# 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.