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Last Updated: October 3, 2013

Player's Choice 21

Introduction


Player's Choice 21 is a blackjack variant I noticed at the Palazzo on August 17, 2013. The thrust of the game is the player starts with three cards and uses them to form two starting hands in blackjack. One card, of the player's choice, will be common to both hands. To pay for this feature, the game mandates a negative-expectation side bet.

Rules

  1. Six or eight ordinary 52-card decks are used.
  2. All cards scored as in conventional blackjack.
  3. Play starts with the player making three wagers — two blackjack wagers and one 3 Card Bonus bet.
  4. The two blackjack wagers must be the same amount and the 3 Card Bonus bet must be at least as much as one of the blackjack wagers.
  5. The player will be given three cards face up and the dealer two cards, one face up and one down.
  6. The 3 Card Bonus bet will be immediately adjudicated at this point according to the player's three cards and the pay table below.
  7. The player shall arrange his cards to form two initial blackjack hands. One card, which the player must declare, is common to both hands. For example, if the player's three cards were a 3, 8, and 10 then the best play would be to make the eight the common card, forming an 11 and 18.
  8. The dealer shall check for blackjack.
  9. After this point, standard blackjack rules are followed. These include allowing double after a split and re-splitting aces but not surrender.
  10. The number of decks (six or eight) and whether the dealer hits or stands on soft 17 are configurable rules.

3 Card Bonus Pay Table

Hand Pays
Mini royal 75
Suited three of a kind 60
Straight flush 20
Three of a kind 10
Straight 2
Flush and pair 1.5
Flush 1.5
Pair 1
All other Loss

Strategy

The following table shows which card to play as the common card, according to the player's three cards and the dealer's up card. This table is for the "hit soft 17" game but should work well for the stand on soft 17 game as well.

Common Card Strategy 8 Decks — Dealer Hits Soft 17

Player
Hand
Dealer Up Card
2 3 4 5 6 7 8 9 X A
2-2-2 2 2 2 2 2 2 2 2 2 2
2-2-3 2 2 2 2 2 2 2 2 2 2
2-2-4 2 2 2 2 2 2 2 2 2 2
2-2-5 2 2 2 2 2 2 2 2 2 2
2-2-6 6 6 2 2 2 6 6 6 6 6
2-2-7 7 7 7 7 7 7 7 7 7 7
2-2-8 8 8 8 8 8 8 8 8 8 8
2-2-9 9 9 9 9 9 9 9 9 9 9
2-3-3 2 3 3 3 3 3 2 2 2 2
2-3-4 3 3 3 3 3 3 3 3 3 2
2-3-5 5 5 5 5 5 5 3 3 3 3
2-3-6 6 6 6 6 6 6 6 6 6 6
2-3-7 7 7 7 7 7 7 7 7 7 7
2-3-8 8 8 8 8 8 8 8 8 8 8
2-3-9 2 2 2 2 2 2 2 2 2 2
2-4-4 4 4 4 4 4 4 4 4 4 4
2-4-5 5 5 5 5 5 5 5 5 5 4
2-4-6 6 6 6 6 6 6 6 6 6 6
2-4-7 7 7 7 7 7 7 7 7 7 7
2-4-8 2 2 2 2 2 2 2 2 2 2
2-4-9 2 2 2 2 2 2 2 2 2 2
2-5-5 5 5 5 5 5 5 5 5 5 5
2-5-6 6 6 6 6 6 6 6 6 6 6
2-5-7 2 2 2 2 2 2 2 2 2 2
2-5-8 2 2 2 2 2 2 2 2 2 2
2-5-9 2 2 2 2 2 2 2 2 2 2
2-6-6 2 2 2 6 6 2 2 2 2 2
2-6-7 2 2 2 2 2 2 2 2 2 2
2-6-8 2 2 2 2 2 2 2 2 2 2
2-6-9 2 2 2 2 2 2 2 2 2 2
2-7-7 2 2 2 2 2 2 2 2 2 2
2-7-8 2 2 2 2 2 2 2 2 2 2
2-7-9 2 2 2 2 2 2 2 2 2 2
2-8-8 2 2 2 2 2 2 2 2 2 2
2-8-9 2 2 2 2 2 2 2 2 2 2
2-9-9 2 2 2 2 2 2 2 2 2 2
3-3-3 3 3 3 3 3 3 3 3 3 3
3-3-4 4 3 3 3 3 3 4 4 4 3
3-3-5 5 5 5 3 3 5 5 5 5 5
3-3-6 6 6 6 6 6 6 6 6 6 6
3-3-7 7 7 7 7 7 7 7 7 7 7
3-3-8 8 8 8 8 8 8 8 8 8 8
3-3-9 3 3 3 3 3 3 3 3 3 3
3-4-4 4 4 4 4 4 4 4 4 4 4
3-4-5 5 5 5 5 5 5 5 5 5 5
3-4-6 6 6 6 6 6 6 6 6 6 6
3-4-7 7 7 7 7 7 7 7 7 7 7
3-4-8 3 3 3 3 3 3 3 3 3 3
3-4-9 3 3 3 3 3 3 3 3 3 3
3-5-5 5 5 5 5 5 5 5 5 5 5
3-5-6 6 6 6 6 6 6 6 6 6 6
3-5-7 3 3 3 3 3 3 3 3 3 3
3-5-8 3 3 3 3 3 3 3 3 3 3
3-5-9 3 3 3 3 3 3 3 3 3 3
3-6-6 3 3 3 3 3 3 3 3 3 3
3-6-7 3 3 3 3 3 3 3 3 3 3
3-6-8 3 3 3 3 3 3 3 3 3 3
3-6-9 3 3 3 3 3 3 3 3 3 3
3-7-7 3 3 3 3 3 3 3 3 3 3
3-7-8 3 3 3 3 3 3 3 3 3 3
3-7-9 3 3 3 3 3 3 3 3 3 3
3-8-8 3 3 3 3 3 3 3 3 3 3
3-8-9 8 8 8 8 8 8 3 3 3 3
3-9-9 9 9 9 9 9 9 9 9 9 9
4-4-4 4 4 4 4 4 4 4 4 4 4
4-4-5 5 5 5 5 5 5 5 5 5 5
4-4-6 6 6 6 6 6 6 6 6 6 6
4-4-7 7 7 7 7 7 7 7 7 7 7
4-4-8 4 4 4 4 4 4 4 4 4 4
4-4-9 4 4 4 4 4 4 4 4 4 4
4-5-5 5 5 5 5 5 5 5 5 5 5
4-5-6 6 6 6 6 6 6 6 6 6 6
4-5-7 4 4 4 4 4 4 4 4 4 4
4-5-8 4 4 4 4 4 4 4 4 4 4
4-5-9 4 4 4 4 4 4 4 4 4 4
4-6-6 4 4 4 4 4 4 4 4 4 4
4-6-7 4 4 4 4 4 4 4 4 4 4
4-6-8 4 4 4 4 4 4 4 4 4 4
4-6-9 4 4 4 4 4 4 4 4 4 4
4-7-7 4 4 4 4 4 4 4 4 4 4
4-7-8 4 4 4 4 4 4 4 4 4 4
4-7-9 4 4 4 4 4 4 4 4 4 4
4-8-8 8 8 8 8 8 8 8 4 4 4
4-8-9 8 8 8 8 8 8 4 4 8 4
4-9-9 9 9 9 9 9 9 9 9 9 9
5-5-5 5 5 5 5 5 5 5 5 5 5
5-5-6 6 6 6 6 6 6 6 6 6 6
5-5-7 5 5 5 5 5 5 5 5 5 5
5-5-8 5 5 5 5 5 5 5 5 5 5
5-5-9 5 5 5 5 5 5 5 5 5 5
5-6-6 5 5 5 5 5 5 5 5 5 5
5-6-7 5 5 5 5 5 5 5 5 5 5
5-6-8 5 5 5 5 5 5 5 5 5 5
5-6-9 5 5 5 5 5 5 5 5 5 5
5-7-7 7 7 7 7 7 7 5 5 5 5
5-7-8 5 5 5 5 5 5 5 5 5 5
5-7-9 5 5 5 5 5 5 5 5 5 5
5-8-8 8 8 8 8 8 8 8 5 5 5
5-8-9 8 8 8 8 8 8 5 8 8 5
5-9-9 9 9 9 9 9 9 9 9 9 9
6-6-6 6 6 6 6 6 6 6 6 6 6
6-6-7 6 6 6 6 6 6 6 6 6 6
6-6-8 6 6 6 6 6 6 6 6 6 6
6-6-9 6 6 6 6 6 6 6 6 6 6
6-7-7 7 7 7 7 7 7 6 6 6 6
6-7-8 6 6 6 6 6 6 6 6 6 6
6-7-9 6 6 6 6 6 6 6 6 6 6
6-8-8 8 8 8 8 8 8 8 8 6 6
6-8-9 8 8 8 8 8 8 8 8 8 6
6-9-9 9 9 9 9 9 9 9 9 9 9
7-7-7 7 7 7 7 7 7 7 7 7 7
7-7-8 7 7 7 7 7 7 7 7 7 7
7-7-9 7 7 7 7 7 7 7 7 7 7
7-8-8 8 8 8 8 8 8 8 8 8 7
7-8-9 8 8 8 8 8 8 8 8 8 8
7-9-9 9 9 9 9 9 9 9 9 9 9
8-8-8 8 8 8 8 8 8 8 8 8 8
8-8-9 8 8 8 8 8 8 8 8 9 9
8-9-9 9 9 9 9 9 9 9 9 9 9
9-9-9 9 9 9 9 9 9 9 9 9 9
A-2-2 A A A 2 2 A A A A A
A-2-3 A A A A A A A A A A
A-2-4 A A A A A A A A A A
A-2-5 A A A A A A A A A A
A-2-6 A A A A A 2 2 A A A
A-2-7 7 7 7 7 7 7 7 2 A 2
A-2-8 8 8 8 8 8 8 8 8 8 8
A-2-9 9 9 9 9 9 9 9 9 9 9
A-3-3 A A A 3 3 A A A A A
A-3-4 A A A A A A A A A A
A-3-5 A A A A A 3 3 A A A
A-3-6 3 6 6 6 6 3 3 3 3 3
A-3-7 7 7 7 7 7 7 7 3 3 3
A-3-8 8 8 8 8 8 8 8 8 8 8
A-3-9 A A A A A A A A A A
A-4-4 A A A A A 4 A A A A
A-4-5 4 4 4 4 4 4 4 4 4 4
A-4-6 4 6 6 6 6 6 4 4 4 4
A-4-7 7 7 7 7 7 7 7 7 7 7
A-4-8 A A A A A A A A A A
A-4-9 A A A A A A A A A A
A-5-5 5 5 5 5 5 5 5 5 5 5
A-5-6 6 6 6 6 6 6 5 5 6 5
A-5-7 A A A A A A A A A A
A-5-8 A A A A A A A A A A
A-5-9 A A A A A A A A A A
A-6-6 A A A A A A A A A A
A-6-7 A A A A A A A A A A
A-6-8 A A A A A A A A A A
A-6-9 A A A A A A A A A A
A-7-7 A A A A A A A A A A
A-7-8 A A A A A A A A A A
A-7-9 A A A A A A A A A A
A-8-8 A A A A A A A A A A
A-8-9 A A A A A A A A A A
A-9-9 A A A A A A A A A A
A-A-2 A A A A A A A A A A
A-A-3 A A A A A A A A A A
A-A-4 A A A A A A A A A A
A-A-5 A A A A A A A A A A
A-A-6 A A A A A A A A A A
A-A-7 A A A A A A A A A A
A-A-8 A A A A A A 8 A A A
A-A-9 9 A A A A 9 9 9 9 9
A-A-A A A A A A A A A A A
X-2-2 2 2 2 2 2 2 2 2 2 2
X-2-3 2 2 2 2 2 2 2 2 2 2
X-2-4 2 2 2 2 2 2 2 2 2 2
X-2-5 2 2 2 2 2 2 2 2 2 2
X-2-6 2 2 2 2 2 2 2 2 2 2
X-2-7 7 7 7 7 7 7 2 2 2 2
X-2-8 8 8 8 8 8 8 8 8 8 8
X-2-9 9 9 9 9 9 9 9 9 9 9
X-3-3 3 3 3 3 3 3 3 3 3 3
X-3-4 3 3 3 3 3 3 3 3 3 3
X-3-5 3 3 3 3 3 3 3 3 3 3
X-3-6 3 3 3 3 3 3 3 3 3 3
X-3-7 7 7 7 7 7 7 3 3 7 3
X-3-8 8 8 8 8 8 8 8 8 8 8
X-3-9 9 9 X X X 9 9 9 9 9
X-4-4 4 4 4 4 4 4 4 4 4 4
X-4-5 4 4 4 4 4 4 4 4 4 4
X-4-6 4 4 4 4 4 4 4 4 4 4
X-4-7 7 7 7 7 7 7 4 7 7 4
X-4-8 8 8 X X X 8 8 8 8 8
X-4-9 X X X X X 9 9 9 9 9
X-5-5 5 5 5 5 5 5 5 5 5 5
X-5-6 5 5 5 5 5 5 5 5 5 5
X-5-7 7 7 X X X 7 7 7 7 5
X-5-8 X X X X X 8 8 8 8 8
X-5-9 X X X X X 9 9 9 9 9
X-6-6 6 6 6 6 6 6 6 6 6 6
X-6-7 X X X X X 7 7 7 7 7
X-6-8 X X X X X 8 8 8 8 8
X-6-9 X X X X X 9 9 9 9 9
X-7-7 7 7 7 7 7 7 7 X X 7
X-7-8 X X X X X X X X X 8
X-7-9 X X X X X X X X X X
X-8-8 X 8 8 8 8 X X X X X
X-8-9 X X X X X X X X X X
X-9-9 X X X X 9 X X X X X
X-A-2 A A A A A A A A A A
X-A-3 A A A A A A A A A A
X-A-4 A A A A A A A A A A
X-A-5 A A A A A A A A A A
X-A-6 A A A A A A A A A A
X-A-7 A A A A A A A A A A
X-A-8 A A A A A A A A A A
X-A-9 A A A A A A A A A A
X-A-A X X X X X X X X X X
X-X-2 X X X X X X X X X X
X-X-3 X X X X X X X X X X
X-X-4 X X X X X X X X X X
X-X-5 X X X X X X X X X X
X-X-6 X X X X X X X X X X
X-X-7 X X X X X X X X X X
X-X-8 X X X X X X X X X X
X-X-9 X X X X X X X X X X
X-X-A A A A A A A A A A A
X-X-X X X X X X X X X X X

Here is a compressed version of the table above, consolidating all hands that don't depend on the dealer card on the right.


After this point, the player should use standard blackjack basic strategy.

The only strategy regarding the 3 Card Bonus bet is to make three bets of equal size. Although betting more on the 3 Card Bonus is allowed, the player should never invoke this option.

3 Card Bonus

The following two tables show the probability and return for each event of the 3 Card Bonus bet for six and eight decks. The lower right cells show a house edge of 25.0% for six decks and 24.3% for eight decks. The math report indicates other pay tables are available, but this is the one seen at the Palazzo.

3 Card Bonus — Six Decks

Hand Pays Combinations Probability Return
Mini royal 75 864 0.000172 0.012926
Suited three of a kind 60 1,040 0.000207 0.012447
Straight flush 20 9,504 0.001896 0.037915
Three of a kind 10 25,272 0.005041 0.050410
Straight 2 155,520 0.031021 0.062043
Flush and pair 1.5 56,160 0.011202 0.016803
Flush 1.5 236,736 0.047221 0.070832
Pair 1 977,184 0.194918 0.194918
All other -1 3,551,040 0.708321 -0.708321
Total 5,013,320 1.000000 -0.250028

3 Card Bonus — Eight Decks

Hand Pays Combinations Probability Return
Mini royal 75 2,048 0.000172 0.012894
Suited three of a kind 60 2,912 0.000244 0.014667
Straight flush 20 22,528 0.001891 0.037824
Three of a kind 10 61,568 0.005169 0.051685
Straight 2 368,640 0.030947 0.061893
Flush and pair 1.5 139,776 0.011734 0.017601
Flush 1.5 561,152 0.047107 0.070661
Pair 1 2,336,256 0.196124 0.196124
All other -1 8,417,280 0.706612 -0.706612
Total 11,912,160 1.000000 -0.243263

Analysis

The following table shows the expected return of the blackjack, 3 Card Bonus, and overall game. The blackjack return shows the ratio of the expected number of units won between two blackjack wagers, based on two blackjack wagers of one unit each. The 3 Card Bonus column shows the expected return of a one-unit wager. The total return column shows the sum of the blackjack and 3 Card Bonus returns, divided by 3. In other words, this is the ratio of how much the player can expect to win to the total amount initially bet. For example, in an eight-deck game where the dealer hits a soft 17, if the player bets $5 on each of the three bets, he can expect to lose -.006365 x $15 = $0.0955.

Player's Choice 21 — Return Table

Decks Soft 17 BJ Return 3 Card Bonus Total Return
6 Stand 0.230456 -0.250028 -0.006524
6 Hit 0.224078 -0.250028 -0.008650
8 Stand 0.230456 -0.243263 -0.004269
8 Hit 0.224169 -0.243263 -0.006365

Acknowledgments

  • Greg Jaffa for his cooperation in the preparation of this page.
  • Charles Mousseau of Total Gaming Science for sharing his math report and spreadsheet on this game. Other than the 3 Card Bonus bet, all the math and strategy on this page is by Charles, whom I trust to be accurate.
  • Beachbumbabs for the compressed strategy table.

Written by: Michael Shackleford

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