Baccarat Probability Calculator

Baccarat drawing rules and exact shoe probability

Cards A through 9 use values 1 through 9, while tens and faces count as zero; hand totals use the last decimal digit. If either initial hand is a natural 8 or 9, both stand. Otherwise Player draws on 0–5 and stands on 6–7. Banker decisions depend on its total and, when Player draws, the value of Player’s third card.

The calculator enumerates every legal value sequence with weights from the remaining counts, without replacement. With an untouched eight-deck standard shoe, it gives approximately 45.8597% Banker, 44.6247% Player and 9.5156% Tie.

For a depleted shoe, supply all ten counts. A running count alone is insufficient to specify that composition. The Pennsylvania baccarat rule chapter identifies the standard drawing and wager framework used here.

Banker commission, Tie payout and expected value

For the standard push-on-tie model, Banker expected net per unit is P(Banker) × (1−commission) − P(Player). Player expected net is P(Player) − P(Banker). Tie expected net is P(Tie) × tie ratio − (1−P(Tie)). Exact probabilities alone do not settle a commission-free variant’s special payout rules.

The optional simulation samples separate rounds from the same entered starting shoe, resetting it each round. It illustrates sampling variation rather than a single continuously depleted shoe. The exact calculation is the reference; simulated frequencies vary.

Probability is not a baccarat predictor

Changing the remaining shoe counts can change probabilities. It does not identify the next cards. This tool evaluates a specified composition and does not recommend a strategy, infer hidden cards or model a proprietary side bet. Use baccarat payouts for a selected winning settlement.