Baccarat odds
Choose the number of decks to see how often banker, player and tie win and what each bet costs.
Banker wins45.86%
Player wins44.62%
Tie9.52%
| Bet | Payout | House edge | Excluding ties |
|---|---|---|---|
| Banker | 19:20 | 1.06% | 1.17% |
| Banker, no commission | 1:1 (6: 1:2) | 1.46% | 1.61% |
| Player | 1:1 | 1.24% | 1.36% |
| Tie 8:1 | 8:1 | 14.36% | – |
| Tie 9:1 | 9:1 | 4.84% | – |
| Player pair | 11:1 | 10.36% | – |
| Banker pair | 11:1 | 10.36% | – |
Calculated exactly. Gambling always involves risk; play in moderation.
How it works
The probabilities are calculated exactly by going through every possible deal from the shoe under the standard drawing rules of punto banco. With eight decks banker wins 45.86% of hands, player 44.62% and tie 9.52%.
Banker wins more often because of the drawing rules, which is why a 5% commission is charged on banker wins. After commission banker is still the best bet, with a house edge of 1.06% against 1.24% for player.
The tie pays 8 to 1 but gives the house 14.36% with eight decks. Pair bets pay 11 to 1 and give the house 10.36%: less than the tie, but far more than banker or player. Some tables pay 9 to 1 on the tie, which lowers the edge to about 4.84%.
In commission-free baccarat, banker pays even money except when it wins with six, which pays half. The house edge is then about 1.46%.
Gambling always involves risk. Play in moderation.
How the probabilities are worked out
The tool works through the first four cards, player, banker, player, banker, by value. Tens and court cards count as 0 and there are 16 of them per deck, against 4 of every other value. Each sequence is weighted by how many cards of that value remain in the shoe. Third cards then follow the rules: if either hand has 8 or 9, no more cards are dealt, the player draws on 0 to 5, and the banker draws on 0 to 5 when the player stands but otherwise follows a table that depends on the player’s third card.
Every hand is counted as six cards, even when fewer are used, so that all hands share the same denominator. With eight decks there are 416 × 415 × 414 × 413 × 412 × 411, or 4,998,398,275,503,360 ordered sequences.
Example: the banker bet step by step
With eight decks, banker wins 45.8597% of hands and player 44.6247%. A banker win pays 0.95 times the stake, and a tie returns the stake. The expected value is 0.95 × 0.458597 − 0.446247 ≈ −0.010579, a loss of 1.06% of the stake. Counted over decided hands only, dividing by 1 − 0.0952, it is 1.17%.
The tool assumes a 5% commission. New Jersey’s casino rules also allow 4%, which cuts the house edge on banker to 0.60%.
Number of decks and side bets
Fewer decks help banker slightly: with one deck the house edge is 1.01% against 1.06% with eight. The pair bets change most. A pair means the first two cards of a hand share a rank, and the chance is (4 × decks − 1)/(52 × decks − 1). With eight decks it is 31/415, or 7.47%, and with one deck 3/51. Paying 11 to 1, that gives a house edge of 10.36% with eight decks, 11.25% with six and 29.41% with one.
New Jersey’s rules also allow commission-free baccarat, in which a banker win with six pays 1 to 2. With eight decks, banker wins with six in 5.39% of hands, and the expected value becomes 0.458597 − 0.5 × 0.053864 − 0.446247 ≈ −0.014581.