Helping with 32 ways theory
June 26, 2018 3:00 AM
by Elliot Frome
Over the past couple of weeks I’ve discussed how strategy is formed in video poker. It all comes down to the expected value of hands. Each 5-card deal could theoretically be played 32 ways. For each of those 32 ways, we take a look at all the possible draws to calculate the expected value.
Whichever way has the highest expected value is the proper way to play the hand. The good news is you don’t have to do this yourself. Computer programs have been created that do all the number crunching. It’s a good thing too as these programs are looking at more than 6.7 trillion combinations of hands.
But with the computers doing the number crunching, how does that help the player? What does the player get from these programs to help him learn the right strategy? The end product of these programs are what is called a strategy table. It categorizes the dealt hands into full and partial hands in Expected Value order from high to low. The player simply needs to start at the top of the strategy table and work his way down.
When the dealt hand matches the hand description on the strategy table, that is the right way to play the hand. Most strategy tables will list out the Expected Values too, but the player doesn’t need know these. It does, however, behoove the player to memorize the order of the strategy table. Otherwise, you may find yourself playing very slowly while trying to figure out how to play each hand.
Strategy tables usually have about 35-40 rows on them. At the top we find mostly the pat hands – the ones that require no draw. At the bottom, we will always find the Razgu – which means to draw all five. In between are all the partial hands – Partial Straights, Flushes and Straight Flushes.
Straights and Straight Flushes are generally categorized by the number of cards in the Straight/Straight Flush, whether it is an outside, inside or double inside Straight and the number of High Cards. To make sure everyone understands these terms, I’m going to do my best to explain them and why they are important.
The easiest one is the number of cards in the Straight. The only way you get paid is if you have a 5-Card Straight. But after the deal, you may not have all five cards. You might only have four cards to the Straight or perhaps only three. I don’t think it will be much of a surprise to find out 4-Card Straights have higher Expected Values than 3-Card Straights as the probability of completing a 4-Card Straight is much higher.
Next up is whether the Straight is outside, inside or double inside. For the most part, this refers to the gaps in the Straight. A 5-6-7-8 is an outside straight. It is called this because to complete it you can do so by getting one card on the outside of either side of the straight (in this case a 4 or a 9).
A Straight is an Inside Straight if there is a one card gap in the middle (5-6-7-9 or 5-6-8 in the case of a 3-Card Straight). A Double Inside Straight is when there are two gaps (or one two-card gap) in the middle and applies only to a 3-Card Straight like a 5-7-9 Straight. This gets a bit confusing when we are talking about Straights at each extreme.
The J-Q-K-A 4-Card Straight is considered an INSIDE Straight because you cannot complete it with a card at either end (a Deuce will not complete the Straight). In similar fashion, an A-2-3 Straight is really a Double Inside Straight because it can only be completed ONE way (with a 4-5) just like a 3-5-7 Straight can only be completed with a 4-6.
Lastly, we keep track of the number of High Cards because holding a High Card increases the probability of drawing a High Pair, which increases the Expected Value of the hand. Thus, a 7-8-9-10 Straight has a lower Expected Value than a 9-10-J-Q Straight. With the latter we have six additional cards that will turn the hand into a High Pair and get us a payout.
Thankfully, Flushes are a bit less complex. In theory, they are categorized by the number of cards in the Flush and the number of High Cards. But in reality, we will find 3-Card Flushes are not playable in most versions of video poker and when we are looking at 4-Card Flushes, the number of High Cards becomes irrelevant. So, while we have a lot of partial Straight Flushes on our Strategy Table, we have just one partial Flush – the 4-Card Flush.
Next week, we’ll begin to dissect the strategy table for Jacks or Better starting with the Royal at the top and working our way down.