# Explaining 5-card deal 32 different ways

March 06, 2018 3:10 AM
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A couple of weeks ago, I discussed how the basic strategy for blackjack uses the same “expected value” concepts my father, Lenny Frome, made famous in the analysis of video poker.

In blackjack, the decisions slice a bit differently, so there was no need to talk about the expected value of each decision. Instead, each combination of player hand and dealer upcard was given an action to utilize – Hit, Stick, Double, Split or Surrender.

Video poker is a bit more complex in terms of the strategy choices. If the decision was just stand pat or draw, we might use the same concept as blackjack. But, there are two clear ways video poker decisions differ from blackjack. The first is hands are not as concrete as in blackjack. In blackjack, your hand is either Hard, Soft or Pair – along with a specific value. You have a Hard 13 vs. a Dealer 8. That’s very definitive.

In video poker, there are 32 different ways to arrange a 5-card deal using anywhere from 0 to 5 cards. This is also the number of ways a player can discard/draw cards. The good news is most of these ways would be nonsensical. You’re not going to split Three of a Kind to play a Pair! Many other possibilities, while they might make you wonder for a split second, will also quickly be dismissed. Would you really throw a High Pair to hold onto a 2-Card Royal? Probably not. But, what about a 3-Card Royal? And a 4-Card Royal? What about just a 4-Card Straight Flush or a 4-Card Flush or a 4-Card Straight.

You begin to see the problem. A hand that is a High Pair might be just that. But, it can also be a 2-Card Royal, a 3-Card Royal, a 4-Card Royal, a 4-Card Straight Flush, a 4-Card Inside Straight Flush and all sorts of partial Straights and Flushes. So, we can’t just say – if you have a High Pair, discard the other three cards and play the Pair!

A five-card hand can be described many different ways. We must assign an expected value to each of these ways and then the best we can do is tell the player to play it whatever way has the highest expected value.

For example, a High Pair, by itself has an expected value of 1.54. A 4-Card Flush has an expected value of 1.22. We know from this if the hand is both, then we play it as a High Pair. A 3-Card Royal has an expected value of 1.41. So, again we know if a hand is both a High Pair and a 3-Card Royal, we still play it as a High Pair. This also obviously removes 2-Card Royals and 3-Card Straight Flushes from consideration.

A 4-Card inside Straight Flush has an expected value of 2.39. So, if you are dealt a High Pair that is also a 4-Card Inside Straight Flush, then the hand should be played as a 4-Card Inside Straight Flush. Again, this inherently means 4-Card Straight Flushes and any 4-Card Royals would be played over the High Pair too.

This is not a tough part of the strategy to remember. But, hands can be all sorts of combinations. It could be a 3-Card Straight Flush while also being a 4-card Flush or a 4-Card Straight. Some of these expected values only differ by a few decimal points. Adding to the fun is some of these hands can swap relative values depending on the exact pay table. If a Flush pays 5 instead of 6, all partial Flushes have their expected values reduced while Straights stay put. This is why each variant of video poker has its own strategy table.

While there can be a few minor changes in strategy in a game like blackjack if you change the number of decks you are playing with or some of the basic rules (like Hit or Stick on a Dealer Soft 17), these changes are relatively minor compared to video poker. It is very important to learn the strategy table for the particular game you are playing.

In the coming weeks, I’ll discuss how video poker expected value is calculated and how to use a strategy table to teach you how to play.