Video Poker — Probability of winning hand by number of cards held

I have always wondered if I ever did get a royal flush in video poker would it likely be after holding 3, 4, or some other numbers of cards on the deal. This section answers that question, not just for royal flushes but every hand. Everything is based on full pay deuces wild and optimal strategy. When the player holds four deuces the program holds all five cards.

 

The above table shows that 54% of royals will come after holding 3 to a royal, and 32% after holding 4 to a royal. Four deuces will come along 34% of the time holding 3 deuces and 37% holding 2 deuces.

The next table shows the overall probability of each hand according to the number of cards held on the deal

 

The final table summarizes this information, showing the probability of holding each number of cards, the expected value, and the contribution to the total return. This table shows among other things that the most common play is holding 2 cards and the most of the return comes when holding 3 cards.

 

Finally, here are the number of royal flush combinations in 9/6 Jacks or Better, out of a possible 19,933,230,517,200, by the number of cards held. The right column shows the ratio of all royals according to number of cards held.

 

Written by: Michael Shackleford