Mastering Baccarat Odds: From Basic Probabilities to Informed Wagering

The premise of the baccarat is quite simple. There are two hands, the player and the banker, and you must bet on which will have a higher value, or whether the hands will be of equal value. You have three standard bets, each with its own fixed payouts and probabilities. However, with the inclusion of the third card rule, the statistical possibilities of what will happen are far more complicated and open the doors to lots of different possible outcomes.

Baccarat can be enjoyed by players of all levels, and underlying any level of expertise, luck is a crucial element to winning. There are also plenty of variants of baccarat, each with its own alterations in the rules or the payout structure, all of which you can master within minutes. Here, we are going to analyze exactly how the game works and explore how the house edge works. Understanding the commission on banker bets, when third cards are drawn, and the probability is all imperative to building your expert baccarat strategy.

Gameplay and Third Card Rule

In each round, the dealer will draw 2 cards each for the player and the banker. Tens, Jacks, Queens and Kings count as 0 and the cards numbered 2-9 are taken at face value. Aces count as 1. The player will draw a third card on the following conditions:

• Value of the first 2 cards is 0, 1, 2, 3, 4, or 5
• Banker doesn't have 8 or 9

If the player has a value of 6 or 7, they stand, and if they have a value of 8 or 9, the banker cannot draw. The banker will draw a third card if the following happens:

• 0, 1 or 2 – Banker always draws
• 3 – Banker draws unless the player's third card is 8
• 4 – Banker draws unless the player's third card is 0, 1, 8 or 9
• 5 – Banker draws only if the player's third card was 4, 5, 6 or 7
• 6 – Banker draws only if the player's third card was 6 or 7
• 7 – Banker stands

There are conditions in which both the player and the banker will get a third card. As well as cases where just one of them will draw a third card, and cases in which none do.

Third Card Possibilities

There are over 200 different possible outcomes (based on points value), of which the banker wins 93, the player 90, and there are 21 ties.

These are merely the full possible set of outcomes. They don't all have an equal chance of winning. We go into the real probabilities after assessing the full range of possible outcomes. These possibilities were counted based on the points scored, and we didn't factor in that the number “0” appears more often than all the other numbers (30.73% to 0.07%).

But the numbers are still quite fascinating, as they show us that based on the sheer volume of possible points outcomes, we get the following:

• Banker Bets – 93 winning outcomes (45.36%)
• Player Bets – 90 winning outcomes (43.9%)
• Tie – 21 outcomes (10.24%)
• 205 Overall possible points outcomes

Let's break down those numbers further.

2 Cards for Player, 2 for Banker (Small Hand)

Also called small hand, these are the outcomes when both the player and banker stand on 2 cards. It can happen when either has a “natural” 8 or 9, or if both hands have a value of 6 or 7 each.

• 40 outcomes
• Player wins 18 (45%)
• Banker wins 18 (45%)
• 4 ties (10%)

2 Cards for Player, 3 for Banker (Big Hand)

The player always stands on a 6 or 7, but if the banker has a value of 0, 1 or 2, they must draw a third card. This is quite rare.

• 20 outcomes where: player has 2, banker has 3 cards
• Player wins 13 (65%)
• Banker wins 5 (25%)
• 2 Ties (10%)

3 Cards for Player, 2 for Banker (Big Hand)

The player draws if they have a value of 0 to 5. The following scenarios only work out if the banker has a total of 7, or if the banker's total and the player's third card meet the right conditions (listed above).

• 45 outcomes where: Player has 3, banker has 2 cards
• Player wins 15 (33.3%)
• Banker wins 25 (55.6%
• 5 Ties (11.1%)

3 Cards for Player, 3 for Banker

Having 6 cards drawn naturally opens up the most possible scenarios. But in terms of how often these occur, they are far more seldom than 4 hand cards. The conditions are basically met when the player draws (they have 5 or less), and the banker does (if the conditions are right). None should have a natural 8 or 9.

• 100 outcomes
• Player wins 45 (45%)
• Banker wins 45 (45%
• 10 Ties (10%)

Actual Probabilities

With an 8 card deck, the most likely outcome is that only 4 cards will be drawn:

• 4 Cards – 37.89%
• 5 Cards – 30.34%
• 6 Cards – 31.77

Concluding these numbers, we find that drawing a third card often damages a hand's chances of winning. The third card does not always signal that the hand will lose, but in most cases it is unwanted. Just look at how the game is built. The player almost always draws if they have a value of 5 or below. Whereas the banker has some rigid rules in place to ensure they only draw when the player's third card is favorable to their chances of winning.

Please note: these odds may vary depending on how many decks are used and any rule deviations. We used 8 decks and the standard, baccarat with commission.

Baccarat Standard Bets House Edge

Overall, the banker has a better chance of winning, and this is why the casinos cannot offer the player and banker bets at the same price.

• Banker Bets = Pays 1:1 (minus 4% or 5% commission)
• Player Bets = Pays 1:1
• Ties = Pays 8:1 or 9:1

With a 5% commission on banker bets, the house edge stands at 1.06%. For the player bet, the house has an edge of around 1.24%. And for ties, the house edge is the greatest, at 14.36% (if the payout is 8:1).

• Banker Bets = 1.06% house edge
• Player Bets = 1.24% house edge
• Ties = 14.36% house edge

Even with the small commission, the baccarat banker bets are the most profitable for players. The house edge is lower than what you get in European/French Roulette (2.7%) and lower than some forms of Blackjack (2% – without blackjack basic strategy).

Side Bets House Edge and Probabilities

Most baccarat games have side bets that you can place each round. These often involve aspects such as what cards will be drawn, the winning margin, and whether there will be 4, 5 or 6 cards drawn. Bear in mind though, that side bets often come with the greatest house edge.

Banker/Player Pair = 11:1

These are bets that you can make on either the player's hand or the banker's hand to have a pair. This can be a pair of the same number or are of the same suit. The house edge on this bet is around 10.36%, but it varies depending on the game.

Perfect Pairs 25:1

This is a bet on the banker's and player's cards (2 and 2) to be of either the same number or the same suit. It is quite commonly offered in conventional online baccarat games, and carries a house edge of around 13%.

Small Hand = 1.5:1

This is a wager on a hand of baccarat to comprise exactly 4 cards. Neither player nor banker will draw a third card. It has a house edge of 5.27%.

Big Hand = 0.54:1

The big hand is a side bet on the round to have exactly 5 cards. Either the banker or the player draws a third card, but both cannot. The house edge is quite small here, at 4.35% on average.

Dragon Bonus – Varies

The dragon bonus side bet is used in mini baccarat and some baccarat variants. It is a standard wager that comes with a flexible paytable. A natural win (2 cards equalling 8 or 9) pays out at 1:1. But if you draw a third card and win, then your winnings depend on the margin you beat the opposing hand by. Winning by 4 to 5 points gets a 2:1 payout, and if you win by 9 points, you can win up to 30:1.

The payouts and house edge varies depending on the game, but the house edge varies from around 2.7% and can go up to 9.4% or even higher.

How No Commission Baccarat Works

Zero commission baccarat is an attractive proposition for any players who specifically target banker bets. It removes the 4 or 5% commission on the banker bets, giving players 1:1 payouts if the banker wins. But, to make the game still profitable for casinos, the house edge is integrated in another way.

There may be certain conditions under which the banker bet does not pay out at 1:1. For example, in some zero commission baccarat, if the banker wins on a 6, they only pay 1:2. Or, other variants where the banker bet pushes if it wins with three cards and totals 7 points.

While the probability of those instances occurring is quite small, it is enough to raise the house edge enough for the casino to make a profit. The house edge on the banker bet where wins on a 6 pay out at 1:2 is 1.46% – higher than the edge with conventional baccarat.

How to Build Your Baccarat Strategy

There are baccarat gaming strategies for players of all levels and budgets. Some players may stick to the Banker and Player bets, alternating between the two and using some progressive betting systems to try to build profit. Others may diversify their bets using perfect pairs or the dragon bonus side wagers. While these do have a higher house edge, they pay out a lot more than the standard two, making them attractive propositions for anyone looking to have a little money riding on the side.

Table Limits and Stake Size

No baccarat strategy works without a rock-tight bankroll. To ensure you don't go bust during your gaming, you must figure out exactly how much you are willing to set aside for each gaming session. Then, break this number down into a nominal stake amount. We looked at an example in our guide to baccarat bankroll management in which a player makes a $25 weekly ($100 per month) bankroll. Presuming they play 3-4 times a week), this becomes around $7.50 per session. And then, considering the tables have 50 hands per hour, the player is spending around 30 cents a stake for half an hour of baccarat.

You need a table that suits your needs and can accommodate your budget, however high or low. The baccarat betting strategies often involve changing your stake, and they are designed for long-term play.

Betting Strategies for Baccarat

The strategies mostly involve either changing your stake after each round or playing with a fixed rate (also called flat betting). Some players may lower their stake amount if they go through a losing streak, or increase their stake if they are winning. But instead of playing it by ear, you can use mathematically proven betting systems.

For baccarat, the Labouchere system, D'alembert, and Fibonacci sequence are quite effective. They involve you changing your stake after each hand, either increasing it or decreasing it. The Martingale, while very popular among roulette players, carries a lot of risk. It can also be used in baccarat, but you must start with a very small stake and have enough to keep going if you lose numerous rounds in a row.

Mastering the Odds of Baccarat

Ultimately, there is no way of knowing if the cards are going to turn in your favor or not. The house edge, while low, is very consistent. Unlike a game of blackjack, where you can count cards and find out when the edge tilts in your favor. In baccarat, there are no effective card counting strategies. Why? because you are not trying to reach 21 here, you are figuring out which of two hands will score higher.

Banker bets in traditional baccarat (with commission) have the lowest house edge, and are mathematically the best wagers for players. Yet the probability of the banker winning is very close to the likelihood of the player winning, and after losing 3 rounds on the banker you may feel inclined to alternate. Understanding the odds, house edge, and mathematical statistics gives you the best chance to make the most out of your gaming.