Video Poker Strategy and Penalty Cards

Trying to master a video poker game when your goal is to play with 100% accuracy becomes very difficult.  Even for the simplest video poker game, Jacks or Better, players should to build a strategy card and practice many hours to work out kinks in their game before attempting to beat the casino for real money.  One area that I’ve overlooked for a long time is penalty cards.  These are cards that if thrown away will impact the likelihood of other paying hands on the draw. The difference is small, most of the time it turns out to be about a nickel per hand for dollar players. But if you’re trying to play with 100% accuracy, penalty cards matter.

An example of a penalty card situation would be if you are dealt: Ac Qd Td 3s 5d.  My strategy card says the higher value hold is Qd Td, and most of the time it is. But because holding these two cards would result in throwing away the 5d, it would reduce my chances of making a flush, and it makes the 5d a penalty card.  The correct play in this case is to hold the Ac Qd. Even though they are off-suited high cards, some of the value of Qd Td comes from the chance to make a flush. In this case, holding the two high cards, has an expected value of 0.474314 according to the Wizard of Odds video poker hand analyzer.   Holding the Qd Td has an expected value of 0.469812.  For a dollar player, this translates into the correct play having an expected value of $2.3715 (0.474314 * $5) and the incorrect play having an expected value of $2.3491 (0.469812 * $5) for a difference of 2.24 cents. Without the diamond, the better play is to dump the Ac and hold Qd Td.