The exact win frequencies for Banker, Player and Tie, the fixed drawing tableau that produces them, and how the 5% commission is set.
I. A game with no decisions
Baccarat — in its dominant Punto Banco form — is the purest expected-value object on the casino floor, because nothing about the deal is optional. The bettor picks one of three bets (Player, Banker, Tie) before any card is turned. After that, whether a third card is drawn to either hand is settled entirely by a fixed rulebook called the tableau. No one at the table chooses. That is exactly what makes the probabilities computable to the last decimal: there is no human strategy to model, only a deck and a set of rules.
Card values run modulo ten — tens and faces count zero, the ace counts one, and a hand's value is the last digit of the pip sum (a 7 and an 8 total 15, which is a 5). The higher of the two final totals wins.
II. The drawing tableau
Two rules govern everything. First, a natural: if either hand totals 8 or 9 on its first two cards, both hands stand and the coup is decided immediately. Otherwise the Player hand draws first, then the Banker hand reacts.
| Player two-card total | Action |
|---|---|
| 0 – 5 | Draws a third card |
| 6 – 7 | Stands |
| Banker total | Banker draws when Player's third card is… |
|---|---|
| 0, 1, 2 | Always draws |
| 3 | Any card except an 8 |
| 4 | 2, 3, 4, 5, 6 or 7 |
| 5 | 4, 5, 6 or 7 |
| 6 | 6 or 7 |
| 7 | Always stands |
If the Player stood (had 6 or 7), the Banker simply draws on 0–5 and stands on 6–7. That asymmetric tableau — the Banker's action depends on what the Player drew, but not vice-versa — is the entire source of the Banker's edge.
III. The three frequencies
Enumerate every possible eight-deck deal through that tableau and the win frequencies are fixed quantities:
| Outcome | Share of all hands | Share of decided hands (ties removed) |
|---|---|---|
| Banker wins | ≈ 45.86% | ≈ 50.68% |
| Player wins | ≈ 44.62% | ≈ 49.32% |
| Tie | ≈ 9.52% | — |
Premise. Standard eight-deck shoe, standard Punto Banco tableau. Six-deck and single-deck shoes move these figures by hundredths of a percent — not enough to reorder which bet is best.
IV. Why the Banker wins more often
The Banker acts second and with information: it sees the Player's third card before deciding whether to draw its own. A hand that can adjust its final decision to the opponent's revealed card wins slightly more than a hand that cannot. Across a full shoe that informational asymmetry is worth just over one percentage point of decided hands — Banker 50.68% versus Player 49.32%. It is small, permanent, and entirely a product of the tableau's ordering, not of any luck that can be pressed.
V. The 5% commission, derived
Here is the arithmetic the whole game turns on. Suppose the Banker bet paid even money with no commission. Its expected value per unit would be:
EV = (+1 × 0.4586) − (1 × 0.4462) = +0.0124
Ties push, so they drop out. A commission-free Banker bet would favour the player by about 1.24% — the house cannot offer it.To reverse that, the house charges 5% on Banker wins. The cost of that charge per unit bet is 5% times the frequency of Banker wins:
0.05 × 0.4586 ≈ 0.0229 per unit bet
EV = +0.0124 − 0.0229 ≈ −0.0105 → house edge ≈ 1.06%
The commission is not arbitrary. It is calibrated to overcome the Banker's ~1.24% natural advantage and leave the house a thin 1.06%.VI. House edge on all three bets
| Bet | Payout | House edge |
|---|---|---|
| Banker | 1:1 less 5% commission | ≈ 1.06% |
| Player | 1:1 | ≈ 1.24% |
| Tie | 8:1 | ≈ 14.4% |
| Tie | 9:1 (where offered) | ≈ 4.8% |
The Player bet skips the commission but wins less often, landing at 1.24%. The Tie, despite its glamour, is the trap: even the generous 9:1 payout leaves an edge several times the Banker's, and the common 8:1 payout makes it one of the most expensive standing bets in the building.
- Baccarat has no decisions — the fixed tableau makes all draws, so the probabilities are exact.
- For an eight-deck shoe: Banker ≈ 45.86%, Player ≈ 44.62%, Tie ≈ 9.52% of all hands.
- Banker wins more because it draws with knowledge of the Player's third card.
- The 5% commission is calibrated to convert Banker's ~1.24% player advantage into a ~1.06% house edge.
- The Tie bet is a mathematical trap — roughly 14.4% edge at 8:1.
For where these edges sit against every other game, see what the house edge actually is and the downloadable baccarat probability reference dossier.