Baccarat Odds: House Edge by Bet and Rule Set

Baccarat is a card game with three bets and three very different costs. The banker bet costs about 1.06% of turnover, the player bet about 1.24%, and the tie bet about 14.36%. Those figures are not opinions; they come from the payout table and the number of outcomes, and they change if the rules change. This page derives each one, states the rules the figures depend on, and converts them to money per hour at a stated stake and round rate.

The three bets and their payouts

In punto banco, the version dealt in most casinos and online, the rules for drawing a third card are fixed. The player and banker hands are dealt two cards each. A third card may be drawn according to a table that depends on the total. The player bet pays 1 to 1. The banker bet pays 1 to 1 minus a 5% commission on the win. The tie bet pays 8 to 1 in most casinos, though some pay 9 to 1. The 8 to 1 payout is the one used here; the 9 to 1 version is noted where it changes the figure.

A tie bet wins when both hands finish with the same total. When a tie occurs, banker and player bets are usually returned as a push, not lost. That push is part of the arithmetic.

The number of outcomes

The eight-deck shoe is standard. With eight decks, the number of possible two-card combinations is large, but the relevant count is the number of final hand totals. The probabilities of banker, player, and tie outcomes under the standard drawing rules are approximately:

• Banker wins: 45.86%
• Player wins: 44.62%
• Tie: 9.52%

These are the figures for an eight-deck game with the standard third-card rules. They change slightly with fewer decks or different drawing rules, but the eight-deck standard is the one quoted by most operators and the one used here.

Deriving the banker edge

The banker bet pays 1 to 1, but the casino takes 5% commission on the win. So a 1 unit winning banker bet returns 1 unit profit minus 0.05 units commission, or 0.95 units net. A losing banker bet loses 1 unit. A tie is a push.

Expected value per 1 unit staked on banker:

• Win: 0.4586 × 0.95 = 0.43567
• Lose: 0.4462 × (−1) = −0.4462
• Tie: 0.0952 × 0 = 0

Sum: 0.43567 − 0.4462 = −0.01053

So the house edge on the banker bet is about 1.05%, often rounded to 1.06% depending on the exact probability table used. The commission is what makes this non-obvious: without it, the banker bet would have a positive expectation for the player, because banker wins more often than player. The 5% commission flips that.

Deriving the player edge

The player bet pays 1 to 1 with no commission. A winning player bet returns 1 unit profit. A losing player bet loses 1 unit. A tie is a push.

Expected value per 1 unit staked on player:

• Win: 0.4462 × 1 = 0.4462
• Lose: 0.4586 × (−1) = −0.4586
• Tie: 0.0952 × 0 = 0

Sum: 0.4462 − 0.4586 = −0.0124

So the house edge on the player bet is about 1.24%. The player bet wins less often than banker, and it pays even money, so it costs more than the banker bet despite having no commission.

Deriving the tie edge

The tie bet pays 8 to 1. A winning tie bet returns 8 units profit. A losing tie bet loses 1 unit. There is no push on the tie bet itself; if the hands do not tie, the bet loses.

Expected value per 1 unit staked on tie:

• Win: 0.0952 × 8 = 0.7616
• Lose: (1 − 0.0952) × (−1) = 0.9048 × (−1) = −0.9048

Sum: 0.7616 − 0.9048 = −0.1432

So the house edge on the tie bet is about 14.32%, commonly quoted as 14.36% depending on the probability table. At 9 to 1, the edge falls to about 4.84%, but 9 to 1 is rare. The 8 to 1 version is the one to assume unless the table states otherwise.

What the edge depends on

Every figure above depends on the rule set. The table below lists the conditions that change the number.

A 4% commission on banker lowers the edge to about 0.60%. A 6% commission raises it to about 1.46%. The commission is not always 5%, so the figure must be checked against the table’s rule card. The number of decks matters less: a six-deck game shifts the banker edge by a few hundredths of a percent. The drawing rules matter more in variants like no-commission baccarat, where a banker win with a total of 6 pays 0.5 to 1 instead of 1 to 1. That variant changes the edge on banker to about 1.46% and on player to about 1.29%, depending on the exact rules.

Money per hour

A percentage of turnover is not a quantity anyone can feel. At a 1 unit stake and 200 rounds per hour, the expected loss per hour is the house edge times the stake times the number of rounds.

For banker at 1.06%:

• Edge per unit: 0.0106
• Stake: 1
• Rounds per hour: 200
• Expected loss per hour: 0.0106 × 1 × 200 = 2.12

So at 1 per round, 200 rounds per hour, the banker bet costs about 2.12 per hour in expectation. At 10 per round, it costs about 21.20 per hour. At 100 per round, about 212 per hour.

For player at 1.24%:

• 0.0124 × 1 × 200 = 2.48 per hour at 1 per round
• 24.80 per hour at 10 per round
• 248 per hour at 100 per round

For tie at 14.36%:

• 0.1436 × 1 × 200 = 28.72 per hour at 1 per round
• 287.20 per hour at 10 per round
• 2,872 per hour at 100 per round

The tie bet is not a slightly worse bet; it is an order of magnitude worse. The difference between banker and player is small by comparison: 2.12 versus 2.48 per hour at 1 per round. The difference between either and tie is the difference between a modest cost and a severe one.

These figures assume 200 rounds per hour. Live baccarat online often runs slower, perhaps 40 to 60 rounds per hour, because of the dealer and the streaming. A physical table with a full complement of players may run 50 to 80 rounds per hour. A software baccarat game with fast dealing can run 300 or more. The hourly cost scales with the round rate, so the same edge produces a much smaller hourly figure at a live table than at a fast software table.

Worked example with a different stake

Suppose the stake is 25 per round on banker, and the table runs 60 rounds per hour. The expected loss per hour is:

• Edge: 0.0106
• Stake: 25
• Rounds: 60
• Expected loss: 0.0106 × 25 × 60 = 15.90 per hour

Over a four-hour session, the expected loss is 15.90 × 4 = 63.60. That is the mean outcome. Actual results will vary; the standard deviation is large. The point is that the edge is a rate, not a guarantee, and the hourly figure is the rate applied to a stated stake and round rate.

What people get wrong

The most common mistake is treating the banker bet as free money because it wins more often than player. It does win more often, but the 5% commission means the payout is less than the true odds. The commission is not a fee on top; it is built into the payout. A 1 unit banker win returns 0.95 units profit, and that 0.05 is what turns a positive expectation into a negative one.

The second mistake is assuming the tie bet is a reasonable long shot. At 8 to 1, the true odds against a tie are about 9.5 to 1. The payout is short by about 1.5 units per unit staked, which is why the edge is 14.36%. The tie bet is not a lottery ticket with a small cost; it is a bet with a large cost per round.

The third mistake is believing that patterns in the shoe predict the next hand. Scorecards, roads, and trends are decoration. Each hand is dealt from a shuffled shoe, and the probabilities of banker, player, and tie are the same on every hand regardless of what came before. The shoe does not have a memory. A run of banker wins does not make player more likely, and a run of player wins does not make banker more likely. The drawing rules and the composition of the shoe determine the probabilities, and the composition changes only slightly as cards are removed. That slight change is not predictable in a way that overcomes the house edge.

The fourth mistake is thinking that a staking system changes the edge. Martingale, d’Alembert, Fibonacci, and Labouchere change the distribution of outcomes: they make many small wins and occasional large losses, or the reverse. They do not change the mean. The expected loss per unit staked is the same regardless of how the bets are sized. A progression can make a session last longer or shorter, but it cannot turn a negative expectation into a positive one.

Rule variants and their effect

No-commission baccarat is a variant where the banker bet pays 1 to 1 on all wins except when the banker wins with a total of 6, in which case it pays 0.5 to 1. This changes the banker edge to about 1.46% and the player edge to about 1.29%, depending on the exact rules. The variant is not better for the player; it shifts the cost from a commission on all wins to a larger penalty on a specific win.

Some tables pay 9 to 1 on tie. That reduces the tie edge to about 4.84%, which is still much higher than banker or player. A 9 to 1 tie bet is less bad than an 8 to 1 tie bet, but it is not a good bet.

Fewer decks change the probabilities slightly. A six-deck game has a banker edge of about 1.06% and a player edge of about 1.24%, essentially the same as eight decks. The difference is small enough that the deck count is not the main thing to check. The commission rate and the tie payout are the main things.

Reading the table

The figures on this page are for the standard eight-deck punto banco game with a 5% commission on banker and an 8 to 1 payout on tie. If the table states a different commission or a different tie payout, the figures change. The method for deriving them is the same: multiply each outcome’s probability by its payout, sum, and the result is the expected value per unit staked. The negative of that is the house edge.

Baccarat online and live baccarat use the same arithmetic. The difference is the round rate and the stake limits. A live baccarat table with a 25 minimum and 60 rounds per hour costs about 15.90 per hour on banker at 25 per round. A software baccarat game with a 1 minimum and 300 rounds per hour costs about 3.18 per hour on banker at 1 per round. The edge is the same; the hourly cost is not.

The game is not a way to make money. The expectation is negative on every bet. The banker bet is the least costly of the three, and the tie bet is the most costly. That is the whole of the arithmetic.