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Two Card Joker Poker
Introduction
Two Card Joker Poker is a poker-based game seen at the Foxwoods casino in April, 2009. It is similar to Three Card Poker, except a regular deck with two jokers is used, and each hand consists of only two cards.
Rules
- A 54-card deck is used, including two jokers. The jokers may only be used to complete a pair.
- Player makes an Ante and/or Pair Up bet.
- The dealer gives each player and himself 2 cards. The player may examine his cards. The dealer's cards are dealt face down.
- If the player made the Ante bet, he must fold or call.
- If the player folds, he forfeits his Ante wager.
- If the player calls, he must make a Call bet, exactly equal to his Ante bet.
- The dealer will reveal his cards.
- The dealer needs a Queen high or better to qualify.
- If the dealer does not qualify, the player wins even money on the Ante bet.
- If the dealer qualifies, the dealer's hand is compared to the player's hand according to the hand ranking chart below, the higher hand wins.
- If the dealer has the higher hand, then the Ante and Call bets lose.
- If the dealer has an identical hand, then the Ante and Call bets push.
- If the player has the higher hand, then the Ante bet pays even money and the Call bet pays according to the pay table below.
- The Pair Up bet pays based solely on the rank of the player's hand, as shown in the Pair Up section below.
Pay Table
Hand | Pays |
---|---|
Pair of Jokers | 8 to 1 |
Royal Flush | 5 to 1 |
Straight Flush | 3 to 1 |
All other | 1 to 1 |
Strategy
Strategy for the ante bet is extremely simple: raise with Queen-Five or better, and fold with Queen-Four or lower. For example, King-Two is higher than Queen-Five, and Jack-Nine is lower thanQueen-Five.
Ante Game Analysis
The following table lists all possible outcomes. The lower-right corner shows a house edge of 3.15%. The average wager is 1.672956 times the Ante bet, which makes the element of risk for this game 1.88%, a better bet than Three Card Poker.Ante Return Table
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Win with Pair of Jokers | 9 | 894 | 0.000471 | 0.00424 |
Win with Royal Flush | 6 | 3560 | 0.001876 | 0.011257 |
Win with Straight Flush | 4 | 43252 | 0.022794 | 0.091177 |
Win with Straight | 2 | 130676 | 0.068867 | 0.137734 |
Win with Pair | 2 | 111864 | 0.058953 | 0.117906 |
Win with Flush | 2 | 114460 | 0.060321 | 0.120643 |
Win with High Card | 2 | 52344 | 0.027586 | 0.055171 |
Dealer Not Qualified | 1 | 389736 | 0.205394 | 0.205394 |
Push | 0 | 5178 | 0.002729 | 0 |
Fold | -1 | 620568 | 0.327044 | -0.327044 |
Lose | -2 | 424974 | 0.223965 | -0.447929 |
Total | 1897506 | 1 | -0.031451 |
Pair Up Side Bet Analysis
The Pair Up side bet is similar to the Pair Plus bet in Three Card Poker, and can be made in addition to or instead of the ante wager. The following table shows the different possible outcomes for this bet. The lower-right cell shows a house edge of 2.0964%.
Pair Up Return Table
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Pair of Jokers | 40 | 1 | 0.000699 | 0.027952 |
Royal Flush | 20 | 4 | 0.002795 | 0.055905 |
Straight Flush | 5 | 48 | 0.033543 | 0.167715 |
Straight | 3 | 156 | 0.109015 | 0.327044 |
Pair | 1 | 182 | 0.127184 | 0.127184 |
All other | -1 | 1040 | 0.726765 | -0.726765 |
Total | 1431 | 1 | -0.020964 |
Detailed Hand Analysis
The following table shows the expected value of every possible hand. Hands with an expected value greater than -1 should be called, because they will lose less on average than the unit that would be lost by folding.
Ante Bet Expected Value Table
Hand | Expected Value | Correct Play |
---|---|---|
Pair - Jokers | 6.393665 | Call |
Suited KA | 4.351433 | Call |
Suited TJ | 3.061086 | Call |
Suited 9T | 3.036199 | Call |
Suited JQ | 3.031674 | Call |
Suited 89 | 3.018100 | Call |
Suited 78 | 3.000000 | Call |
Suited QK | 2.995475 | Call |
Suited 67 | 2.981900 | Call |
Suited 56 | 2.963801 | Call |
Suited 45 | 2.945701 | Call |
Suited 34 | 2.927602 | Call |
Suited 23 | 2.916290 | Call |
Suited 2A | 2.855204 | Call |
Wild Pair - AA | 1.518854 | Call |
Unsuited KA | 1.497738 | Call |
Unsuited QK | 1.464555 | Call |
Unsuited JQ | 1.446456 | Call |
Unsuited TJ | 1.426094 | Call |
Unsuited 9T | 1.387632 | Call |
Unsuited 89 | 1.351433 | Call |
Unsuited 78 | 1.315234 | Call |
Unsuited 67 | 1.279035 | Call |
Unsuited 56 | 1.242836 | Call |
Unsuited 45 | 1.206637 | Call |
Unsuited 34 | 1.170437 | Call |
Unsuited 23 | 1.136501 | Call |
Unsuited 2A | 1.099548 | Call |
Pair - AA | 1.078431 | Call |
Pair - KK | 1.042232 | Call |
Wild Pair - KK | 1.031674 | Call |
Wild Pair - QQ | 1.001508 | Call |
Pair - QQ | 1.000000 | Call |
Pair - JJ | 0.993967 | Call |
Wild Pair - JJ | 0.989442 | Call |
Wild Pair - TT | 0.957014 | Call |
Pair - TT | 0.947210 | Call |
Wild Pair - 99 | 0.926848 | Call |
Pair - 99 | 0.904977 | Call |
Wild Pair - 88 | 0.896682 | Call |
Wild Pair - 77 | 0.866516 | Call |
Pair - 88 | 0.862745 | Call |
Wild Pair - 66 | 0.836350 | Call |
Pair - 77 | 0.820513 | Call |
Wild Pair - 55 | 0.806184 | Call |
Pair - 66 | 0.778281 | Call |
Wild Pair - 44 | 0.776018 | Call |
Wild Pair - 33 | 0.745852 | Call |
Pair - 55 | 0.736048 | Call |
Wild Pair - 22 | 0.717949 | Call |
Pair - 44 | 0.693816 | Call |
Pair - 33 | 0.651584 | Call |
Pair - 22 | 0.613876 | Call |
Suited JA | 0.577677 | Call |
Suited QA | 0.568627 | Call |
Suited TA | 0.566365 | Call |
Suited 9A | 0.557315 | Call |
Suited 8A | 0.548265 | Call |
Suited 7A | 0.539216 | Call |
Suited 6A | 0.530166 | Call |
Suited 5A | 0.521116 | Call |
Suited 4A | 0.512066 | Call |
Suited 3A | 0.503017 | Call |
Suited JK | 0.469080 | Call |
Suited TK | 0.457768 | Call |
Suited 9K | 0.448718 | Call |
Suited 8K | 0.439668 | Call |
Suited 7K | 0.430618 | Call |
Suited 6K | 0.421569 | Call |
Suited 5K | 0.412519 | Call |
Suited 4K | 0.403469 | Call |
Suited 3K | 0.394419 | Call |
Suited 2K | 0.384615 | Call |
Suited TQ | 0.352187 | Call |
Suited 9Q | 0.343137 | Call |
Suited 8Q | 0.334087 | Call |
Suited 7Q | 0.325038 | Call |
Suited 6Q | 0.315988 | Call |
Suited 5Q | 0.306938 | Call |
Suited 4Q | 0.297888 | Call |
Suited 3Q | 0.288839 | Call |
Suited 2Q | 0.279035 | Call |
Suited 9J | 0.267722 | Call |
Suited 8J | 0.258673 | Call |
Suited 7J | 0.249623 | Call |
Suited 6J | 0.240573 | Call |
Suited 5J | 0.231523 | Call |
Suited 4J | 0.222474 | Call |
Suited 3J | 0.213424 | Call |
Suited 2J | 0.203620 | Call |
Suited 8T | 0.174962 | Call |
Suited 7T | 0.165913 | Call |
Suited 6T | 0.156863 | Call |
Suited 5T | 0.147813 | Call |
Suited 4T | 0.138763 | Call |
Suited 3T | 0.129713 | Call |
Suited 2T | 0.119910 | Call |
Suited 79 | 0.096531 | Call |
Suited 69 | 0.087481 | Call |
Suited 59 | 0.078431 | Call |
Suited 49 | 0.069382 | Call |
Suited 39 | 0.060332 | Call |
Suited 29 | 0.050528 | Call |
Suited 68 | 0.030166 | Call |
Suited 58 | 0.021116 | Call |
Suited 48 | 0.012066 | Call |
Suited 38 | 0.003017 | Call |
Suited 28 | -0.006787 | Call |
Suited 57 | -0.024133 | Call |
Suited 47 | -0.033183 | Call |
Suited 37 | -0.042232 | Call |
Suited 27 | -0.052036 | Call |
Suited 46 | -0.066365 | Call |
Suited 36 | -0.075415 | Call |
Suited 26 | -0.085219 | Call |
Suited 35 | -0.096531 | Call |
Suited 25 | -0.106335 | Call |
Suited 24 | -0.115385 | Call |
Unsuited QA | -0.161388 | Call |
Unsuited JA | -0.170437 | Call |
Unsuited TA | -0.199849 | Call |
Unsuited 9A | -0.226998 | Call |
Unsuited 8A | -0.254148 | Call |
Unsuited 7A | -0.281297 | Call |
Unsuited 6A | -0.308446 | Call |
Unsuited 5A | -0.335596 | Call |
Unsuited 4A | -0.362745 | Call |
Unsuited 3A | -0.389894 | Call |
Unsuited JK | -0.496229 | Call |
Unsuited TK | -0.525641 | Call |
Unsuited 9K | -0.552790 | Call |
Unsuited 8K | -0.579940 | Call |
Unsuited 7K | -0.607089 | Call |
Unsuited 6K | -0.634238 | Call |
Unsuited 5K | -0.661388 | Call |
Unsuited 4K | -0.688537 | Call |
Unsuited 3K | -0.715686 | Call |
Unsuited 2K | -0.749623 | Call |
Unsuited TQ | -0.842383 | Call |
Unsuited 9Q | -0.869532 | Call |
Unsuited 8Q | -0.896682 | Call |
Unsuited 7Q | -0.923831 | Call |
Unsuited 6Q | -0.950980 | Call |
Unsuited 5Q | -0.978130 | Call |
Unsuited 4Q | -1.005279 | Fold |
Unsuited 3Q | -1.032428 | Fold |
Unsuited 2Q | -1.066365 | Fold |
Unsuited 35 | -1.115385 | Fold |
Unsuited 36 | -1.115385 | Fold |
Unsuited 37 | -1.115385 | Fold |
Unsuited 38 | -1.115385 | Fold |
Unsuited 39 | -1.115385 | Fold |
Unsuited 3T | -1.115385 | Fold |
Unsuited 46 | -1.115385 | Fold |
Unsuited 47 | -1.115385 | Fold |
Unsuited 48 | -1.115385 | Fold |
Unsuited 49 | -1.115385 | Fold |
Unsuited 4T | -1.115385 | Fold |
Unsuited 57 | -1.115385 | Fold |
Unsuited 58 | -1.115385 | Fold |
Unsuited 59 | -1.115385 | Fold |
Unsuited 5T | -1.115385 | Fold |
Unsuited 68 | -1.115385 | Fold |
Unsuited 69 | -1.115385 | Fold |
Unsuited 6T | -1.115385 | Fold |
Unsuited 79 | -1.115385 | Fold |
Unsuited 7T | -1.115385 | Fold |
Unsuited 8T | -1.115385 | Fold |
Unsuited 24 | -1.122172 | Fold |
Unsuited 25 | -1.122172 | Fold |
Unsuited 26 | -1.122172 | Fold |
Unsuited 27 | -1.122172 | Fold |
Unsuited 28 | -1.122172 | Fold |
Unsuited 29 | -1.122172 | Fold |
Unsuited 2T | -1.122172 | Fold |
Unsuited 3J | -1.122172 | Fold |
Unsuited 4J | -1.122172 | Fold |
Unsuited 5J | -1.122172 | Fold |
Unsuited 6J | -1.122172 | Fold |
Unsuited 7J | -1.122172 | Fold |
Unsuited 8J | -1.122172 | Fold |
Unsuited 9J | -1.122172 | Fold |
Unsuited 2J | -1.128959 | Fold |
For academic purposes only, a strategy that raises every hand would yield a house edge of 6.8067% and an element of risk of 3.4034%.
Acknowledgements
I would like to thank J.B. for his analysis of this game.