KEY TAKEAWAYS
In an eight-deck baccarat game where winning Banker bets pay 0.95 to 1 (a 5% commission) and Tie bets pay 8 to 1, the house edge is about 1.06% on Banker, about 1.24% on Player and about 14.36% on Tie. Each figure is the expected loss per $1 of the initial wager, calculated from the probability of each of the three possible outcomes of a hand.
The reason these numbers differ is simple. Banker and Player win with nearly the same probability, but Banker wins slightly more often, and the 5% commission only partly offsets that advantage. The Tie bet wins rarely, and its 8-to-1 payout falls well short of the true odds of about 9.51 to 1 against it, so its edge is more than ten times larger.
This guide shows the three-outcome expected value calculation step by step, explains why ties matter to the definition of the edge, compares a Tie pay of 8 to 1 with 9 to 1, and converts the percentages into expected dollar losses. The outcome probabilities come from a published eight-deck analysis, and every result is a long-run average, not a prediction for any single hand.
Where the Baccarat House Edge Comes From
Every baccarat hand ends in one of three outcomes: Banker wins, Player wins, or the hand is tied. Three outcomes change the arithmetic compared with a two-outcome bet such as red or black. A Banker or Player wager is returned unchanged on a tie (a push), so ties neither win nor lose money on those bets, but they still count as hands that were played.
The probabilities of the three outcomes follow from the fixed drawing rules and the composition of the shoe. Working them out by hand is long, so published analyses are used. For eight decks they are: Banker wins 45.8597% of hands, Player wins 44.6247% and a Tie occurs 9.5156%. These three probabilities sum to 100%, which is the first check any set of outcomes should pass.
The house edge is then built in two different ways. On the Player bet, the edge is purely the gap in win rates: Player wins slightly less often than Banker, and the payout is even money. On the Banker bet, the higher win rate is partly taken back by the 5% commission, which is why winning Banker bets pay 0.95 rather than 1.
The same principle explained in true odds vs payout odds applies to the Tie bet: the payout is lower than the true odds against the outcome, and the gap is the casino’s expected profit.
The Baccarat Edge Formulas
Let B, P and T stand for the probabilities of a Banker win, a Player win and a Tie. Expected value per $1 wagered is the sum of each outcome’s probability times its net result.
where:
B = probability that Banker wins (0.458597 in an eight-deck game).
P = probability that Player wins (0.446247).
T = probability of a Tie (0.095156).
0.95 = the net payout per $1 on a winning Banker bet after the 5% commission.
t = the Tie payout, 8 in the standard game.
Ties do not appear in the Banker and Player formulas because a push contributes zero to the average result. The Tie formula has no push term, since every non-tie result loses the bet. Dividing by the initial wager is what this article uses throughout, and RTP (return to player) is simply 100% minus the house edge.
Two assumptions apply: an eight-deck shoe played under the standard drawing rules, and the stated payouts. Other deck counts, commission levels or Tie payouts change the figures slightly or substantially.
Worked Example: All Three Bets
Use B = 0.458597, P = 0.446247 and T = 0.095156.
Banker. Step 1: 0.95 × 0.458597 = 0.435667. Step 2: subtract the Player win probability: 0.435667 − 0.446247 = −0.010580. Step 3: the house edge is 1.058%, about 1.06%, so the RTP is about 98.94%.
Player. Step 1: 0.446247 − 0.458597 = −0.012350. Step 2: the house edge is 1.235%, about 1.24%, so the RTP is about 98.77%.
Tie at 8 to 1. Step 1: 8 × 0.095156 = 0.761248. Step 2: 1 − 0.095156 = 0.904844. Step 3: 0.761248 − 0.904844 = −0.143596. The house edge is about 14.36%, so the RTP is about 85.64%.
The true odds against a Tie are 0.904844 ÷ 0.095156 ≈ 9.51 to 1, yet the bet pays 8 to 1, and that shortfall of roughly 1.51 to 1 multiplied by the 9.52% chance of a Tie reproduces the same 14.36% edge. In plain terms, wagering $100 on the Banker bet is expected to lose about $1.06 on average, while wagering $100 on the Tie is expected to lose about $14.36.
Comparing Bets, Tie Payouts and Expected Loss
| Bet | Pays | Win probability | EV per $1 | House edge |
|---|---|---|---|---|
| Banker | 0.95 to 1 | 45.8597% | -0.01058 | 1.06% |
| Player | 1 to 1 | 44.6247% | -0.01235 | 1.24% |
| Tie | 8 to 1 | 9.5156% | -0.14360 | 14.36% |
| Tie (variant pay) | 9 to 1 | 9.5156% | -0.04844 | 4.84% |
The last row shows how sensitive the edge is to the payout: raising the Tie pay from 8 to 9 to 1 changes the EV from 8 × 0.095156 − 0.904844 to 9 × 0.095156 − 0.904844, so the edge falls from 14.36% to about 4.84%. Always confirm the payout posted on the specific table.
The edge also depends on how it is defined. If ties are ignored and only resolved hands are counted, Banker wins 0.458597 ÷ 0.904844 ≈ 50.68% of resolved hands and the edges become about 1.17% for Banker and 1.36% for Player. Counting per initial wager is the better guide to total cost, because ties still use up time and bankroll.
Converting to dollars shows the cost. Suppose a hypothetical player wagers $25 per hand at 70 hands per hour for three hours, so 210 hands and $5,250 wagered. The expected loss is about $55.55 on Banker (5,250 × 0.01058), about $64.84 on Player and about $753.88 on Tie at 8 to 1. These averages sit alongside large swings, as discussed in expected loss per hour.
Common Mistakes About the Baccarat Edge
The first is confusing win frequency with edge. Banker wins 45.86% of hands, which is less than half, and still carries the lowest house edge. The edge depends on the payout as well as the probability.
The second is forgetting the commission. A $100 winning Banker bet returns $95 profit, not $100, and treating Banker as even money would show a positive EV that does not exist.
The third is assuming past results change the next hand. Each hand is a fresh draw from the shoe’s remaining composition, and shoe-tracking patterns do not alter the stated edges for a fresh eight-deck shoe. The same reasoning applies to staking plans, which, as explained in the Martingale system guide, change the shape of results but not their average.
The fourth is mixing rule sets. A figure for eight decks, 5% commission and 8-to-1 Ties cannot be reused for a table with different decks, a different commission or a different Tie pay.
Quick Reference and Check Your Answer
| Step | Action | Banker example |
|---|---|---|
| 1 | List B, P, T and confirm they sum to 1 | 0.458597 + 0.446247 + 0.095156 = 1.000000 |
| 2 | Apply payouts to each outcome | 0.95 × 0.458597 = 0.435667 |
| 3 | Subtract losing probability | 0.435667 − 0.446247 = −0.010580 |
| 4 | Flip the sign for the edge | 1.06% |
Check the result two ways: confirm the three probabilities sum to 100%, and confirm that RTP plus house edge equals 100% (98.94% + 1.06%). For the Tie bet, test that the payout is below the true odds against it; if it were above, the EV would be positive, which would signal an arithmetic error.
Related Concepts and Next Steps
For another worked derivation of an edge from outcome probabilities, see the roulette house edge calculation and the craps house edge breakdown, which uses dice combinations. The relationship between payout and true odds that drives the Tie bet is explained in true odds vs payout odds.
Converting an edge into a cost per session is covered in expected loss per hour. A lower edge does not make a loss unlikely on any one session; it only means the average cost per dollar wagered is smaller.
Frequently Asked Questions
