Punto Banco from an eight-deck shoe. Bet on Player, Banker or a Tie, follow the scoreboards, and see the exact odds of the next hand from the cards still in the shoe.
Casinos post these boards so players can chase streaks and patterns. Every hand is still a fresh draw from the shoe — the patterns predict nothing.
| Bet | Win | Edge |
|---|---|---|
| Player | 44.625% | 1.235% |
| Banker | 45.860% | 1.058% |
| Tie | 9.516% | 14.360% |
| Player Pair / Banker Pair | 7.470% | 10.361% |
Computed from the 416 cards you haven’t seen (burned cards count as unseen). The odds drift as the shoe is dealt, but the main bets almost never turn in your favor.
Baccarat has no decisions, so its odds can be computed exactly: enumerate every way the next six cards can come out of the shoe and play each one by the drawing rules. Nothing on this tab is simulated.
| Outcome | Probability | Ways | Ignoring ties |
|---|---|---|---|
| Banker wins | 45.8597% | 2,292,252,566,437,888 | 50.682% |
| Player wins | 44.6247% | 2,230,518,282,592,256 | 49.318% |
| Tie | 9.5156% | 475,627,426,473,216 | — |
| 100% | 4,998,398,275,503,360 |
Out of all 4,998,398,275,503,360 orderings of the next six cards (a hand that uses fewer cards is counted once for every way the unused cards could fall), so each probability is an exact fraction.
| Bet | House edge | Pays | Win | Push |
|---|---|---|---|---|
| Banker (EZ, 3-card 7 pushes) | 1.018% | 1:1 | 43.606% | 11.769% |
| Banker (5% commission) | 1.058% | 0.95:1 | 45.860% | 9.516% |
| Player | 1.235% | 1:1 | 44.625% | 9.516% |
| Tie at 9:1 | 4.844% | 9:1 | 9.516% | — |
| Dragon 7 (EZ) | 7.611% | 40:1 | 2.253% | — |
| Panda 8 (EZ) | 10.188% | 25:1 | 3.454% | — |
| Player / Banker Pair | 10.361% | 11:1 | 7.470% | — |
| Tie at 8:1 | 14.360% | 8:1 | 9.516% | — |
Edge per hand dealt, counting a push as a bet returned. The commission turns the Banker’s head start into a 1.06% house edge; the EZ table waives it but pushes the 2.25% of hands the Banker wins with a three-card 7 — slightly cheaper at 1.02%. Some casinos pay 9:1 on the Tie, which cuts its edge from 14.4% to 4.8%.
A natural (8 or 9 on two cards) on either side ends the hand. Otherwise the Player draws on 0–5 and stands on 6–7, then the Banker follows this chart:
| Banker total | Player stood | Player’s third card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
| 0 | D | D | D | D | D | D | D | D | D | D | D |
| 1 | D | D | D | D | D | D | D | D | D | D | D |
| 2 | D | D | D | D | D | D | D | D | D | D | D |
| 3 | D | D | D | D | D | D | D | D | D | S | D |
| 4 | D | S | S | D | D | D | D | D | D | S | S |
| 5 | D | S | S | S | S | D | D | D | D | S | S |
| 6 | S | S | S | S | S | S | S | D | D | S | S |
| 7 | S | S | S | S | S | S | S | S | S | S | S |
The Player’s rule ignores the other hand, but the Banker sees the Player’s third card before deciding — standing on 3 against an 8, drawing on 6 against a 6 or 7. That information is worth about 1.2 points of win probability, which the 5% commission takes back.
The first two cards of a hand share a rank with probability (4·8 − 1)/(52·8 − 1) = 31/415 ≈ 7.47%: the second card must be one of the other 31 cards of the first card’s rank. At 11:1 that is a 10.36% house edge.
Barely for the main bets. Fewer decks make card removal stronger: the Banker gets a little better, the Tie a little worse — and pairs get much rarer.
| Decks | Banker (5% commission) | Player | Tie at 8:1 | Player / Banker Pair |
|---|---|---|---|---|
| 1 | 1.012% | 1.286% | 15.746% | 29.412% |
| 2 | 1.039% | 1.256% | 15.023% | 18.447% |
| 4 | 1.052% | 1.242% | 14.592% | 13.043% |
| 6 | 1.056% | 1.237% | 14.438% | 11.254% |
| 8 | 1.058% | 1.235% | 14.360% | 10.361% |