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Vegas Three Card Rummy

Introduction

Vegas Three Card Rummy is a poker variation found at Internet casinos using Cryptologic and Real Time Gaming software. The rules are similar to Three Card Poker, except hands are scored much differently and there is no ante bonus. Additionally, the raise bet pays up to 4 to 1 for premium hands.

Rules

  1. The game is played with a single 52-card deck.
  2. All cards are ranked according to their poker value, except aces are always low.
  3. The object is to have fewer points than the dealer.
  4. Play starts with the player making an ante bet plus an optional bonus bet.
  5. The player and dealer will each receive three cards. The dealer cards will be dealt face down. Both hands will be scored according to the table below. In the event a hand may be scored more than one way the lower total will be used.

  • Singleton aces count as 1 point, 2 to 10 count according to pip value, and faces cards are 10 points.
  • Pairs, three of a kind, and runs of at least 2 suited cards count as zero points.
  • After the player reviews his hand he has the choice of raising or folding. If the player raises he must make an additional bet equal to his ante bet.
  • The dealer will turn over his cards.
  • The dealer must have 20 points or less to qualify. If the dealer does not qualify, any remaining ante bets will pay even money and raise bets will push.
  • If the dealer does qualify the player and dealer totals will be compared, the lower total wins.
  • If the player has the lower total, the ante will pay even money and the raise according to following table. If the dealer has the lower total, the ante and raise will lose. A tie will result in a push.

    • Raise Pay Table

    Player Points Pays
    0 4 to 1
    1 to 5 2 to 1
    6 or more 1 to 1
  • The bonus bet will pay according to the pay table below.

    • Bonus Bet Pay Table

    Event Pays
    Suited A23 100 to 1
    0 points 25 to 1
    1 to 6 points 2 to 1
    7 to 10 points 1 to 1
    11 to 12 points 4 to 1
    13 to 30 points Loss

    In the following picture I bet $25 each on the ante and bonus bet. I then bet $25 on the raise bet. With a three of a kind my score was 0. The dealer's suited 10-jack is worth 0 points and the singleton 5 is worth 5, for a total of 5. My 0 beats the dealer's 5 so I won 1 to 1 or $25 on the ante, 4 to 1 or $100 on the raise, and 25 to 1 or $625 on the bonus bet, for a total win of $750.

    If these rules were not clear please have a look at how they are expressed at Bovada.

    Ante Bet Analysis

    The following table shows the possible outcomes of the ante bet assuming optimal player strategy. The lower right cell shows a house edge of 3.23%.

    Ante Bet Return Table

    Event Pays Combinations Probability Return
    Player beats dealer with 0 points 5 1188508 0.002919 0.014595
    Player beats dealer with 1-5 points 3 24911320 0.061182 0.183545
    Player beats dealer with 6 or more points 2 59776920 0.146811 0.293621
    Dealer doesn't qualify 1 91156848 0.223879 0.223879
    Tie 0 11459864 0.028145 0
    Player folds -1 132800192 0.326154 -0.326154
    Dealer beats player -2 85876748 0.210911 -0.421822
    Total 407170400 1 -0.032337

    The player will raise 67.38% of the time, for an average bet of 1.6738 units. The element of risk is thus 3.2337%/1.6738 = 1.93%.

    Bonus Bet Analysis

    The following table shows the possible outcomes of the bonus bet. The lower right cell shows a house edge of 3.46%.

    Bonus Bet Return Table

    Event Pays Combinations Probability Return
    Suited A23 100 4 0.000181 0.0181
    0 points 25 92 0.004163 0.104072
    1 to 6 points 2 2712 0.122715 0.24543
    7 to 10 points 1 3592 0.162534 0.162534
    11 to 12 points 4 644 0.02914 0.116561
    13 to 30 points -1 15056 0.681267 -0.681267
    Total 22100 1 -0.03457

    The bonus bet is always one unit so the element of risk is the same as the house edge at 3.54%.

    Strategy

    On the ante bet the player should have the same folding point as the dealer, raising with 20 or fewer points, and folding with 21 or more.

    In my opinion for purposes of comparing one bet to another the element or risk should be used, which is 1.96% for the ante bet, and 3.46% for the bonus bet. So between the two the ante is the better bet.

    Written by: Michael Shackleford