# One-Eyed Jacks

## Introduction

One-Eyed Jacks is a video poker variation in which, you guessed it, one-eyed jacks (in hearts and spades) are wild. An exception is that a natural royal flush in hearts or spades counts, in other words the one-eyed jack is not forced to be wild.

## Return

### 75-50 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 517357408 0.000026 0.020764
Wild Royal Flush 200 5389058980 0.00027 0.054071
Five of a kind 75 9264247202 0.000465 0.034857
Straight Flush 50 40238004250 0.002019 0.100932
Four of a kind 15 402672195348 0.020201 0.303016
Full House 5 385743244800 0.019352 0.096759
Flush 3 351977034740 0.017658 0.052973
Straight 2 597327460550 0.029966 0.059933
Three of a kind 1 3688210843150 0.185028 0.185028
Two pair 1 1883259382770 0.094478 0.094478
Nonpaying hand 0 12568631688002 0.630537 0
Total   19933230517200 1 1.002811

### 80-50 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 513965766 0.000026 0.020627
Wild Royal Flush 180 5298275364 0.000266 0.047844
Five of a kind 80 9267845694 0.000465 0.037196
Straight Flush 50 40384893940 0.002026 0.1013
Four of a kind 15 402731777210 0.020204 0.303061
Full House 5 385817595960 0.019355 0.096777
Flush 3 351926707766 0.017655 0.052966
Straight 2 602973269682 0.03025 0.060499
Three of a kind 1 3687272139870 0.184981 0.184981
Two pair 1 1884221825082 0.094527 0.094527
Nonpaying hand 0 12562822220866 0.630245 0
Total   19933230517200 1 0.999779

### 75-45 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 519410406 0.000026 0.020846
Wild Royal Flush 200 5448315596 0.000273 0.054666
Five of a kind 75 9299546704 0.000467 0.03499
Straight Flush 45 39050705070 0.001959 0.088158
Four of a kind 15 404633593424 0.020299 0.304492
Full House 5 386766114210 0.019403 0.097015
Flush 3 349839099492 0.017551 0.052652
Straight 2 594391657846 0.029819 0.059638
Three of a kind 1 3703131704080 0.185777 0.185777
Two pair 1 1886760249222 0.094654 0.094654
Non-paying hand 0 12553390121150 0.629772 0
Total   19933230517200 1 0.992888

### 75-50 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 505681268 0.000025 0.020295
Wild Royal Flush 150 5183731554 0.00026 0.039008
Five of a kind 75 9264459196 0.000465 0.034858
Straight Flush 50 40624300588 0.002038 0.101901
Four of a kind 15 402596706420 0.020197 0.302959
Full House 5 385895841162 0.019359 0.096797
Flush 3 351974241246 0.017658 0.052973
Straight 2 610971665120 0.030651 0.061302
Three of a kind 1 3685952524350 0.184915 0.184915
Two pair 1 1884765467190 0.094554 0.094554
Non-paying hand 0 12555495899106 0.629878 0
Total   19933230517200 1 0.989562

### 75-45-15 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 508886194 0.000026 0.020424
Wild Royal Flush 150 5227969762 0.000262 0.039341
Five of a kind 75 9298239632 0.000466 0.034985
Straight Flush 45 39509893244 0.001982 0.089195
Four of a kind 15 404465659466 0.020291 0.304365
Full House 5 386848774332 0.019407 0.097036
Flush 3 350062001952 0.017562 0.052685
Straight 2 609840773972 0.030594 0.061188
Three of a kind 1 3699607396442 0.1856 0.1856
Two pair 1 1887943844064 0.094713 0.094713
Non-paying hand 0 12539917078140 0.629096 0
Total   19933230517200 1 0.979533

### 75-40-15 One-Eyed Jacks

Hand Pays Combinations Probability Return
Nat. Royal Flush 800 512466912 0.000026 0.020567
Wild Royal Flush 150 5270391894 0.000264 0.03966
Five of a kind 75 9323709972 0.000468 0.035081
Straight Flush 40 38815598626 0.001947 0.077891
Four of a kind 15 405683180324 0.020352 0.305282
Full House 5 386978190204 0.019414 0.097069
Flush 3 345061035094 0.017311 0.051933
Straight 2 617328690676 0.03097 0.06194
Three of a kind 1 3702984527850 0.185769 0.185769
Two pair 1 1883911002996 0.094511 0.094511
Non-paying hand 0 12537361722652 0.628968 0
Total   19933230517200 1 0.969703

## Strategy

Sorry, I don't have a strategy for this game. My computer figures out the optimal strategy by brute force. All I can give you is the following table, which shows the frequency of each number of discards for the 100.28% game.

### One-Eyed Jacks Number of Discards

0 34774 1.34%
1 299746 11.53%
2 465710 17.92%
3 1406832 54.13%
4 124722 4.80%
5 267176 10.28%
Total 2598960 100.00%

Other information: Bob Dancer addresses lists the returns for this game and many others in A Player's Guide to Good Video Poker Games (Strictly Slots, Nov. 2003).

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