Baccarat Probability Models: Banker vs. Player Odds

Baccarat is not very hard to learn, but beneath the tidy structure of the table is a collection of rules that create mathematical models. They dictate how the banker will win slightly more often than the player. Knowing the numbers will never guarantee profit, nor will the house ever fail to have the edge, but it does allow players to know how the game works.

How baccarat is structured

In baccarat, cards are dealt to the player and banker of the two table positions. Bets are placed on which side gets closest to nine. Both sides receive two cards, with a possibility of a third card being drawn under very strict rules. Face cards and tens count for nothing; aces for one. The rest are still face value. Anything more than nine is subtracted by ten, so seven and eight (15) counts for five.

Because the drawing rules are computer regulated, the game does away with subjective decisions. With blackjack, there is no strategy on when to hit or stand. This allows mathematicians to calculate the exact probabilities of each occurrence.

Why the banker has an edge

Ties occur close to 10% of the time (around 9.52% if you’re after specifics). The banker hand wins about 45.86% of the time. The player hand wins around 44.62%. The small advantage for bankers comes from the drawing rules. In some cases, the banker draws a third card while the player must stand, giving bankers slightly better chances to improve weak totals.

Casinos charge a 5% commission on banker bets to balance this plus. Without the commission, bankers would be the clear best bet. With the fee levied, the long-term return for banker and player bets comes much closer.

The commission also applies in online casinos, and also in the traditional physical casinos. There are websites that offer baccarat games with no commission. No Commission baccarat games are explained in the baccarat websites in the list of CTO.

Calculating the odds

Here the numbers are assumed based on an eight-deck shoe, which is the standard setup in casinos. The single-deck versions slightly change the numbers, but not much.

If ties are ignored in the calculation and banker against player is the only consideration, banker will win about 50.68% of the time. The player will win about 49.32%. The rest of the difference is due to the charge that casinos would prefer to make.

Expected value of each bet

Expected value tells us what the typical result of a bet will be after many rounds. For baccarat, expected value depends on both chance of win and payoff.

• A banker bet wins 1 to 1 less 5% commission. The house edge is around 1.06%.
• A player bet wins 1 to 1 without commission. The house edge is around 1.24%.

How the third card rule works

When a side has eight or nine with the first two cards, both of these must stay. These are called natural hands. Otherwise, the player side can draw a third card when they have zero to five. With six or seven, the player remains.

The choice of the banker is more elaborate. When the player stands, the banker picks up amounts between zero and five and stands on six or seven. When the player receives a card, the action for the banker will be based on its total as well as on the value of the player's third card.

For example, if a banker has three, it will draw except if the third card of the player happens to be an eight. These rules create slight biases that favor bankers. 

How ties complicate things

At face value, the tie bet may be justified because both sides have an equal chance to win. The frequency of a tie is under 10%, and thus the payout ratio does not reflect the reality. With an 8 to 1 payment, the expected return is very negative.

Even casinos that offer 9 to 1 still gain an advantage over the player. The veteran players of baccarat thus avoid tie bets as a rule.

Quick tips for novices - in a nutshell

Understanding the odds makes some of the game's mystique disappear. Understanding that the banker bet has an advantage explains why players are attracted to it. Understanding that the value of ties saves money in the long term. And understanding the commission rule avoids confusion when it comes to getting paid.

Baccarat compared to other games in the casino

Single-zero roulette has a 2.70% edge. Double-zero American roulette = 5.26%. Simple blackjack, using optimal strategy, can whittle the edge down to around 0.50%, but that takes experience and ability. Baccarat comes in between: easy to play with an edge of nearly 1% for the big bets.

Streaks and illusions

Players may observe streaks where the banker will consistently win. This is to be expected in any game of chance with odds close to equal.

There will also be clusters of tails or heads resulting from a fair toss of a coin. The key is that every round of baccarat is independent. There are numerous decks in the shoe, but the manner in which cards are drawn still inhibits consistent prediction.