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Ultimate Three Card Poker

Last Update: Jul 02, 2010

Introduction

Ultimate Three Card Poker is a variation on Three Card Poker I noticed at the Silver Legacy in Reno on Feb. 26, 2010. If you already know the rules for regular Three Card Poker, the rules for Ultimate Three Card Poker are the same, except:

  • The player may raise up to 3x his Ante bet if he has a pair or better.
  • The player must make an additional Blind bet, which most of the time will push or lose.
  • The player does not automatically win one unit if the dealer does not qualify; he still has to beat the dealer to win.
  • A winning raise bet pays even money only.

The full rules are as follows:

Rules

  1. A single 52-card deck is used.
  2. Hands are ranked in the following order, from highest to lowest:
    • Mini royal flush (suited AKQ)
    • Straight flush
    • Three of a kind
    • Straight
    • Flush
    • Pair
    • Ace high or less
  3. Play starts with the player making Ante and Blind bets, which must be equal. The player may also make a Pairplus bet, which is explained later.
  4. The player and dealer will each receive three cards. The dealer cards will be dealt face down.
  5. The player must decide to fold or raise. If the player has less than a pair, then the raise bet must be equal to the Ante bet. If the player has a pair or greater, then the raise bet must be equal to at least the Ante bet, and no more than three times the Ante bet.
  6. After the players have acted, the dealer will turn over his cards. If the dealer has a queen high or better, then the dealer will "qualify."
  7. The player's hand will be compared to the dealer's hand, and the one with the higher poker value shall win.
  8. The following is how each bet shall be adjudicated.

    Ante: If the dealer qualifies then the higher hand shall win. Ties push and wins pay even money. If the dealer does not qualify then the Ante shall push.
    Raise: The higher hand shall win. Ties push and wins pay even money.
    Blind: The higher hand shall win. Wins pay as follows:

    Blind Pay Table
    QuinellaPays
    Mini royal 100 to 1
    Straight flush 20 to 1
    Three of a kind 10 to 1
    Straight 2 to 1
    Flush 1 to 1
    Pair or less Push

  9. The Pairplus bet pays according to the poker value of the player's hand only. I have an unconfirmed report that the following pay table is used.

    Blind Pay Table
    QuinellaPays
    Mini royal 50 to 1
    Straight flush 40 to 1
    Three of a kind 30 to 1
    Straight 6 to 1
    Flush 4 to 1
    Pair 1 to 1
    Ace high or less Loss

Strategy

  • Fold with any hand less than J74
  • Raise 1x with better than J74 but less than pair
  • Raise 3x with a pair of better

Analysis

The following table shows the probability and contribution to the return for all possible outcomes. The "pays" column shows the combined win between the Ante, Blind, and Raise bets.

Ante&Blind Analysis
EventPaysCombinationsProbalityReturn
Raise of 3, dealer does qualify, player wins with mini royal 104 46804 0.000115 0.011955
Raise of 3, dealer does qualify, player wins with straight flush 24 570240 0.001400 0.033612
Raise of 3, dealer does qualify, player wins with three of a kind 14 665776 0.001635 0.022892
Raise of 3, dealer does qualify, player wins with straight 6 8975484 0.022044 0.132261
Raise of 3, dealer does qualify, player wins with flush 5 12793544 0.031421 0.157103
Raise of 3, dealer does qualify, player wins with pair 4 36168624 0.088829 0.355317
Raise of 3, dealer does qualify, player wins with less than pair 4 0 0.000000 0.000000
Raise of 3, dealer doesn't qualify, player wins with mini royal 103 26880 0.000066 0.006800
Raise of 3, dealer doesn't qualify, player wins with straight flush 23 239316 0.000588 0.013518
Raise of 3, dealer doesn't qualify, player wins with three of a kind 13 288960 0.000710 0.009226
Raise of 3, dealer doesn't qualify, player wins with straight 5 4001004 0.009826 0.049132
Raise of 3, dealer doesn't qualify, player wins with flush 4 6135276 0.015068 0.060272
Raise of 3, dealer doesn't qualify, player wins with pair 3 20926080 0.051394 0.154182
Raise of 3, dealer doesn't qualify, player wins with less than pair 3 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with mini royal 102 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with straight flush 22 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with three of a kind 12 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with straight 4 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with flush 3 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with pair 2 0 0.000000 0.000000
Raise of 1, dealer does qualify, player wins with less than pair 2 38197044 0.093811 0.187622
Raise of 1, dealer doesn't qualify, player wins with mini royal 101 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with straight flush 21 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with three of a kind 11 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with straight 3 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with flush 2 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with pair 1 0 0.000000 0.000000
Raise of 1, dealer doesn't qualify, player wins with less than pair 1 63271332 0.155393 0.155393
Raise of 3, dealer does qualify, push 0 32952 0.000081 0.000000
Raise of 3, dealer doesn't qualify, push 0 0 0.000000 0.000000
Raise of 1, dealer does qualify, push 0 246888 0.000606 0.000000
Raise of 1, dealer doesn't qualify, push 0 35052 0.000086 0.000000
Raise of 3, dealer does qualify, dealer wins -5 13408900 0.032932 -0.164660
Raise of 3, dealer doesn't qualify, dealer wins -4 0 0.000000 0.000000
Raise of 1, dealer does qualify, dealer wins -3 102146232 0.250869 -0.752606
Raise of 1, dealer doesn't qualify, dealer wins -2 609852 0.001498 -0.002996
Player folds -2 98384160 0.241629 -0.483258
Total 407170400 1.000000 -0.054235

The lower right cell shows a house edge of 5.42%. The average final wager is 3.270588 units, making the element of risk 5.42%/3.27 = 1.66%.

Pairplus Analysis
EventPaysCombinationsProbalityReturn
Mini royal 50 4 0.000181 0.009050
Straight flush 40 44 0.001991 0.079638
Three of a kind 30 52 0.002353 0.070588
Straight 6 720 0.032579 0.195475
Flush 4 1096 0.049593 0.198371
Pair 1 3744 0.169412 0.169412
Ace high or less -1 16440 0.743891 -0.743891
Total 0 22100 1.000000 -0.021357

The lower right cell shows a house edge of 2.14% on the Pairplus, which is the best I've ever seen.

Acknowledgement

I would like to thank Shufflemaster for providing me the math report by Elliot Frome for this game. My results agree exactly with Frome's.

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