A couple of weeks ago I discussed how the expected value of a hand is calculated and how it guides the player’s strategy when playing video poker. Nobody expects any player to calculate the expected value on the fly. Except for hands where you draw only one card, it would be nearly impossible for almost everyone to do so.

Analysts such as myself have already done all the work for the player. We’ve calculated the expected value of all 2,598,960 hands. These hands are then categorized and put into a strategy table.

A strategy table is just a list of playable hands and their respective expected value. Ironically, the specific value is just for information purposes. All a player really needs is a list of hands in expected value order. The player simply needs to start at the top and work his way down until he finds a hand category that matches the hand that was dealt.

So, if the hand dealt was a Low Pair and also a 4-Card Straight and also a 2-Card Royal, the player just scans from the top and the first of the hands will be the Low Pair unless the hand is the one type of 4-Card Straight that plays over the Low Pair. This is the 10-J-Q-K. If the fifth card is another 10, the player would still play the 4-Card Straight.

The strategy table would be much shorter if not for the fact that Straights and Straight Flushes must be broken down by how many High Cards there are in them. Each High Card presents an opportunity to draw to a High Pair. When you are talking about partial Straight hands, the probability of winding up with a High Pair contributes greatly to the expected value. In the case of 10-J-Q-K, there 9 cards that will give us a High Pair and 8 which will give us our Straight.

The strategy table would be much shorter if not for the fact that Straights and Straight Flushes must be broken down by how many High Cards there are in them. Each High Card presents an opportunity to draw to a High Pair. When you are talking about partial Straight hands, the probability of winding up with a High Pair contributes greatly to the expected value. In the case of 10-J-Q-K, there 9 cards that will give us a High Pair and 8 which will give us our StraightWow! Congratulations to this lucky @Caesars_Rewards member for winning $120,000 playing video poker!ðŸ¤‘ pic.twitter.com/jU0QJvqlTE

— Horseshoe Tunica (@Horseshoetunica) October 27, 2020

If you recall from a few weeks ago about how to calculate the expected value, we take these numbers and multiply them by their respective payouts. So, we have 8 Straights x 4 plus 9 High Pairs x 1. This adds up to 41. We divide this by 47 for the number of possible draws and we get 0.87. If the Straight were 9-10-J-Q, then we would still have eight cards to draw the Straight, but only six to give us a High Pair. This calculates to an expected value of 0.81.

That’s not a big difference. But the Low Pair has an expected value of 0.82, right in between. Thus, if we have a Low Pair with a 4-Card Straight with 2 High Cards, we play the Low Pair. But if it has 3 High Cards, we discard the Low Pair.

There are obviously two other types of 4-Card Straights — those with 1 High Card and those with 0 High Cards. Their expected values are 0.74 and 0.68, respectively. If we were to lump all 4-Card Straights together, we would get a weighted average based on the frequency of each.

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Not surprisingly, 4-Card Straight with 0 High Cards are the most common. We’d probably wind up with 0.75 or 0.76 and we would wind up playing a number of hands incorrectly, including the Low Pair and 4-Card Straight with 3 High Cards. There would also be a number of 3-Card Straight Flushes that would be played incorrectly, when they also form a 4-Card Straight.

Any single hand might not add up to a big difference, but, remember that the Grand Canyon was formed by a relative trickle of water.