Craps Odds

Craps odds begin with a fixed object: two fair six-sided dice have 36 ordered combinations. From that grid you can answer three different questions that players often mix together: How likely is a total on the next roll? What is the chance a point appears before 7? What payoff would be fair for that race? Keeping those questions separate makes the rest of craps math much easier.

Build the two-dice map before talking about strategy

The number of combinations rises toward 7 and then falls symmetrically.

Seven is common because it can be formed six ways: 1-6, 2-5, 3-4, 4-3, 5-2 and 6-1. Four appears only three ways: 1-3, 2-2 and 3-1.

Those counts—not table energy, shooter rhythm or recent history—are the foundation for the standard probability model.

For an independent mathematical reference, see the Wizard of Odds craps basics. For the raw combinatorial view, continue to Craps Dice Combinations.

Next-roll probability and point-race probability answer different questions

Saying “5 has an 11.11% chance on the next roll” is correct because 4 of 36 combinations total 5.

After 5 becomes the Pass Line point, however, rolls of 2, 3, 4, 6, 8, 9, 10, 11 and 12 do not settle the contract. For the eventual point decision, only 5 and 7 matter. There are four ways to make 5 and six ways to make 7.

So:

P(5 before 7) = 4 / (4 + 6) = 40%
P(7 before 5) = 6 / (4 + 6) = 60%

Both the 11.11% next-roll figure and the 40% point-race figure are true. They use different denominators.

True odds are the price that exactly matches the point race

The fair right-side payoff is determined by the ratio of losing combinations to winning combinations.

If point 4 wins only one-third of decisive outcomes, a $10 fair wager must earn $20 when it succeeds. The two losing $10 outcomes are then balanced by one $20 win in expectation.

This is why the added odds wager behind Pass or Come is described as a zero-edge bet when the casino pays true odds exactly.

Laying odds reverses both the probability and the stake relationship

Don’t Pass and Don’t Come players can lay odds after a point exists. They are backing the more likely 7 against the less likely point, so they risk more than they can win.

The fair lay relationships are the reverse of the right-side payoffs:

A larger amount at risk does not mean the wager has a house edge. It reflects the fact that 7 is more likely to arrive first.

Place odds are shorter than the fair ratios

Place bets let a player back a number directly without first establishing a Pass/Come contract, but the casino pays less than true odds.

On 6 or 8, fair odds against the number are 6:5. The common Place payoff is 7:6. On 5 or 9, fair is 3:2 while the common Place payoff is 7:5. On 4 or 10, fair is 2:1 while the common Place payoff is 9:5.

That gap creates the house edge:

See Place Bet House Edge for the complete derivation.

The Pass Line edge does not come from the odds portion

A common mistake is to say, “Pass with odds has a 0% house edge.” That overstates the case.

The added odds portion has 0% edge. The flat Pass wager still includes the come-out rules and even-money settlement that create an overall house advantage of about 1.41% on the flat contract.

Adding odds reduces the blended percentage price of the combined dollars because more of the money is now on a fair component. It also increases dollar variance because more money is exposed when the point resolves.

This distinction is worked through in Odds Bet House Edge and Combined House Edge with Odds.

Probability does not remember a player’s recent results

If the dice are fair and rolls are valid, a run of sixes does not make another 6 more or less likely on the next throw. The 5/36 next-roll probability remains the standard model.

That does not mean every statement in craps should use the word “independent” carelessly. The important practical point is that ordinary dice rolls do not remove faces from the dice or alter the combination grid the way card removal changes a finite shoe. The physical system resets to the same six faces on each die.

A streak can be emotionally vivid and still provide no predictive information about the next fair roll.

Odds, payout and house edge are three different columns

A useful craps analysis should keep these concepts separate:

• Probability — how often the event occurs under the defined model.
• True odds — the fair risk/reward ratio implied by that probability.
• Casino payout — what the table actually pays.
• House edge — the expected cost created when the casino payout is shorter than fair value or when game rules favor one side.

A wager can have a low hit rate and a fair payout. It can have a high hit rate and a bad payout. “I win this often” is not enough to tell you whether the bet is expensive.

One worked comparison shows the whole chain

Take number 4 after it is relevant against 7.

There are 3 combinations for 4 and 6 for 7. So the eventual race is 3 wins to 6 losses.

A fair $10 right-side wager therefore pays $20 profit when 4 wins:

Expected result = (3/9 × $20) - (6/9 × $10) = $0

A standard $10-equivalent Place 4 does not pay the full 2:1 fair ratio; the common 9:5 schedule is shorter, which creates the casino advantage. A Buy 4 may restore true-odds-style pricing but add a commission instead. Same dice. Different contract.

Use the odds page as the probability layer of the site

This page should answer the mathematical questions underneath the game, not duplicate every payout table or every strategy recommendation.

Use Craps Payouts when you want settlement amounts. Use Craps Odds Chart when you need a compact reference. Use Craps House Edge when the question is price, and Craps RTP when you want to translate that price into return-to-player language.

The craps odds calculator is useful for checking a specific point, stake and payoff without turning the whole game into memorization.