Advanced Video Poker Strategy: QJs in AKQJx

[givememyleg]

A player recently submitted the following question:


On your simulator I got dealt Ace clubs, Jack spades, King Diamonds, Queen Spades, and 4 clubs. I held Ace clubs, Jack clubs, King Diamonds, Queen Spades but your simulator indicates Jack spades and queen of spades is the proper play, from everything I read 4 card straight with 2 high card beats 2 card royal flush?

http://www.winnergambling.com/casino-games/video-poker/jacks-or-better/

http://www.americancasinoguide.com/vp/vp-strategy-9-6.pdf

Here was my response:

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Running this hand on our calculator backs up our trainer: http://www.videopokertrainer.org/calculator/#AcJsKdQs4c-jb-mc96

It shows holding QsJs has an EV of 3.002 whereas holding AKQJ has an EV of 2.979. So this is a difference in EV of 0.023.

The charts you are referencing give basic strategy tips, but advanced play has some exceptions and rule changes. For example, the http://www.winnergambling.com/casino-games/video-poker/jacks-or-better/ rules state that following their strategy, you can expect a return of 99.52%. However, using advanced strategy this return is increased to 99.5439%. The reason you see more basic strategy rules is because the EV increase from basic to advanced is rather small and the rules are more complicated to explain. Most players can get by just fine playing based on basic strategy.

Your hand is an example of a small variation to the basic rules which is hard to explain. To complicate it even more, in your example holding QJs is the correct play, but if you were dealt AKs, AQs, AJs, KQs, or KJs in the same hand, it would be correct to hold the 4 big cards. QJs is the lone exception to the rule.

You can also reference http://wizardofodds.com/games/video-poker/hand-analyzer/ and input your hand, which shows the same results as our calculator.

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I thought posting it could help spark some discussion. What other exceptions are there from basic to advanced/optimal strategy?

[givememyleg]

This is even more interesting that I originally thought. It turns out if the random card is the same suit as the suit of QJs, it's a better play to hold AKQJ. In other words, changing the 4:c: to 4:s: changes the best play:

#1 A:c:J:s:K:d:Q:s:4:c:

Best Play, hold Q:s:J:s: (EV 3.002)

http://www.videopokertrainer.org/calculator/#AcJsKdQs4c-jb-mc96

#2 A:c:J:s:K:d:Q:s:4:s:

Best Play, hold A:c:J:s:K:d:Q:s: (EV 2.979)

http://www.videopokertrainer.org/calculator/#AcJsKdQs4s-jb-mc96

The extra spade reduces the EV of holding QJs to 2.919, a decrease of 0.083.

Situations like this are so minuscule in terms of EV, so have a very very minor impact on overall return, but are interesting nonetheless.

[givememyleg]

Found another exception, JTs beats KJo unless there is a flush card penalty. In other words:

J:c:T:c:K:d:6:h:5:d:

Best Play, hold J:c:T:c:

J:c:T:c:K:d:6:h:5:c:

Best Play, hold K:d:J:c:

Never knew about the flush penalty cards until now.