Why does a Banker win on 6 pay half?
If you have ever wondered about this, you are not alone.
This table shows the Probability and House Edge for Baccarat (where Banker wins pay 0.95:1). Notice the House Edge on Banker (in bold):
| Wager | Permutations | Probability | Break-Even | House Edge |
| Player | 2,230,518,282,592,260 | 0.4462466093 | 1.02768 | 0.012351 |
| Banker | 2,292,252,566,437,890 | 0.4585974226 | 0.97307 | 0.010579 |
| Tie | 475,627,426,473,216 | 0.09516 | 9.50906 | 0.143596 |
| Total | 4,998,398,275,503,360 |
The House Edge means, theoretically in the long-term, for every dollar wagered, a player is expected to lose 1.05 cents.
This is a table with the House Edge on Baccarat, comparing what the House Edge would be if Banker were paid half on wins of 1 to 9:
| Banker Win On: | Permutations | Probability | Banker Win on Any Other Result | Player Win | Difference | House Edge |
| 1 | 24,291,119,898,624 | 0.004859781 | 2,267,961,446,539,260 | 2,230,518,282,592,260 | – 49,588,723,896,320.0 | -0.009920923 |
| 2 | 44,681,581,871,104 | 0.00893918 | 2,247,570,984,566,780 | 2,230,518,282,592,260 | – 39,393,492,910,080.0 | -0.007881223 |
| 3 | 72,927,778,568,192 | 0.01459023 | 2,219,324,787,869,700 | 2,230,518,282,592,260 | – 25,270,394,561,536.0 | -0.005055698 |
| 4 | 163,359,790,133,248 | 0.032682428 | 2,128,892,776,304,640 | 2,230,518,282,592,260 | 19,945,611,220,992.0 | 0.003990401 |
| 5 | 216,715,928,915,968 | 0.043357075 | 2,075,536,637,521,920 | 2,230,518,282,592,260 | 46,623,680,612,352.0 | 0.009327724 |
| 6 | 269,232,304,455,680 | 0.053863716 | 2,023,020,261,982,210 | 2,230,518,282,592,260 | 72,881,868,382,208.0 | 0.014581045 |
| 7 | 384,279,324,919,808 | 0.076880493 | 1,907,973,241,518,080 | 2,230,518,282,592,260 | 130,405,378,614,272.0 | 0.026089433 |
| 8 | 529,914,458,673,152 | 0.106016854 | 1,762,338,107,764,740 | 2,230,518,282,592,260 | 203,222,945,490,944.0 | 0.040657614 |
| 9 | 586,850,279,002,112 | 0.117407667 | 1,705,402,287,435,780 | 2,230,518,282,592,260 | 231,690,855,655,424.0 | 0.04635302 |
Notice that on Banker wins on 1 – 3, if the House were to pay half, there would be a long-term negative edge for the House.
For wins on 4 and 5, the edge is below that of normal Baccarat. At wins on 6, that is where the House Edge comes closest to that of normal Baccarat.
If the House were to pay half on a Banker win that best profited the House, then the obvious choice would be to pay half on Banker wins on 9, which gives a House Edge 4 times that of normal Baccarat.
Do realize, that these numbers are based on an 8-deck shoe, before any cards have been dealt. Once cards are removed from the shoe, the probabilities change dynamically.
Good luck.
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