Craps Odds & Payout Calculator
Calculate the true odds, house edge, and potential payout for any standard craps bet. Select your bet type, enter your wager, and see the full breakdown instantly.
Formulas Used
Probability of Winning:
P(win) = Ways to Win ÷ (Ways to Win + Ways to Lose)
Gross Payout:
Gross Payout = Wager × (Payout Numerator ÷ Payout Denominator)
Commission (Buy/Lay bets):
Buy: Commission = Wager × Commission Rate (paid up front)
Lay: Commission = Gross Win × Commission Rate (paid on win)
Net Win:
Buy: Net Win = Gross Payout (commission already deducted from total return)
Lay: Net Win = Gross Payout − Commission
Expected Value (EV):
EV = (P(win) × Net Win) − (P(lose) × Wager at Risk)
House Edge (Buy, 5% commission):
HE = Commission Rate ÷ (1 + Commission Rate) × 100
≈ 0.05 ÷ 1.05 × 100 ≈ 4.76%
House Edge (Lay, 5% commission):
HE = Commission Rate × P(win) × 100
True Odds:
True Odds = Ways to Lose : Ways to Win
(e.g., Place 6: 6 ways to lose vs 5 ways to win → true odds 6:5)
Assumptions & References
- A standard pair of fair six-sided dice produces 36 equally probable outcomes.
- Pass Line / Don't Pass house edges are computed over the full multi-roll sequence using the standard 244/251 and 949/976 win/lose ratios (Scarne, 1974).
- Field Bet assumes 2 pays 2:1 and 12 pays 3:1 (common Las Vegas strip rule); house edge = 5.56%.
- Buy/Lay commission defaults to 5% (industry standard). Some casinos charge commission only on wins — adjust the commission field accordingly.
- Free Odds bets pay true odds and carry zero house edge; they must be backed by a Pass/Come or Don't Pass/Don't Come bet.
- Hard Way bets: ways to win/lose are computed over the conditional sample space (point must be made the hard way before an easy way or 7).
- Big 6 / Big 8 pay even money (1:1) vs. Place 6/8 which pay 7:6 — always prefer Place 6/8 over Big 6/8.
- Expected Value is per-bet resolved (not per-roll) for multi-roll bets.
- References: Scarne's New Complete Guide to Gambling (1974); The Wizard of Odds (wizardofodds.com); Stanford Wong, Casino Craps for the Winner.