# Buffalo Blackjack

## Introduction

Buffalo Blackjack is a standard blackjack game with two side bets. Normally, I would address the side bets separately as there is no need to re-analyze blackjack. However, the outcome of the 21 Magic side bet is strategy dependent, necessitating making significant strategy changes to maximize the entire return, that I consider it a significantly different game from ordinary blackjack and worthy of a separate page.

What is noteworthy of this game is a strong player advantage if the player is allowed to bet equally on the blackjack and 21 Magic bets, which is sometimes the case.

## Base Game Rules

Following are the rules of the overall game, without getting into the details of the side bets.

1. The game is based on standard blackjack, which I assume the reader is already familiar with.
2. Two side bets are added, the 21 Magic and the Bust Bonus.
3. Limits may be imposed on the maximum ratio of the 21 Magic bet to the blackjack wager.

## 21 Magic Rules

Following are the rules for the 21 Magic side bet.

1. The wager shall lose if the player does not get to 21 points or a blackjack.
2. The wager shall push in the event of a 21/21 tie or a blackjack/blackjack tie.
3. The wager shall pay as follows for a winning 21-point hand or a blackjack:
• 2 cards or blackjack: 6 to 1
• 3 cards: 8 to 1
• 4 cards: 9 to 1
• 5 cards: 10 to 1
• 6 cards: 10 to 1
• 7 cards: 25 to 1

4. If the player doubles, then he only doubles the blackjack wager, not the 21 Magic.
5. If the player splits, then he must also make an additional 21 Magic bet for each additional hand.

## Strategy

All the following strategies assume six decks, double after split is allowed, and re-splitting aces are allowed.

Following is the strategy for a maximum 21 Magic bet of 100% of the blackjack bet and dealer hits a soft 17.

Following is the strategy for a maximum 21 Magic bet of 100% of the blackjack bet and dealer stands on a soft 17.

Following is the strategy for a maximum 21 Magic bet of 20% of the blackjack bet and dealer hits a soft 17.

As you can see in the analysis page below, the if the 21 Magic bet is capped at 20% of the blackjack bet, then the player should bet nothing on the 21 Magic and play according to conventional basic strategy.

## Analysis

The following table shows the house edge under the three sets of rules provided in the strategy section. The "Maximum 21 Magic" column refers to the maximum amount the player may bet on the 21 Magic relative to his blackjack bet. The right two columns show the expected value to the player expressed in two ways, one relative to the blackjack wager only and one relative to the sum of the two initial bets. For example, under the rules where the player can bet 100% of the blackjack wager on the 21 Magic and the dealer hits a soft 17, if the player bets \$100 on each bet, then he can expect to win \$6.82 per hand.

### Table Title

Maximum
21 Magic
Dealer
Soft 17
Relative
BJ bet only
Relative
Total
Initial Bets
100% Hit 6.82% 3.41%
100% Stand 7.48% 3.74%
20% Hit -3.84% -3.20%

## Acknowledgements

I would like to thank the following people for their help with this analysis. While I did my own infinite-deck analysis in Excel I am very thankful to those below who shared their results with me, giving me something to compare my work against. This game was a tough analysis so I greatly appreciate having the safety net of peer review to ensure accuracy.

• Daniel Dale -- who did both a combinatorial analysis and random simulation of all three sets of rules above, who kindly shared his analysis with me with permission to publish.
• Cartwright -- for his math analysis on the game.