Baccarat (in its common casino form, punto banco) offers three main bets: banker, player and tie. The player makes no decisions: fixed drawing rules decide everything. That makes baccarat a pure probability problem, and one we can solve exactly. We enumerated every possible sequence of cards from an 8-deck shoe. Here are the results.
How a hand works
- Each side receives two cards. Tens and face cards count 0, aces 1, others their face value. Only the last digit of the total counts: 7 + 8 = 15 counts as 5.
- A total of 8 or 9 on either side is a "natural" and ends the hand.
- Otherwise, the player side draws a third card on 0 to 5 and stands on 6 or 7.
- The banker side follows a table of rules that depends on its own total and on the player's third card.
The exact probabilities
| Outcome | Probability |
|---|---|
| Banker wins | 45.86% |
| Player wins | 44.62% |
| Tie | 9.52% |
Our own exact calculation, enumerating every card sequence from a full 8-deck shoe with the standard punto banco drawing rules. The results match the figures commonly published for this game.
The banker wins more often because its drawing rules let it act after seeing whether the player drew a third card, and what that card was.
Why the banker pays a commission
If the banker bet paid even money, it would favour the player. So casinos usually take a 5% commission on banker wins. With the commission:
| Bet | Payout | House edge |
|---|---|---|
| Banker | 1 to 1, minus 5% commission | 1.06% |
| Player | 1 to 1 | 1.24% |
| Tie | 8 to 1 | 14.36% |
Worked example: How the banker edge is calculated. Ties are a push for banker bets. The expected result per unit is 0.4586 × 0.95 − 0.4462 × 1 = −0.0106, an edge of 1.06%. For the player bet it is 0.4462 − 0.4586 = −0.0124, an edge of 1.24%.
The tie bet
A tie happens about 9.5% of the time. A fair payout would be roughly 9.5 to 1; paying 8 to 1 gives the house an edge of 14.36%, more than ten times the banker bet. Some tables pay 9 to 1, which lowers the edge but still leaves it far above the main bets.
Key point: Patterns on baccarat scoreboards ("the banker is on a streak") are a classic illusion. Hands from a shuffled shoe are almost independent, and no visible pattern changes the edges above.
Variations to check
- No-commission tables often pay less on a banker win with a total of 6, which raises the house edge.
- Side bets usually carry much higher edges than the main bets.
- Number of decks changes the figures slightly.
Watch out: Even the best bet in baccarat loses about 1 unit in every 94 staked over the long run. Expected loss is always the total amount bet times the house edge.
Compare baccarat with other games in House Edge of Every Casino Game, Ranked.
- In 8-deck punto banco, banker wins 45.86%, player 44.62% and ties 9.52% of hands.
- With a 5% commission, the banker bet has the lowest edge (1.06%), then player (1.24%).
- The 8-to-1 tie bet has a 14.36% house edge.
Sources
- Baccarat — Wikipedia: punto banco rules and edges
- Gambler's fallacy — Wikipedia
18+ only. No betting system changes the house edge. See our Responsible Gambling page.
RTP Data explains the mathematics of casino games, with every figure sourced or worked out in the text.