Baccarat is a simple casino card game played under fixed house rules where each round can end in one of three possible outcomes, Player, Banker, or Tie. As is the case with all gambling games, the winning odds in baccarat are tilted in favor of the house which retains a minimum of one percent of all money wagered in the long run.
The precise house edge fluctuates across the three possible outcomes patrons can bet on. Deck number is another factor that influences the casino advantage the game yields. Baccarat is normally dealt out of a shoe that contains eight preshuffled decks, although some variants of the game use six packs of cards.
Which is the better alternative for the player in terms of winning odds, eight-deck or six-deck baccarat? We provide the answer to this question in today’s article as we examine the effect of deck number on the theoretical return and winning probabilities in baccarat.
The House Edge in Baccarat
You are perhaps familiar with the drawing rules, card values, and payouts in baccarat if you are interested in how deck number affects your winning odds.
Let’s skip straight to the mathematics of baccarat and look into the probabilities of a standard eight-deck game with a 5% commission on Banker and even-money payouts on winning Player hands. Tie bets pay at standard odds of 8 to 1 when successful.
The Likelihood of Outcomes with Ties Included
Ties between Player and Banker occur approximately 9.51% of the time.
The Player hand wins approximately 44.62% of the time and loses the remaining 45.87% of the rounds.
The Banker hand is successful approximately 45.87% of the time and loses the remaining 44.62% of the rounds.
The Likelihood of Outcomes with Ties Excluded
Ignoring the ties, the Player hand pays out roughly 49.32% of the time and loses the other 50.68% of the rounds.
The percentages are reversed for the Banker side as it pays out 50.68% of the rounds on average and loses 49.32% of the rounds.
You have surely noticed the winning probability of the Banker side exceeds fifty percent in the second case where we ignored the ties.
Casino operators offset this advantage by imposing a 5% commission on all winning Banker hands. Gamblers receive 95 cents per every dollar wagered on Banker. The bet thus yields a house edge that is nearly identical to that of the Player side.
When we know the probabilities of all three possible outcomes in the game, we can easily calculate their house edges.
All we have to do is multiply the winning probability by the wager and then add the losing probability multiplied by the losses to that result. The losses correspond to a negative expected value (EV), hence the minus sign. In turn, this negative EV reflects the house edge of a bet.
- Expected Value of the Player Bet
(1 x 0.446246) + (-1 x 0.458597) + (0 x 0.095155) = -0.012351
- Expected Value of the Banker Bet
(0.95 x 0.458597) + (-1 x 0.446246) + (0 x 0.095155) = -0.010578
- Expected Value of the Tie Bet
(8 x 0.095155) + (-1 x 0.458597) + (-1 x 0.446246) = -0.143603
When you convert these probabilities into percentages, you get the expected value of all three possible outcomes in baccarat. It is obviously negative and corresponds to the house edges yielded by the Player, Banker, and Tie bets.
- House Edge of the Player Bet = -0.012351 x 100 = 1.24%
- House Edge of the Banker Bet = -0.010578 x 100 = 1.06%
- House Edge of the Tie Bet = -0.143603 x 100 = 14.36%
Note that the percentages above correspond to the long-term advantage the casino holds per hand played since ties are included. The house edges of the Player and Banker bets increase further to 1.36% and 1.17% when we ignore the ties as you can see from the calculations below.
- Expected Value of Player Wagers per Bet Resolved
(1 x 0.4932) + (-1 x 0.5068) = -0.0136
- Expected Value of Banker Wagers per Bet Resolved
(0.95 x 0.5068) + (-1 x 0.4932) = -0.0117
For every $100 wagered on Player, Banker, and Tie, gamblers can anticipate losses of $1.24, $1.06, and $14.36 on average. Another important thing to mention is that the house edges above apply to baccarat games that charge a 5% commission on winning Banker hands.
The mathematical advantage the house holds on Banker jumps to 1.46% in commission-free variations. We know this sounds counterintuitive but it is true. Feel free to read our detailed article on commission versus no commission baccarat for further information on this subject.
Deck Number and Winning Probabilities in Baccarat
Baccarat games are normally dealt out of a shoe containing eight full decks, although it is possible to find six-deck variations at some online casinos. Some rare variants available in Macau may use one or two decks as well.
You would perhaps intuitively conclude your odds of winning are higher when fewer cards are in play. However, this is not always the case as you shall see after you examine the table below more closely.
|Deck Number and Winning Probabilities in Baccarat|
|Deck Number||Player Winning Probability||Banker Winning Probability||Tie Winning Probability|
1The Probabilities For Player and Banker Decrease with More Decks
As you have perhaps noticed after a closer inspection of the table, the winning probabilities of the Player and Banker hands decrease proportionately to the number of decks.
The opposite is true for the Tie bet. The likelihood of the Player and Banker pushing increases ever so slightly the more decks you introduce to the shoe.
The Player side will win approximately 44.68% of the time in single-deck games as opposed to 44.62% in eight-deck variations.
We observe a similar tendency with the Banker whose winning probability drops from 45.96% in single-deck games to 45.87% with eight decks.
In the meantime, the likelihood of the two sides pushing jumps from 9.36% with one deck to 9.51% with eight decks.
2Fewer Decks = Fewer Card Combinations
These discrepancies in the winning probabilities for Player and Banker are due to the fact that fewer decks produce a smaller number of possible card combinations. In turn, this also has an impact on the house advantage and your expected value as you shall see shortly.
|Deck Number and Possible Hand Combinations for Player, Banker, and Tie|
|Deck Number||Player Combinations||Banker Combinations||Tie Combinations|
|1 Deck||6.5 Billion||6.7 Billion||1.4 Billion|
|2 Decks||487.8 Billion||501.5 Billion||103.2 Billion|
|6 Decks||392.2 Trillion||403.1 Trillion||83.5 Trillion|
|8 Decks||2.2 Quadrillion||2.3 Quadrillion||475.6 Trillion|
Effect of Deck Number on Theoretical Return in Baccarat
The discrepancies in the probabilities impact the theoretical return players can anticipate when playing baccarat against multiple decks. The long-term return of the Banker bet declines as the deck number increases.
Conversely, the Player and Tie wagers yield slightly better expected value when more decks are utilized. The house edges in eight-deck baccarat are slightly lower than those gamblers face in six-deck variations of the game.
- Expected Value of the Player Bet with One Deck
(1 x 0.446760) + (-1 x 0.459624) + (0 x 0.093615) = -0.01286
- Expected Value of the Banker Bet with One Deck
(0.95 x 0.456924) + (-1 x 0.446760) + (0 x 0.093615) = -0.010117
- Expected Value of the Tie Bet with One Deck
(8 x 0.093615) + (-1 x 0.456924) + (-1 x 0.446760) = -0.157464
- Expected Value of the Player Bet with Six Decks
(1 x 0.446278) + (-1 x 0.458652) + (0 x 0.095068) = -0.012374
- Expected Value of the Banker Bet with Six Decks
(0.95 x 0.458652) + (-1 x 0.446278) + (0 x 0.095068) = -0.010558
- Expected Value of the Tie Bet with Six Decks
(8 x 0.095068) + (-1 x 0.446278) + (-1 x 0.458652) = -0.14438
As you can see, baccarat variants that play with one and six decks offer slightly lower expected value for Player and Tie wagers compared to eight-deck games. Regardless of deck number, the theoretical return is still negative and you will inevitably end up in the red the longer you play. Nonetheless, your odds of winning in games that utilize more decks are still slightly better.
Improving Your Winning Odds in Baccarat
1Learn Card Counting
From what we said so far, it becomes clear baccarat is a negative-expectation game. It is impossible for players to overturn the house edge when betting on the three main outcomes (Player, Banker, and Tie). Some variants support optional side wagers like the Easy 6, Super 6, and Dragon 7 that can yield positive expected value but players must learn to count cards to overcome their house edges.
2Play Eight-Deck Baccarat
One way to improve your odds of winning in the main game is to play baccarat variations that use eight decks. These are broadly available at all online casinos, so the last thing you can complain about is a lack of choice. The house advantage in games that utilize six rather than eight decks is slightly higher for Player (1.26%) and Tie (14.44%) bets.
3Avoid Tie Bets
We recommend you stick to Player and Banker wagers and altogether avoid betting on the Tie. It is among the worst wagers one can possibly make in a casino as it yields very low theoretical returns. With the Tie, you can anticipate winnings of $85.64 per every hundred dollars you wager in the long run. In essence, you are better off playing online slots than betting on ties in baccarat.
4Stay Away from Side Bets
Last but not least, we suggest you steer clear of side bets unless you can exploit them to your advantage through card counting. Some of the optional wagers in baccarat surpass even the Tie bet in terms of house edges and can quickly drain your bankroll if you are not careful.