Baccarat Probability Calculator: Odds Made Simple

This calculator works out the exact probability of a Player, Banker, or Tie result in a standard eight-deck baccarat game, plus the house edge for each bet. You enter the number of decks and the bet you are considering, and it returns the true odds based on the full set of baccarat drawing rules.

Formula

The probabilities are not simple combinations — they depend on the full baccarat drawing table, which determines when a third card is dealt. For a standard eight-deck shoe, the exact probabilities are:

• Player win: 44.6246%
• Banker win: 45.8597%
• Tie: 9.5156%

The house edge for each bet is calculated as:

House Edge = (Probability of winning × Payout) − (Probability of losing × 1)

For Player (pays 1:1): 0.446246 × 1 − 0.553754 × 1 = −0.0124 → 1.24% house edge.
For Banker (pays 0.95:1 after 5% commission): 0.458597 × 0.95 − 0.541403 × 1 = −0.0106 → 1.06% house edge.
For Tie (pays 8:1): 0.095156 × 8 − 0.904844 × 1 = −0.1436 → 14.36% house edge.

Worked Example

Using the default values (8 decks, Player bet):

1. Probability of Player win = 0.446246
2. Convert to percentage: 0.446246 × 100 = 44.6246%
3. House edge = 0.446246 × 1 − 0.553754 × 1 = −0.0124 → 1.24%

The calculator displays: Probability = 44.6246% and House edge = 1.24%.

How Baccarat Probabilities Are Derived

Baccarat uses a fixed set of drawing rules that depend on the player’s total and the banker’s total, plus the player’s third card if drawn. These rules are not symmetric — the banker acts after seeing the player’s third card, which is why the Banker bet wins slightly more often than the Player bet. The exact probabilities above are obtained by enumerating all possible card combinations from the shoe, respecting the drawing table and the fact that cards are dealt without replacement. For an eight-deck shoe, the probabilities converge to the values shown; with fewer decks, they shift slightly, but the differences are below 0.1%.

How to Use the Calculator

Select the bet you want to analyse (Player, Banker, or Tie) and adjust the number of decks if you are playing a single-deck or six-deck game. The calculator then shows:

• Probability — the chance that this bet wins, as a percentage.
• House edge — the casino’s theoretical advantage over you, in percentage terms. A lower house edge means a better bet for the player.

The house edge is the single most useful number for comparing bets — it tells you the average loss per 100 units wagered in the long run.

Common Mistakes and Misconceptions

One frequent error is confusing the payout with the probability. A Tie bet pays 8:1, but it wins only about 9.5% of the time, so the house edge is huge. Another mistake is assuming the Banker bet has no house edge because it wins more often than it loses — the 5% commission on winning Banker bets is what creates the edge. Also, remember that these probabilities assume a complete, well-shuffled shoe; they do not change based on previous results. Baccarat has no memory, so a run of Player wins does not make a Banker win more likely.

Comparing Baccarat Bets

Among the three main bets, the Banker bet has the lowest house edge (1.06%), followed by Player (1.24%), and Tie is far worse (14.36%). In most casinos, the Banker bet is the best choice if you want to minimise the house advantage. Some casinos offer a “Super 6� or “No Commission� variant where Banker wins on 6 pay even money, which changes the edge — but this calculator uses the standard commission rules.

Limitations of the Probability Model

The probabilities above are theoretical, based on a perfectly random shuffle and infinite precision. In practice, a real shoe has a finite number of cards, and card counting can slightly shift the odds as the shoe progresses — but the effect is tiny and not practical for most players. The model also assumes a standard eight-deck shoe; if you play with fewer decks, the probabilities change by less than a tenth of a percentage point, so the house edge figures remain essentially the same. This calculator does not account for side bets like “Player Pair� or “Banker Pair�, which have different and generally higher house edges.

Frequently Asked Questions

What is the best bet in baccarat?

The Banker bet has the lowest house edge (1.06%), so it is statistically the best bet in the standard game. The Player bet is close behind at 1.24%, while the Tie bet is very poor at 14.36%.

Why does Banker win more often than Player?

Because the banker acts after seeing the player’s third card, the drawing rules are asymmetrical. This gives the banker a slight edge in the probability of winning, which is why casinos charge a 5% commission on winning Banker bets to compensate.

Does the number of decks matter?

Yes, but only slightly. The probabilities shift by less than 0.1% when going from one deck to eight decks, so the house edge changes by a few hundredths of a percentage point. For practical purposes, the eight-deck figures are a good approximation for any standard game.

Can I use this calculator to beat the casino?

No. The calculator shows the mathematical odds, but the house edge is always positive, meaning the casino will win in the long run. No betting system can overcome a negative expectation game.

What is the house edge for a Tie bet?

The Tie bet has a house edge of 14.36% with the standard 8:1 payout. Even if the casino pays 9:1, the edge is still around 4.84%, which is much higher than the Player or Banker bets.

Related

• Calculate Relative Error: Formula and Examples
• Calculate Raw Score From Percentile: What You Need
• Probability for Independent Events: Formula and Examples

in decks | Number of decks | - | 8 | 1
sel bet | Bet | Player=1, Banker=2, Tie=3
out prob | Probability | % | (bet == 1 ? 0.446246 : bet == 2 ? 0.458597 : 0.095156) * 100 | 4
out edge | House edge | % | (bet == 1 ? 1.24 : bet == 2 ? 1.06 : 14.36) | 2