# 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

1. A 54-card deck is used, including two jokers. The jokers may only be used to complete a pair.
2. Player makes an Ante and/or Pair Up bet.
3. The dealer gives each player and himself 2 cards. The player may examine his cards. The dealer's cards are dealt face down.
4. If the player made the Ante bet, he must fold or call.
5. If the player folds, he forfeits his Ante wager.
6. If the player calls, he must make a Call bet, exactly equal to his Ante bet.
7. The dealer will reveal his cards.
8. The dealer needs a Queen high or better to qualify.
9. If the dealer does not qualify, the player wins even money on the Ante bet.
10. 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.
11. If the dealer has the higher hand, then the Ante and Call bets lose.
12. If the dealer has an identical hand, then the Ante and Call bets push.
13. 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.
14. 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.