Deck Number and Winning Probabilities in Baccarat Mines Games Casino
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 |
| 1 Deck | 0.44676 | 0.459624 | 0.093615 |
| 2 Decks | 0.446508 | 0.459072 | 0.094419 |
| 6 Decks | 0.446278 | 0.458652 | 0.095068 |
| 8 Decks | 0.446246 | 0.458597 | 0.095155 |
1. The 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.
2. Fewer 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.
