Player's Choice 21

Introduction

I discovered a variant of blackjack called Player's Choice 21 at the Palazzo on August 17, 2013. In this game, players start with three cards which they will use to create two blackjack hands. Notably, one card that the player selects will be shared between both hands. To utilize this feature, the game includes a side bet that generally comes with a negative expected value.

Rules

1. The game is played using either six or eight standard decks of cards, each containing 52 cards.
2. Cards are scored in this game just as they would be in traditional blackjack.
3. The game commences with the player placing three bets: two for blackjack and one for the 3 Card Bonus.
4. The blackjack bets must be equal in amount, while the 3 Card Bonus wager needs to be at least equal to one of the blackjack wagers.
5. Players will receive three cards facing up, while the dealer will have two cards: one face up and the other face down.
6. At this juncture, the 3 Card Bonus bet will be immediately evaluated based on the player’s three exposed cards and the accompanying pay table.
7. Players will arrange their cards to create two initial blackjack hands. They must declare one card that will be common to both hands. For instance, if the player's three cards are a 3, an 8, and a 10, the optimal decision would be to select the 8 as the common card, resulting in hands totaling 11 and 18.
8. The dealer will then check to see if there is a blackjack.
9. After this step, the game will adhere to the standard rules of blackjack. These rules include the option to double down after a split, as well as the ability to resplit aces, but do not permit surrendering.
10. The choice of using six or eight decks of cards and whether the dealer will hit or stand on a soft 17 are adjustable rules within the game.

Strategy

The following table indicates which card to designate as the common card based on the player’s three cards and the dealer's face-up card. While this table applies to the game variant where the dealer hits on soft 17, it can also be effectively used for the version where the dealer stands.

Here is a simplified version of the previous table, combining all combinations that do not rely on the dealer's visible card.

At this stage, players should revert to standard blackjack strategies. A .

Regarding the 3 Card Bonus bet, the only advisable approach is to place three bets of the same amount. While players can choose to wager more on the 3 Card Bonus, it is strongly advised not to do so.

A-7-7

The next two tables present the odds and potential returns for each event involving the 3 Card Bonus for both six and eight decks. The bottom right cells reveal a house edge of 25.0% with six decks and 24.3% with eight decks. The accompanying mathematical analysis suggests that other pay tables may exist, though this is the one currently used at the Palazzo.

A

The following table outlines the anticipated returns from blackjack, the 3 Card Bonus, and the holistic game experience. The blackjack return reflects the ratio of expected winnings from two one-unit blackjack wagers. Meanwhile, the 3 Card Bonus column indicates the expected return from a single one-unit wager. The total return column aggregates the blackjack and 3 Card Bonus returns, then divides this sum by three, representing the player's expected winnings relative to their total initial bets. For instance, in an eight-deck game where the dealer hits on soft 17, if a player wagers $5 on each of the three bets, they can anticipate a loss of -.006365 times $15, equating to approximately $0.0955.

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• Special thanks to Greg Jaffa for his assistance in putting this page together.
• A A Appreciation is extended for sharing his mathematical analysis report and the associated spreadsheet on this game. Other than the 3 Card Bonus bet, all calculations and strategies here were contributed by Charles, whose accuracy I have faith in.
• Acknowledgment to Beachbumbabs for compiling the condensed strategy table.

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