Expected values key to expert video poker
July 25, 2017 3:00 AM
by Elliot Frome
When my father, Lenny Frome, first set out to analyze video poker 25 or 30 years ago, he coined the phrase “expected value” to refer to the average amount returned to the player when playing expert strategy.
The expected value of a Low Pair is 0.82. This means 82 cents of every dollar wagered is returned when the player has a Low Pair, on average. Everything is “on average” or “in the long run.” It’s not possible to have 82% of your wager returned on any single Low Pair. You either don’t improve the hand and lose your wager or get Two Pair or Three of a Kind and win two or three units.
The concept my father used wasn’t really new. The same process had been used to analyze blackjack for years. In video poker, we play the hand whichever way produces the highest expected value. That’s exactly how we determine to hit or stick in blackjack.
There are, however, two distinct differences in these situations. The first, sometimes in blackjack you increase your wager mid-hand – you double down. In these cases, we really need to report the expected value as a percent of the initial wager. After all, which is really better, an expected value of 1.1 on a one-unit wager or 1.08 on a two-unit wager. In the first case, we will win a dime and in the second case you will win 16 cents (assuming a $1 wager).
This leads in well to the second difference. You almost never hear anyone talk about the expected value of a blackjack hand. This is because in blackjack there is a relatively limited and clearly distinct way to play a hand. At most, you can hit, stick, double, split or surrender.
There are only five options and it is rare for more than two or three to come into play. Further, these are the actions we can take and not a description of the hand. Most hands are what they obviously are – a Hard 12 vs. a Dealer 7. You get a few that can be multiple things. You can have a 10, made up of a Pair of 5’s that require a decision as to whether to consider this a Hard 10 or a Pair.
In video poker, the hands are not easily defined. You have five cards that can easily be multiple things at the same time. A hand can be a Low Pair that is a 4-card Straight that can be a 3-Card Straight Flush that is also a 2-Card Royal.
Consider the following hand: 9 clubs, 9, 10, J hearts, Q diamonds. This could conceivably be played as any of the four previously mentioned hands.
Given there are 2,598,960 different five-card deals, it would be absurd to create a strategy that says “if you are dealt a Low Pair that is also a 4-Card open-ended Straight with two High Cards and a 3-Card Straight Flush with one High Card and a 2-Card Royal of 10-J, then play it as xxx.
There would be hundreds of rules for all the hands that are more than one type of hand. If that Queen of Diamonds was a King of Spades, I’d have to describe it differently. That pair of 9’s could be a Pair of Jacks instead and that would be a totally different description.
So, where blackjack describes each hand vs. each dealer upcard and gives you a clear strategy, video poker must do things differently. Instead of listing each combination of hands, we use a strategy table that lists each single type of hand along with its expected value, in order, from highest expected value to lowest.
So, if we look at a video poker strategy table for jacks or better, we will find one entry for each of those four possible hands. We find a Low Pair has an expected value of 0.82. A 4-Card Straight with two High Cards is right below it at 0.81. A 3-Card Straight Flush with one High card is three entries below that at 0.72. Last, and least, we have a 2-Card Royal (10-J), near the bottom of our table at 0.48.
So, rather than replacing the xxx in my prior statement with “then Play as a Low Pair,” we instead tell the player to find the hand with the highest expected value that can be found in the five-card deal and that is how you play the hand. In this case, that means playing the hand as a Low Pair, which had the highest expected value. By doing this, we don’t have to spell out every possible combination of each hand.
The overlap of Pairs with Straights and Straight Flushes is extensive. This is further complicated by needing to know the number of High Cards in the hand as we intend to play it. We wind up with a much more useful strategy by simply listing it out the way we do.
While most strategy tables list the hand as we should play it, the specific expected value is not really needed. The table only needs to be in order from highest to lowest. Listing the expected value does have some benefit, however, in letting the player know how big a mistake he would be making if he chooses to play it another way.
In my example above, playing the hand as a 4-Card Straight with two High Cards would only lower the expected value by 0.01. That doesn’t mean you should do it, but it does mean doing so will not cost you significantly, and should you make an occasional mistake as we humans are prone to do, the impact will be barely perceptible.
On the other hand, if you routinely chase the 2-Card Royal in these cases, you’re likely to run out of money before you get to that Royal.
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