Craps Odds Calculator

Leave Point on 6 and Odds Bet on $100. Calculate. Point Made Probability is 45.45% and Odds Bet Payout is $120.00. Those are the true-odds numbers for a six (or eight): five ways to roll the point on two dice, six ways to roll a seven, eleven relevant outcomes, so 5/11 ≈ 0.4545. A win pays 6:5, which on $100 is $120 profit, $220 returned including stake. The house edge on this bet is zero. The casino is booking a fair game on the odds portion; it earns its money on the flat pass or come bet that you were required to make first.

Change Point to 4. Probability becomes 33.33% (exactly 1/3: three ways to make a four, six ways to seven-out) and payout becomes $200.00 at 2:1. Point 10 is identical. Point 5 or 9 yields 40.00% (four ways versus six, which is 4/10) and $150.00 at 3:2. Point 8 mirrors 6. The select list is only the six point numbers; you cannot set 2, 3, 7, 11, or 12 because those resolve on the come-out and never become a point.

The Odds Bet field is the amount placed behind the flat bet, not the flat bet itself. If the table is 3×-4×-5× odds and your pass-line chip is $10, the maximum odds on a six or eight is $50, on a five or nine $40, on a four or ten $30. Type the actual odds amount you will put down, not the table maximum. Payout scales linearly: $50 on a six pays $60, not $120.

This calculator does not include the pass-line 1.41% edge, the don't-pass 1.36% edge, or any proposition (hardways, horn, field). Combining a $10 pass bet with $100 odds on a six produces a blended edge of 1.41% × 10 / 110 ≈ 0.13% of the total action — which is why serious craps players max odds. Compute the odds half here, then add the flat-bet tax separately if you need a session EV.

If you are laying odds (don't-pass or don't-come), the probabilities invert and the payouts invert: you are now the favourite, laying 6:5 on a six, 3:2 on a five, 2:1 on a four. This tool prices the right-way (taking) odds bet. Do not type a lay amount into Odds Bet and expect the payout field to show the smaller win you would collect as the don't better.

A craps point is established on the come-out when the shooter rolls 4, 5, 6, 8, 9, or 10. From that moment the pass-line waits for that number to repeat before a seven. The odds bet is an optional extra wager, placed behind the line, that pays the true mathematical odds of that race and carries no house edge. It is one of the few publicly offered even games in a casino, sitting next to the rarely dealt "full odds" baccarat banker and a handful of 100% video-poker paytables. Casinos allow it because you cannot make it without a flat bet that does have an edge, and because many players never take odds at all.

John Scarne's mid-century tables and the later work of the Stanford Wong / Peter Griffin generation treated the odds bet as the obvious correction to the 1.41% pass-line. A 3×-4×-5× table (three times odds on 4 and 10, four times on 5 and 9, five times on 6 and 8) is now the Las Vegas Strip standard; downtown and some Indian rooms still post double or even single odds, which leaves more of the flat-bet tax in the blend. The calculator is agnostic about the multiple. It prices whatever dollar amount you enter at the true odds of the selected point.

History of the payouts is just the ratio of losing ways to winning ways. A six loses to a seven, 6 ways to 5, so a fair win pays 6/5 of the stake. A four loses 6 ways to 3, so it pays 2/1. A five loses 6 to 4, paying 3/2. Those ratios have been on American felt since the game standardised in the early twentieth century. They are not a promotion and they do not change at 4 a.m. They also do not apply to the place bets, which pay 9:5 on six and eight (a 1.52% edge) and 7:6 on five and nine (4% edge). If you want a six without a pass-line, you are no longer in zero-edge territory.

Don't-pass odds (laying) are the mirror image and still zero edge, but you must post more money to win less, because you are now the favourite. Some players prefer that shape; most right-way players never switch. Either way, the combinatorial engine is two fair dice, thirty-six equally likely ordered pairs, with the come-out already over.

Limits: no buy-bet 5% commission, no lay-bet vig, no hardway overlay, no free-odds on a come bet that has not yet been placed. The output is the probability that the point is made given that the next resolving roll is either the point or a seven, and the profit on a taking-odds win. Everything else on the layout is a different bet.

Pass-line probability is an enumeration of 36 ordered outcomes of two fair dice, followed by a conditional resolution once a point is established. On the come-out, seven and eleven win immediately (six plus two ways, eight in 36) and two, three, and twelve lose (one plus two plus one, four in 36). The remaining 24 ways set a point among four, five, six, eight, nine, and ten. That point is then made if it appears before the next seven. Combining the immediate wins with the conditional makes yields 244 winning ways against a 495-state generating-function count, so the pass-line win probability is 244/495, approximately 49.29 percent. House edge is one minus twice that probability under even-money settlement, which is 7/495, approximately 1.41 percent. That 1.41 percent is the tax on the line bet. It is not the tax on the odds bet placed behind the line.

True odds behind a point are a different identity, and they are fair by construction of the 36-cell table. After a point n is established, only n and seven resolve the wager. Ways to roll seven: 6. Ways to roll four or ten: 3, so probability 3/9 equal to 1/3, and the fair multiple is 6:3 equal to 2:1. Ways to roll five or nine: 4, probability 4/10 equal to 40 percent, fair multiple 6:4 equal to 3:2. Ways to roll six or eight: 5, probability 5/11 approximately 45.45 percent, fair multiple 6:5. In dollars, an odds stake B pays 2B on four or ten, 1.5B on five or nine, and 1.2B on six or eight.

Worked default point six, odds stake 100. Probability of making the six is 5/11, displayed 45.45 percent. Payout at 6:5 is 120. Expected profit on the odds bet alone is (5/11) times 120 plus (6/11) times minus 100, which is 600/11 minus 600/11, identically zero. Repeat for a four: (1/3) times 200 minus (2/3) times 100 is also zero. The page reports the make probability and the win payout. Expected value of the odds bet is identically zero for every point when posted odds are true. If a floor paid 3:2 on a six, the identity would break; the arithmetic here still assumes posted true odds.

Come-out and line must be kept separate from odds. The 244/495 already includes come-out wins and losses and the point resolutions. Placing odds does not change the 1.41 percent tax on the original line unit; it dilutes the combined edge because a zero-edge wager is sitting next to a 1.41 percent wager. Place bets use still another payout table and are not this lecture. Don't Pass is the complement with twelve as a push on the come-out, a slightly different fraction.

Assumptions. Fair dice. Independent rolls. American come-out: 7 and 11 win, 2, 3, 12 lose, points 4, 5, 6, 8, 9, 10. No bar on twelve for the pass line. Default point six is the teaching even-chance-looking point that is still a 5-to-6 underdog to seven. The 36-cell table is the whole derivation. Superstition about dice setting is not.