Non-Intuitive Video Poker Play II

12 November 2022

By Jerry Stickman

Video poker players enjoy the game for many reasons. They enjoy the fact that they have control over the outcome. They enjoy the higher returns usually afforded to them.

Generally, most video poker playing strategies intuitively makes sense. For example, if you are dealt three cards of a royal flush and a 3-9 off-suit, the logical hold is the three cards of the royal flush.

I get emails from video poker players inquiring why certain strategy plays are not intuitive. This article explores one non-intuitive play and explains the proper play mathematically.

The video poker games included are 9/6 and 8/5 Jacks or Better and 8/5 Bonus poker.

A common question from readers concerns holding an unsuited ace with two other unsuited face cards. This hand is also very difficult for several of my video poker-playing friends to understand.

The playing strategies for each of the three games call for holding a suited ace and face card. They each call for holding an unsuited ace and one face card. They all certainly call for holding a suited ace and two face cards (three of a royal flush). However, when the originally dealt hand contains an unsuited ace and two unsuited face cards plus two garbage cards, they all call for holding the two unsuited face cards and throwing the ace.

None of the strategies call for holding an unsuited ace and two face cards instead of just the two unsuited faces cards.

It is difficult for many players to rationalize discarding the ace which is a high card.

Let us see why it is the right play.

- Statistics for holding three unsuited high cards – the ace and two face cards
• 1,081 possible final hands
• 348 high pairs
• 27 hands with two pairs
• 9 hands with three of a kind
• 16 straights
• 0 flushes
• 0 full houses
• 0 hands with four of a kind
• 0 straight flushes
• 0 royal flushes

- Statistics for holding the two unsuited face cards:
• Also 16,215 possible final hands – 15 times the above
• 4,914 high pairs – ~ 14 times the above
• 711 hands with two pairs – ~ 26 times the above
• 281 hands with three of a kind – ~ 31 times the above
• 112 straights – 7 time the above
• 0 flushes – same as above
• 18 full houses – 18 more than above
• 2 hands with four of a kind – 2 more than above
• 0 straight flush – same as above
• 0 royal flushes – same as above

Holding the two unsuited face cards produces, on average, more hands with:
• a high pair
• two pairs
• three of a kind
• a straight
• a full house
• four of a kind

This hold never produces fewer paying hands.

The total average returns for the hands are close.

9/6 Jacks or Better:
- Holding the two unsuited face cards returns 2.4172 credits for the original five credits bet on average.
- Holding the unsuited ace and two face cards returns 2.2803 credits for the original five credits on average.

8/5 Jacks or Better:
- Holding the two unsuited face cards returns 2.4117 credits for the original five credits bet on average.
- Holding the unsuited ace and two face cards returns 2.2803 credits for the original five credits on average.

8/5 Bonus Poker:
- Holding the two unsuited face cards returns 2.4117 credits for the original five credits bet on average.
- Holding the unsuited ace and two face cards returns 2.2803 credits for the original five credits on average.

Holding just the two unsuited face cards ace is a better hold simply because of all the additional final hands that are possible. The combined additional hands possible by holding the two unsuited face cards outperform adding the ace to the hold.

Summary

While it may appear logical to hold the unsuited ace as well as the two unsuited face cards, the higher occurrence of hands with two pairs, a three of a kind, a full house, and a four of a kind more than offset throwing away a high card.

While it may be difficult for many video poker players – my friends included – the math says it is the proper thing to do.

As always, may all your wins be swift and large, and your losses be slow and small.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot machine play. He is a regular contributor to top gaming magazines. He authored the video poker section of "Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker!" You can contact Jerry “Stickman” at stickmanjerryg@gmail.com