Baccarat odds and probabilities
Baccarat is small enough to solve exactly. Every figure below comes from enumerating every possible deal from a full shoe, weighted by its probability, with no simulation involved.
Short answer
In an eight-deck shoe the Banker hand wins 45.86% of deals, the Player hand wins 44.62%, and 9.52% are ties. Ignoring ties, Banker takes 50.68% of the hands that resolve. A natural appears on 34.30% of deals, the Player hand draws a third card on 50.34% and the Banker hand on 43.54%. The average deal uses 4.94 cards.
Outcome probabilities by shoe size
| Shoe | Banker wins | Player wins | Ties |
|---|---|---|---|
| 8 decks | 45.86% | 44.62% | 9.52% |
| 6 decks | 45.87% | 44.63% | 9.51% |
| 1 deck | 45.96% | 44.68% | 9.36% |
Deck count barely matters. Moving from eight decks to six changes the Banker win rate by about one hundredth of a percentage point. This is the opposite of blackjack, where deck count is a real rule variable.
How often each thing happens
| Event (8 decks) | Frequency |
|---|---|
| Natural 8 or 9 in either hand | 34.30% |
| Player hand takes a third card | 50.34% |
| Banker hand takes a third card | 43.54% |
| Banker wins with a total of 6 | 5.39% |
| Average cards used per deal | 4.94 |
The Banker win with 6 is worth knowing because that is the exact outcome a no-commission table pays at half. It happens often enough that halving it costs more than the 5% commission it replaces. See house edge.
Ties are common enough to be annoying, not enough to bet
One deal in ten is a tie. A Tie bet paying 8 to 1 needs to land more than 11.11% of the time just to break even, and it lands 9.52% of the time. Even the friendlier 9 to 1 version needs 10%. The gap is the house edge, and no shoe composition on a normal table closes it.
Pair frequencies
| Event (8 decks) | Frequency |
|---|---|
| A named hand pairs its first two cards | 7.47% |
| Either hand pairs | 14.38% |
| Both hands pair | 0.56% |
| Either hand makes a perfect pair, same rank and suit | 3.35% |
What those frequencies are worth at the posted payouts is on the side bets page.
Common questions
Are these odds simulated?
No. They are exact. The engine enumerates every ordered deal from a full shoe under the Punto Banco drawing rules and weights each by its probability, so the numbers are computed rather than sampled. The Banker, Player and Tie probabilities sum to 1 to twelve decimal places.
Why is the Banker win rate higher?
The Banker hand acts after the Player hand and its draw table is keyed to the Player third card. That extra information is worth about 1.24 percentage points of win rate, which the 5% commission is designed to claw back.
Do the odds change during a shoe?
Slightly, as cards are removed, but far too little to act on. The swing available from a depleted baccarat shoe is a small fraction of the house edge, which is why counting works in blackjack and not here.