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Last updated: July 17, 2013
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Six Card Poker
Rules
Six♣️ Card
Poker is a poker variant game played heads up against the dealer. The object of the
game is to♣️ win by having a better five-card poker hand than the dealer using six cards.
The game is played using one♣️ standard 52-card deck. The game uses standard poker rules
for scoring and comparing hands. To begin, the player makes an♣️ Ante Bet. The dealer
deals six cards face down to the player. The dealer deals to himself, three cards face
♣️ up and three cards face down. The player examines his cards and must either fold the
hand, losing his Ante,♣️ or raise by making an additional wager that is equal to his
Ante. Players may not share information about their♣️ cards with other players. The
dealer reveals his hole cards and compares his best five-card hand to the player’s best
♣️ five-card hand. The dealer must qualify with ace-king or higher. If the dealer does not
qualify, then the player’s Ante♣️ bet is a push. The raise bet is resolved as follows: If
the dealer's hand beats the player's hand, then♣️ the player loses his raise bet.
If the
player's hand beats the dealer's hand, then the player is paid 1 to♣️ 1 on his raise
bet.
In the event of a tie, the player’s raise bet is a push. If the dealer♣️ does
qualify: If the dealer's hand beats the player’s hand, then the player loses his Ante
and raise bets.
If the♣️ player's hand beats the dealer’s hand, then the player is paid 1
to 1 on his Ante and raise bets.
In♣️ the event of a tie, the player’s Ante and raise
bets push. There are also two optional side bets, the♣️ Aces Up and Two-Way Bad Beat,
which are explained below.
Analysis
Ante Bet Analysis Outcome Dealer Qualifies Net Win
Combinations Probability Return♣️ Player Wins yes 2 1,040,023,036,938,350 0.272693
0.545387 Player Wins no 1 755,514,209,224,548 0.198095 0.198095 Ties yes 0
210,847,746,240 0.000055 0.000000♣️ Ties no 0 50,992,983,876 0.000013 0.000000 Fold - -1
1,149,186,512,820,950 0.301316 -0.301316 Dealer Wins no -1 2,937,744,249,924 0.000770
-0.000770 Dealer♣️ Wins yes -2 865,968,968,971,212 0.227056 -0.454113 Total
3,813,892,312,935,100 1.000000 -0.012717
Strategy
Fold if dealer has a higher ranked
hand using his three♣️ up cards alone. This rule supersedes all other rules. Fold with
ace-10 or lower. Raise with ace-king or higher. With♣️ ace-queen, fold if the dealer is
showing an ace or king. With ace-jack, fold if the dealer is showing an♣️ ace, king, or
queen.
Fold if dealer has a higher ranked hand using his three up cards alone. This
rule supersedes♣️ all other rules. Raise with ace-king. Fold otherwise.
With optimal
play, the house edge is 1.27%.
Using the intermediate basic strategy, the♣️ house edge is
1.48 %.
Using the simple basic strategy, the house edge is 1.63%.
Aces Up
The game was
analyzed through brute♣️ force, combinatorial analysis. The following table summarizes
the analysis results. The bottom left cell shows the house edge of 1.2717%.♣️ With an
average bet size of 1.6987, the element of risk is 0.7486%.Two basic playing strategies
are presented below.
Aces Up♣️ is a side bet based on the poker-value of the player's
hand only. The following table shows what each hand♣️ pays, the probability, and
contribution to the return. The lower right cell reflects a house edge of 3.30%.
Aces
Up Analysis♣️ Event Pays Combinations Probability Return Royal flush 500 188 0.000009
0.004617 Straight flush 100 1,656 0.000081 0.008134 Four of a♣️ kind 30 14,664 0.000720
0.021609 Full house 10 165,984 0.008153 0.081530 Flush 8 205,792 0.010108 0.080867
Straight 6 361,620 0.017763♣️ 0.106576 Three of a kind 4 732,160 0.035963 0.143853 Two
pair 2 2,532,816 0.124411 0.248821 Aces 1 751,332 0.036905 0.036905♣️ Loser -1 15,592,308
0.765886 -0.765886 Total 20,358,520 1.000000 -0.032973
Two-Way Bad Beat
The "Two-Way
Bad Beat" pays if either you or the♣️ dealer has at least a pair of aces and loses. The
higher the losing hand, the more the bet pays.♣️ In other words, it pays based on the
worse hand between you and the dealer, as long as they don't♣️ tie.
The following table
shows all the odds. The zeros for the probability and return of a losing straight flush
are♣️ not a mistake. The probability of that is about 1 in 25 trillion. Such a situation
was the basis of♣️ the movie Honeymoon in Vegas, but I'm getting off topic. The lower
right cell of the table below shows a♣️ house edge of 10.84%.
Two-Way Bad Beat Analysis
Event Pays Probability Return Straight Flush 10000 0.000000 0.000000 Four of a Kind
♣️ 5000 0.000001 0.006250 Full House 500 0.000099 0.049370 Flush 200 0.000307 0.061440
Straight 100 0.000972 0.097168 Three of a Kind♣️ 35 0.004056 0.141965 Two Pair 10
0.034513 0.345127 Pair of Aces 9 0.015036 0.135328 Loser -1 0.945016 -0.945016 Total
1.000000♣️ -0.108367
Acknowledgments
Usually, I like to do my own math. However, in this
case ShuffleMaster, who is marketing the game, kindly provided♣️ the math report by
mathematician Cindy Liu, which the Ante bet analysis is based on. The Two Way Bad Beat
♣️ is based on the work of Elliot Frome. I did the analysis of Aces Up.
Written by:
Michael Shackleford
