Baccarat House Edge Calculation
September 14th, 2016 at 3:00:59 PM
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I decided to work out the house edge for the Baccarat dealer/banker bets by hand. Maybe someone else has already done this but I've only seen calculations that figure every valid permutation ( 4,998,398,275,503,360 of them for 8 decks) and include the effect of removal.
This calculation is straightforward. I assumed infinite deck since I knew the effect of removing 6 cards from 8 decks would be miniscule and also since it greatly simplifies the calculation. I believe that before computers the calculation was done this way since an exact manual calc is not feasible.
If the banker played by the same rules as the player then there would be no house edge with even money payouts on both bets. So it's only necessary to examine the 4 instances when the banker plays differently than the player:
1) Banker has 2-card hand worth 3 and Player's third card is 8 - Banker stays instead of taking a third card
2) Banker has 2-card hand worth 4 and Player's third card is 8 through 1 - Banker stays instead of taking a third card
3) Banker has 2-card hand worth 5 and Player's third card is 8 through 3 - Banker stays instead of taking a third card
4) Banker has 2-card hand worth 6 and Player's third card is 6 through 7 - Banker takes a third card instead of staying
Each of these change the bankers/player wins and pushes by the following amounts:
Wins , Pushes, Net Effect
1) (400), 880, 80
2) 4,560, 3,600, 12,720
3) 21,440, 2,800, 45,680
4) 720, (640), 800
Total 26,320, 6,640, 59,280
So the player's return is lowered by 26,320 * 2 plus 6,640 *1 = 59,280. 59,280 / (13*13*13*13*13*13) is 1.228 %. The exact edge on 8 deck baccarat is 1.235% so very close.
The banker calculation takes one extra step since the payoff is 0.95 not even money. I calculated the amount of ties as 453,961 if the banker and player used the same rules. Therefore the banker and player would both win/lose (13^6 - 453,961) /2 = 2,186,424.
So the edge on the Banker bet is (2,186,424 * (-.05) + 26,320 * 1.95 + 6,640 * 1) / 13^6 = 1.064%. The exact edge on 8 deck baccarat is 1.058% so again very close.
As a side note this calculation made me wonder why rules 1 and 4 even exist in Baccarat. You could remove them both and the percentages are barely affected (player goes to 1.210% and banker to 1.082%). I've never actually played Baccarat so maybe it would make sense if I did.
This calculation is straightforward. I assumed infinite deck since I knew the effect of removing 6 cards from 8 decks would be miniscule and also since it greatly simplifies the calculation. I believe that before computers the calculation was done this way since an exact manual calc is not feasible.
If the banker played by the same rules as the player then there would be no house edge with even money payouts on both bets. So it's only necessary to examine the 4 instances when the banker plays differently than the player:
1) Banker has 2-card hand worth 3 and Player's third card is 8 - Banker stays instead of taking a third card
2) Banker has 2-card hand worth 4 and Player's third card is 8 through 1 - Banker stays instead of taking a third card
3) Banker has 2-card hand worth 5 and Player's third card is 8 through 3 - Banker stays instead of taking a third card
4) Banker has 2-card hand worth 6 and Player's third card is 6 through 7 - Banker takes a third card instead of staying
Each of these change the bankers/player wins and pushes by the following amounts:
Wins , Pushes, Net Effect
1) (400), 880, 80
2) 4,560, 3,600, 12,720
3) 21,440, 2,800, 45,680
4) 720, (640), 800
Total 26,320, 6,640, 59,280
So the player's return is lowered by 26,320 * 2 plus 6,640 *1 = 59,280. 59,280 / (13*13*13*13*13*13) is 1.228 %. The exact edge on 8 deck baccarat is 1.235% so very close.
The banker calculation takes one extra step since the payoff is 0.95 not even money. I calculated the amount of ties as 453,961 if the banker and player used the same rules. Therefore the banker and player would both win/lose (13^6 - 453,961) /2 = 2,186,424.
So the edge on the Banker bet is (2,186,424 * (-.05) + 26,320 * 1.95 + 6,640 * 1) / 13^6 = 1.064%. The exact edge on 8 deck baccarat is 1.058% so again very close.
As a side note this calculation made me wonder why rules 1 and 4 even exist in Baccarat. You could remove them both and the percentages are barely affected (player goes to 1.210% and banker to 1.082%). I've never actually played Baccarat so maybe it would make sense if I did.
