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