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Last Updated: February 12, 2019

# Opponent Poker

## Introduction

Opponent Poker is a video poker variation I noticed at the Red Rock Resort on December 17, 2006. The first five credits bet plays like ordinary video poker, and the second five credits are pooled together with two computer opponents, the best video poker hand takes all.

## Rules

1. The player may bet 0, 1, 2, 3, 4, 5, or 10 credits.
2. If the player bets 5 or fewer credits the game will play like ordinary video poker.
3. If the player bets ten credits, five will act as a normal video poker bet. The other five credits will be used to play against two computer opponents.
4. Assuming ten credits are bet, after the initial five cards are dealt both computer opponents will indicate which cards they will hold. According to the game rules the opponent strategy is "a standard poker strategy." I do not know this strategy, but based on playing Opponent Poker myself it is usually, but not always, optimal video poker strategy.
5. The player will choose which cards he wishes to hold.
6. The player and both opponents will be dealt replacement cards from the same 52-card deck.
7. If the player has a higher paying video poker hand than the other two computer opponents then he shall win the video poker winnings from all three hands.
8. In the event two or three participants tie for the highest paying video poker hand then the pot of combined video poker winnings shall carry over to the next hand.
9. In the event of a tie between hands the player may opt to split the pot. Split pots will be rounded down to the nearest credit.
10. The pot will automatically be split if there is a dealt royal flush, the player cashes out, or the player switches games.

## Strategy

I don't know what the "standard poker strategy" for the computer opponents is so I can not quantify an optimal player strategy. I tend to think that if the player followed optimal video poker strategy for the given pay table his return would be greater than that of conventional video poker. The player should not always play the same way as the computer opponents. As one example the hand on the deal wasKAQ89.Both computer opponents held the queen, king, and ace. Optimal video poker strategy is to hold the king and queen only. Holding the same cards as the computer opponents always results in the same expected value as conventional video poker. In this case holding the three high cards has an expected value of 4.560592 credits (2.280296 credits for both the video poker and opponent bet). Holding the queen and king only has an expected value of 4.863301 credits (2.397471 for the video poker hand and 2.46583 for the opponent bet). This just goes to show (1) the opponents don't always follow optimal video poker strategy, and (2) you should not always play the same way as the opponents.

## Return

As stated in the strategy section I don't know "standard poker strategy" and thus can neither quantify either a perfect strategy nor the maximum return. All I can do is indicate the return tables for the video poker tables observed at the Red Rock Resort. I do believe the maximum return is slightly higher than the returns below.

### "9/5" Jacks or Better

Hand Payoff Combinations Probability Return
Royal flush 800 496237776 0.000025 0.019916
Straight flush 50 2137447980 0.000107 0.005362
4 of a kind 25 47100799404 0.002363 0.059073
Full house 9 229510637676 0.011514 0.103626
Flush 5 217120426644 0.010892 0.054462
Straight 4 223861063908 0.011231 0.044922
3 of a kind 3 1484332642620 0.074465 0.223396
Two pair 2 2577431192796 0.129303 0.258606
Jacks or better 1 4288342040640 0.215135 0.215135
Nothing 0 10862898027756 0.544964 0.000000
Total   0 1.000000 0.984498

### "8/5" Bonus Poker Deluxe

Hand Payoff Combinations Probability Return
Royal flush 800 491855652 0.000025 0.019740
Straight flush 50 2154130740 0.000108 0.005403
4 of a kind 80 47005788324 0.002358 0.188653
Full house 8 228890564676 0.011483 0.091863
Flush 5 216493699248 0.010861 0.054305
Straight 4 260258167080 0.013056 0.052226
3 of a kind 3 1475243948064 0.074009 0.222028
Two pair 1 2556435840408 0.128250 0.128250
Jacks or better 1 4216703051664 0.211541 0.211541
Nothing 0 10929553471344 0.548308 0.000000
Total   19933230517200 1.000000 0.974009

### "9/5" Double Double Bonus — 97.87%

Hand Payoff Combinations Probability Return
Royal flush 800 497516688 0.000025 0.019967
Straight flush 50 2123092824 0.000107 0.005326
4 aces + 2-4 400 1228310184 0.000062 0.024648
4 2-4 + A-4 160 2854473252 0.000143 0.022912
4 aces + 5-K 160 3459809880 0.000174 0.027771
4 2-4 + 5-K 80 7662852888 0.000384 0.030754
4 5-K 50 32536223652 0.001632 0.081613
Full house 9 216639836640 0.010868 0.097814
Flush 5 218785162368 0.010976 0.054880
Straight 4 257980198392 0.012942 0.051769
3 of a kind 3 1501776975600 0.075340 0.226021
Two pair 1 2454744788496 0.123148 0.123148
Jacks or better 1 4227940545588 0.212105 0.212105
Nothing 0 11005000730748 0.552093 0.000000
Total 0 19933230517200 1.000000 0.978729

### Deuces Wild — 97.58%

Hand Payoff Combinations Probability Return
Natural royal flush 800 452258388 0.000023 0.018151
Four deuces 200 3681116136 0.000185 0.036934
Wild royal flush 20 35519655168 0.001782 0.035639
Five of a kind 12 59450103984 0.002982 0.035790
Straight flush 10 109163645748 0.005476 0.054765
Four of a kind 4 1213460173776 0.060876 0.243505
Full house 4 520454143512 0.026110 0.104439
Flush 3 420473233680 0.021094 0.063282
Straight 2 1160573109144 0.058223 0.116446
Three of a kind 1 5318990094612 0.266840 0.266840
Nothing 0 11091012983052 0.556408 0.000000
Total 0 19933230517200 1.000000 0.975791

One interesting thing about this game is that according to the rules the pot can grow infinitely. This does not seem to run afoul of Nevada Gaming Control Board regulation 14.2.070, which states if the probability of hitting the top jackpot is less than 1 in 100 million then that probability must be prominently displayed. On any given hand the highest award is the pot plus 8000 credits, for a dealt royal, and that probability is 1 in 649,740.

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