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Last Updated: March 7, 2022

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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.

  1. Eight 52-card decks are used.
  2. Cards are scored as follows:
    • Aces = 1 point
    • 2-9 = Pip value
    • Tens, face cards = 0 points
  3. 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.
  4. The dealer shall deal two cards to the Banker hand.
  5. The Natural 8 bet wins and pays 9 to 1 if the total points of the Banker hand is exactly 8.
  6. 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.


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