Bad hands are just as important as good hands

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I’ve spent the past few weeks walking through the strategy table for full-pay jacks or better video poker. This week, we are in the heart of the table, which is to say we are in the middle of the really bad hands.

The bad hands are the harder hands to play correctly and just as important as the good hands in achieving the theoretical strategy of any particular game. We finished up last week with the 4-card Straights. From here the hands only get uglier.

The next several entries are:

• 3-card Double Inside Straight Flush with 2 High Cards

• 3-card Inside Straight Flush with 1 High Card

• 3-card Straight Flush with 0 High Cards

• 2-card Royal Flush-V3

This part of the table gives you a doozy of a headache! The good news is it is not nearly as confusing as it might appear. Many of the hands listed above cannot co-exist – meaning you can’t have more than one in a particular hand.

Remembering the exact order may not be as important as it might appear to be. For example, you can’t have a 3-card Double Inside Straight Flush with 2 High Cards in the same hand as a 3-card Straight with 0 High Cards. You’d either have to have at least 4 cards of one suit or have two sets of 3-cards of different suits – rather difficult with 5 cards.

There are still important things we can learn from this section of the table. We separate the hands the way we do because in some games the impact of the subtle differences and the order of the hands will be different and thus become pertinent.

The first thing you might notice is the relationship of the top three hands. We get a sense of the importance of a High Card. A 3-card Double Inside Straight Flush with 2 High Cards has a higher expected value than a 3-card Inside Straight Flush with only 1 High Card. Essentially, the value of the extra High Card is greater than the value of the additional Straight Flushes (and Straights) that may occur as a result of having an Open vs. Inside vs. Double Inside Straight Flush.

What this should also tell us is you shouldn’t hold your breath for those Straight Flushes. They will occur, but not often. At the same time, I have written at length over the years about how the Straight Flush is the forgotten hand of video poker.

Playing 3-card Straight Flushes correctly is very important to drawing them in proper abundance. While their pays are far short of the Royal, they still pay double what Quads pays so their value should not be dismissed.

Next up is the 2-card Royal Flush-“V3.” 2-card Royals are given four different designations from “V0” to “V3.” We need to do this because the expected values of many of the hands in this part of the table differ by only 0.01 or 0.02. As not all 2-card Royals have identical expected values.

V3 means the 2-card Royal contains neither a 10 nor an Ace. An Ace in a 2-card Royal essentially makes it a Double Inside Royal. All 2-card Royals have the same number of ways to make a Royal – one. But, with the Ace, we eliminate all ways to make a Straight Flush. While a 10 doesn’t have this problem, it does have the problem that it is not a High Card. So, Aces are worth less than Jacks, Queens and Kings and 10’s are worth less than Aces.

A 2-card Royal with neither an Ace nor a 10 is the one with the highest expected value. A V2 2-card Royal means the 2-card Royal has an Ace, but no 10. A V1 2-card Royal is one that has no Ace, but does have a 10. Lastly, a V0 2-card Royal consists of a 10 AND an Ace.

For the moment, I’ll jump to below the strategy table – to the V0 2-card Royal. We are below the strategy table because this hand does not exist on the strategy table for full-pay jacks or better. This means we DO NOT PLAY an A-10 2-card Royal. Barring the other three cards forming an otherwise playable hand, we would simply hold the single Ace. More on that in a couple of weeks.

The proper play of 2-card Royals is critical to learning how to master video poker strategy. Unlike the prior three hands, 2-card Royals overlap with everything. You’ll have 2-card Royals with High Pairs, Low Pairs, 4-card Straights, 4-card Flushes, 3-card Straight Flushes, 3-card Inside Straight Flushes, etc.

If you blindly go after every 2-card Royal, you’ll hit more than your fair share of Royals, but you’ll lower the payback of your play. If you ignore 2-card Royals, you’ll miss your fair share of Royals and lower the payback of your play.

The only answer is to play them when you are supposed to. Based on the portion of the strategy table shown, you can easily have a 3-card Double Inside Straight Flush with 2-High Cards AND a 2-card Royal-V3. For example, you could have 8-J-Q suited.

From the strategy table, we learn that we keep the 8 in this case. You might also have a 3-card Straight Flush completely apart from a 2-card Royal. For example, 3H, 4H, 5H, JD, QD. In this case, we discard the 2-card Royal in favor of the 3-card Straight Flush with 0 High Cards. I’ve now covered about 2/3 of the strategy table for Jacks or Better video poker.

Next week, we continue through the rest of the messy hands.

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected] .

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About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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