 to 1 |
| 10 | (4+6, 5+5, 6+4) | 8.33% | 11 to 1 |
| 11 | (5+6, 6+5) | 5.56% | 17 to 1 |
| 12 | (6+6) | 2.78% | 35 to 1 |
Low-Edge Fundamental Bets
These are the safest bets for a long-term session in Aotearoa:
- Don’t Pass / Don’t Come: 1.36% House Edge.
- Pass Line / Come: 1.41% House Edge.
- Place 6 & 8: 1.52% House Edge.
High-Edge Proposition Bets
These “one-roll” bets are exciting but carry a heavy cost. In 2026, we recommend these only for small “fun” wagers:
- The Field: 2.78% to 5.56% (depending on the 2/12 multiplier).
- Any Craps: 11.11% House Edge.
- Any Seven: 16.67% House Edge. (Statistically the worst bet on the table).
The Zero-Edge Advantage: Taking Odds
- Why it’s unique: The casino has a 0.00% House Edge on this bet. They make no profit on it.
- The Payouts: If the point is 4 or 10, it pays 2:1. If it’s 5 or 9, it pays 3:2. If it’s 6 or 8, it pays 6:5.
- The 2026 Strategy: By maximizing your “Odds” bet and keeping your “Pass Line” bet at the table minimum, you can lower the overall house edge of your total money to below 1%.
Frequently asked questions
How many equally likely outcomes do two fair dice have?
There are 36 ordered outcomes: six possibilities on the first die multiplied by six on the second. Different totals can be formed in different numbers of ways.
Why is a total of seven more likely than twelve?
Seven has six ordered combinations, while twelve has only one: six and six. This distinction comes from the dice combinations, not past rolls.
Can past rolls make a total due?
With independent fair rolls, no. A sequence of previous results does not change the combinations possible on the next roll.
Can information about craps guarantee a winning result?
No. Understanding rules does not remove uncertainty or the risk of loss. A game’s payout schedule is not a promise about the result of a particular round or session.
Which rules should I use when checking a craps example?
Use the rules and paytable for the exact version being discussed. Different editions can change payouts, optional features and settlement conditions. General examples do not override those published rules.
Does this guide confirm that a service is authorised in New Zealand?
No. An information page, payment logo or software listing does not establish a particular operator’s status. Check current DIA information for online casino customers and the rules for the specific service.
