Calculation of the Video Poker Strategy
Above all, the exact play of every video poker hand is necessary for a perfect strategy in a long time. Every hand consists of five cards and every card has two opportunities: hold or discard. Therefore there are 2*2*2*2*2=32 ways to play each hand. To a perfect play it is required to select the only one way out of 32 that has maximum player edge on average. Note, the perfect way depends on hands payoff and the same hand with another payoff may have the different way to discard! So every video poker hand has the expected return that is the average win of the perfect discard way.
How many unique hands are in video poker? If the deck has 52 cards without wilds, then the first card is dealt out of 52, the second is dealt out of 51, etc. Thus, there are 52*51*50*49*48 = 311 875 200 video poker hands that could be dealt! This is the large value, let's try to reduce this number.
Firstly, the order of cards does not matter, i.e. 10,J,Q,K,A is the same as A,K,Q,J,10. It is possible to reduce the total number of hands 1*2*3*4*5=120 times and to get 2 598 960 hands.
In the second place, the suit order is not important also, i.e. 2,3,8,A,10 of hearts and 2,3,8,A,10 of spades are equal for strategy calculations. This condition allows to reduce the total number of hands to 134 459. It is not so easy to get this value manually as in previous paragraph; we use computer to calculate this number.
Therefore, the total expected return of video poker is the expected value of average wins of 134 459 hands. The perfect strategy is a set of 134 459 rules for playing all unique hands. These rules can be grouped together in more general laws to make the strategy suitable for humans. The human strategy usually consists of 20-40 rules for playing initial hand.
The next chapters contain the computation of total return for basic variations of video poker. All computations are made by Video Poker Calculator. You can use VP Calculator to get the more detailed information about various video pokers and to calculate all indexes for any game not found in this source.