Don’t allow a few statistics to scare you!
When I explain how Expected Value is calculated in video poker, it leaves many people a bit confused.
So we’ll start with a very simple initial deal: 3d, 3c, 3h, 8s, Qh.
You’re going to keep the Three of a Kind. You’re going to win way more money holding the 3’s. We calculate Expected Value by playing out every possible draw once we hold only the Three-of-a Kind. There are 1,081 possible 2-card draws. Of these, 46 will be Four-of-a-Kind, 66 will be Full Houses and the remaining 969 will be Three-of-a-Kinds.
We multiply these values by the payouts of these hands (25, 9 and 3 respectively), add them up and arrive at a value of 4,651. We then divide this by the 1,081 possible hands to arrive at our expected value of 4.30. Through math, it’s the best way to play the hand.
Here is a more complex case: 5d, 6d, 7d, 8c, 8s.
Of the 32 ways to play the hand, 29 will be quickly discarded, leaving three possible plays. You can either hold the 3-Card Straight Flush, the 4-Card Straight or the Pair. In each case, we are drawing a different number of cards, which is why we divide our result by the number of possible draws.
A computer program plays out each of the possible draws for each of our three scenarios and sums up the payouts. We find the 3-Card Straight Flush has an expected value of about 0.63, the 4-Card Straight about 0.68 and the Low Pair 0.82.
Expert Strategy dictates we play the highest expected value, which is to hold the Low Pair. Because the expected value is below 1, it means that in the long run this hand is a loser. Very few hands are actually winners. In this case we are actually trying to minimize our loss.
You do have to memorize the relative order of each hand in the strategy table. From this example, we play a Low Pair over a 4-Card Straight with no High Cards, and a 3-Card Straight Flush with no High Cards. If we didn’t have the Low Pair, we would play the 4-Card Straight over the 3-Card Straight Flush.