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Banker Natural 8 and 9
Introduction
Beat the Dealer by Edward Thorp mentions a now-defunct side bet in baccarat that he beat and caused the casinos to remove. Some research showed there were two such beatable side bets, on a Banker natural 8 and a Banker natural 9, both paying 9 to 1.
Rules
As usual, when discussing anything to do with baccarat, I use capital letters when referring to the names of bets and lower case to refer to those playing/banking the game. It is not necessary to explain the full rules of baccarat to explain these side bets, so I won't.
- Eight 52-card decks are used.
- Cards are scored as follows:
- Aces = 1 point
- 2-9 = Pip value
- Tens, face cards = 0 points
- In addition to the usual bets, which I won't get into, the are side bets on a Banker Natural 8 and Banker Natural 9.
- The dealer shall deal two cards to the Banker hand.
- The Natural 8 bet wins and pays 9 to 1 if the total points of the Banker hand is exactly 8.
- The Natural 9 bet wins and pays 9 to 1 if the total points of the Banker hand is exactly 9.
Banker Natural 8 Analysis
The following table shows my analysis of the Banker Natural 8 side bet. It shows a probability of winning of 9.45% and a house edge of 5.47%.
Banker Natural 8 Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 9 | 472,508,456,071,680 | 0.094532 | 0.850788 |
| Loss | -1 | 4,525,889,819,431,680 | 0.905468 | -0.905468 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.054680 |
Banker Natural 9 Analysis
The following table shows my analysis of the Banker Natural 9 side bet. It shows a probability of winning of 9.45% and a house edge of 5.10%.
Banker Natural 9 Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 9 | 474,361,430,409,216 | 0.094903 | 0.854124 |
| Loss | -1 | 4,524,036,845,094,140 | 0.905097 | -0.905097 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.050973 |
Card Counting
Thorp and his team beat these bets by card counting. He used a count of 8's against the Banker Natural 8 side bet and another for 9's for the Banker Natural 9. He says the casinos removed these bets, which I assume was because of him.
External Links
A Favorable Side Bet in Nevada Baccarat by Edward O. Thorp — Article from the Journal of the American Statistical Association, June 1966, Vol. 61, part I, pp. 313-328.