Craps odds come from the 36 possible combinations of two dice. Seven is the most common total, with 6 combinations. Point numbers have fewer combinations: 6 and 8 have 5 each, 5 and 9 have 4 each, and 4 and 10 have 3 each. True odds compare the point’s combinations against the 7.
Quick Facts
- Two dice create 36 ordered combinations.
- Seven appears 6 ways, or 16.67% of rolls.
- Six and eight appear 5 ways each, or 13.89% each.
- Five and nine appear 4 ways each, or 11.11% each.
- Four and ten appear 3 ways each, or 8.33% each.
- Odds bets pay true odds and carry 0% house edge.
- Place, field, hardway, and proposition payouts usually pay less than true odds.
Plain Talk
Craps odds are not based on opinion, table energy, or the shooter’s rhythm. They come from counting dice combinations.
There are 36 ordered ways to roll two six-sided dice. The total 7 appears more often than any other number because it can be made six ways: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1.
That single fact explains the entire game. After a point is set, the point is racing against the 7. If the point is 4, there are 3 ways to roll 4 and 6 ways to roll 7. The 7 is twice as likely, so fair odds pay 2:1 on the 4.
This page is about probability and true odds. For payout charts, use Craps Payouts and Craps Odds Chart. For casino advantage, use craps house edge.
For external checks, see Wizard of Odds dice probabilities, the Wizard of Odds craps house-edge table, and the University of Wisconsin pass line and odds explanation for a probability-based treatment of line bets.
How It Works
The 36-Combination Grid
| Total | Combinations | Probability | Table meaning |
|---|---|---|---|
| 2 | 1 | 2.78% | Rare, craps on come-out |
| 3 | 2 | 5.56% | Craps on come-out |
| 4 | 3 | 8.33% | Point number |
| 5 | 4 | 11.11% | Point number |
| 6 | 5 | 13.89% | Point number |
| 7 | 6 | 16.67% | Natural on come-out, killer after point |
| 8 | 5 | 13.89% | Point number |
| 9 | 4 | 11.11% | Point number |
| 10 | 3 | 8.33% | Point number |
| 11 | 2 | 5.56% | Natural on come-out |
| 12 | 1 | 2.78% | Craps on come-out, often Don’t Pass push |
True Odds After a Point
Once a point is established, only two results matter for the line bet: the point or the 7. Other totals are temporary noise.
| Point | Ways to roll point | Ways to roll 7 | Fair odds against point | Right-side odds payout |
|---|---|---|---|---|
| 4 or 10 | 3 | 6 | 2:1 | 2:1 |
| 5 or 9 | 4 | 6 | 3:2 | 3:2 |
| 6 or 8 | 5 | 6 | 6:5 | 6:5 |
Probability of Making the Point
| Point | Chance point hits before 7 | Chance 7 hits first |
|---|---|---|
| 4 or 10 | 3 / 9 = 33.33% | 6 / 9 = 66.67% |
| 5 or 9 | 4 / 10 = 40.00% | 6 / 10 = 60.00% |
| 6 or 8 | 5 / 11 = 45.45% | 6 / 11 = 54.55% |
Notice that even the “good” points 6 and 8 are still underdogs against the 7 after the point is on.
Craps Table Example
You have $10 on the Pass Line. The come-out roll is 4. The puck moves ON to 4.
You take $20 odds behind the line. That odds bet pays 2:1 because there are 6 ways to roll 7 and only 3 ways to roll 4. If the shooter hits 4 before 7, your $20 odds earns $40 profit.
The table may cheer because “the point hit,” but the math was never even. The 4 was a one-in-three winner in the point race. The fair 2:1 payout is what makes the odds bet fair.
Now compare that with a Place 4 paying 9:5. A $25 Place 4 pays $45 profit. True fair odds would be 2:1, or $50 profit. That missing $5 is the house edge.
From the Casino Side:
Casinos are not afraid of fair dice probabilities because payouts control the business. A fair dice roll can still produce a profitable game when most bets pay less than true odds.
The crew does not calculate odds from scratch every roll. The layout, procedures, and payout standards already encode the math. Dealers know the standard payoffs. The boxman watches larger payouts and unusual bets. Surveillance cares that dice are thrown legally, hit the back wall, and are not manipulated or switched.
The casino offers odds bets because they are attached to line or come bets that already carry edge. The fair bet is not free-floating. It is tied to a priced bet.
Common Mistakes
- Thinking 6 and 8 are favorites against 7 after a point is on.
- Confusing a 0% odds bet with a safe bet.
- Comparing payouts without counting combinations.
- Assuming a number is “due” after being absent.
- Treating hot shooters as proof that probability has changed.
- Forgetting that odds bets increase variance.
- Using place-bet payouts as if they were true odds.
Hard Truth
The 7 is not lucky or unlucky. It is just the most common total, and craps is designed around players forgetting that when the table gets loud.
FAQ
What are the odds of rolling a 7?
Six combinations out of 36, or 16.67%.
What are the odds of rolling a 6 or 8?
Each has 5 combinations out of 36, or 13.89%.
Why do odds on 4 and 10 pay 2:1?
Because after 4 or 10 is the point, there are 6 ways to roll 7 and 3 ways to roll the point. The fair ratio is 6:3, reduced to 2:1.
Are odds bets really fair?
Yes. When paid at true odds, the expected value is zero before practical issues like rounding or table limits.
Does a hot shooter change the odds?
No. Each legal roll of fair dice remains independent.
Why does the Pass Line still have a house edge?
Because the come-out and point phases combined slightly favor the casino under the even-money Pass Line payout.
Are place bets the same as odds bets?
No. Place bets are independent number bets with casino payouts. Odds bets are attached to line or come bets and pay true odds.
Deeper Insight
Craps probability has two layers.
The first layer is one-roll probability. This answers: what is the chance of rolling a 7 on the next roll? That answer is 6/36.
The second layer is conditional point probability. This answers: once the point is 5, what is the chance that 5 appears before 7? In that race, other totals are ignored because they do not resolve the bet. The 5 has 4 combinations and the 7 has 6. So the point-hit probability is 4 / (4 + 6), or 40%.
This is why casual explanations can mislead. Saying “5 rolls 11.11% of the time” is true for one roll. Saying “a point of 5 has a 40% chance to be made before 7” is true in the point race. Both are correct, but they answer different questions.
Formula / Calculation
P(total) = combinations for that total / 36
P(point before 7) = point combinations / (point combinations + seven combinations)
True Odds Payout = seven combinations / point combinationsExamples:
P(7) = 6 / 36 = 16.67%
P(point 5 before 7) = 4 / (4 + 6) = 4 / 10 = 40.00%
True odds against point 5 = 6 / 4 = 3 / 2Formula Explanation in Plain English
One-roll odds count all 36 dice outcomes. Point odds count only the outcomes that settle the point race. If the point is 5, rolls like 2, 3, 4, 6, 8, 9, 10, 11, and 12 do not decide the Pass Line. Only 5 and 7 matter, so the true payout compares those two groups.
Related Reading
Start with Craps Dice Combinations if you want the raw grid. Then use Craps Payouts and Craps Odds Chart to compare fair ratios with table payoffs. For cost, read craps house edge and test your examples with the craps odds calculator or expected loss calculator. For bankroll swings, use the variance simulator before assuming a fair bet cannot hurt.