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Ten Deck Baccarat
Introduction
Some tables in Singapore use a ten-deck shoe in baccarat. Here is the math for the major bets in baccarat using ten decks. The lower right cell shows a house edge of 1.23%.
As usual, when writing about baccarat, I use upper cast to refer to the bets and lower case in referring to people, to avoid confusion.
The following table shows my analysis of the Player bet.
Player Bet — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1 | 8,570,454,841,408,000 | 0.446227 | 0.446227 |
| Tie | 0 | 1,828,629,499,384,000 | 0.095209 | 0.000000 |
| Loss | -1 | 8,807,402,586,035,200 | 0.458564 | -0.458564 |
| Total | 19,206,486,926,827,200 | 1.000000 | -0.012337 |
The following table shows my analysis of the Banker bet when all wins pay 19 to 20 (or even money less a 5% commission). The lower right cell shows a house edge of 1.06%.
Banker Bet (19 to 20) — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 0.95 | 8,807,402,586,035,200 | 0.458564 | 0.435636 |
| Tie | 0 | 1,828,629,499,384,000 | 0.095209 | 0.000000 |
| Loss | -1 | 8,570,454,841,408,000 | 0.446227 | -0.446227 |
| Total | 19,206,486,926,827,200 | 1.000000 | -0.010591 |
The following table shows my analysis of the commission-free version of the Banker bet when a win on a six pays 1 to 2. The lower right cell shows a house edge of 1.46%.
Banker Bet (Win on 6 Pays Half) — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Banker win other than 6 | 1 | 7,772,649,045,452,800 | 0.404689 | 0.404689 |
| Banker win with 6 | 0.5 | 1,034,753,540,582,400 | 0.053875 | 0.026938 |
| Tie | 0 | 1,828,629,499,384,000 | 0.095209 | 0.000000 |
| Player win | -1 | 8,570,454,841,408,000 | 0.446227 | -0.446227 |
| Total | 19,206,486,926,827,200 | 1.000000 | -0.014601 |
The following table shows my analysis of the commission-free version of the Banker bet when a win on a three-card seven is a push. The lower right cell shows a house edge of 1.02%.
Banker Bet (Win on 6 Pays Half) — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Banker win other than 3-card 7 | 1 | 8,374,622,242,806,400 | 0.436031 | 0.436031 |
| Banker win with 3-card 7 | 0 | 432,780,343,228,800 | 0.022533 | 0.000000 |
| Tie | 0 | 1,828,629,499,384,000 | 0.095209 | 0.000000 |
| Player win | -1 | 8,570,454,841,408,000 | 0.446227 | -0.446227 |
| Total | 19,206,486,926,827,200 | 1.000000 | -0.010196 |
The following table shows my analysis of the Tie bet. The lower right cell shows a house edge of 14.31%.
Tie Bet — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 8 | 1,828,629,499,384,000 | 0.095209 | 0.761672 |
| Loss | -1 | 17,377,857,427,443,200 | 0.904791 | -0.904791 |
| Total | 19,206,486,926,827,200 | 1.000000 | -0.143119 |
The following table shows my analysis of the Player Pair and Banker Pair bets. The lower right cell shows a house edge of 9.83%.
Player Pair/Banker Pair — Ten Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 11 | 10,140 | 0.075145 | 0.826590 |
| Loss | -1 | 124,800 | 0.924855 | -0.924855 |
| Total | 134,940 | 1.000000 | -0.098266 |
Comparison to Eight Decks
The following table shows a comparison of all the major bets between ten and eight decks. The difference column is the expected value of ten decks minus eight decks. Thus, a positive difference means a change from eight to ten decks is good for the player and negative is bad. As you can see, the difference in the Player and Banker bets is negligible. The house edge on the Tie bet is 0.05% less. However, the big different is the house edge on the Player and Banker pair bets is 0.53% less, for obvious reasons.
Ten vs. Eight Deck Comparison
| Bet | Ten Decks | Eight Decks | Difference |
|---|---|---|---|
| Banker (19 to 20) | -0.010591 | -0.010579 | -0.000012 |
| Banker (wins on 6 pays half) | -0.014601 | -0.014581 | -0.000020 |
| Banker (wins on 3-card 7 push) | -0.010196 | -0.010183 | -0.000013 |
| Player | -0.012337 | -0.012351 | 0.000014 |
| Tie | -0.143119 | -0.143596 | 0.000477 |
| Pairs | -0.098266 | -0.103614 | 0.005349 |