# High-card angst

Nov 16, 2004 12:48 AM

By Elliot Frome

They’re not the hands you really want to get, but they are among the most common hands in video poker. They’re the hands without a pair or better, without a four-card straight or flush, without a three-card straight flush or without a three-card royal.

They’re the high card hands and they’re not without hope.

At first glance, these hands would seem to abe pretty simple to rank. Three high cards are better than two high cards, which are better than one high card. As easy as one, two, three, right?

Well, as I’ve said many times before, what seems like it should be true is not always correct. The rankings are not quite this simple.

First of all, we only play three high cards if it is a jack, queen, king combination. This is because, in video poker, the ace is generally no better than other high cards unless you are talking about four of them. Because the ace can only be part of one possible straight combination (A through 10) when held with another high card, it really is less powerful in terms of expected value (rate of return per bet) relative to other high cards.

Thus, a J-Q-K has a higher expected value than a J-Q-A because we have additional opportunities to make straights. In fact, the difference becomes so significant that we are actually better off holding the J-Q instead of the J-Q-A. The expected value (EV) of J-Q-K is 0.52. The expected value of J-Q is 0.51. The expected value of J-Q-A is only 0.46.

You’ll note from this that holding the K doesn’t really improve our hand much. While we increase our chances for a straight, we reduce our chances for pairs and trips (three of a kinds) and totally eliminate a chance at quads (four of a kinds). It should also be noted that not all two high-card hands have the same expected value. J-Q has a higher EV than J-K, which has a higher EV than J-A. This, again, is because of the reduction in the number of possible straights that can be made.

All of the above examples assume that no two high cards are of the same suit. If you have three high cards of the same suit, you have a powerful three-card royal opportunity. What if two of the cards are of the same suit? Well, as shown above, three high cards are only a slight improvement over two high cards.

If two of the high cards are of the same suit, we leave ourselves with at least a possibility of drawing the royal flush. This slim possibility, however, increases the expected value to the point where it pays to hold the two high cards of matching suit instead of the three high cards of mismatched suit. In this case, because of the large difference in expected value based on the specific two-card royal, we actually break them down by type.

If the hand consists of a J-Q, J-K or Q-K, it has an expected value of 0.60. If the hand contains a J, Q or K and an ace, it has an expected value of 0.58. Both of these possibilities rank higher than a three high-card hand and thus are played as two-card royals instead of a three high-card hand.

If the combination of cards contains a 10 plus a J, Q or K, its expected value is only 0.49. If the combination contains a 10 and an ace, it is a playable hand because the lone ace has a higher expected value.

I realize all of this theory sounds like a math lesson, but expert strategy is based on sound mathematical principles. Two-card royals, one high-card, two high-card and three high-card hands make up nearly 38 percent of all hands dealt. While any one mistake may only cost a few pennies, over an hour those pennies will add up quickly, as you’ll be making mistakes on more than one out of three hands!

I strongly recommend learning a complete strategy table for any game you want to play. If, however, you’re going to head to the casino without one, keep these basic strategy tips in mind: Never play three high cards where one is an ace unless they are suited; play only the two high cards; if you’re dealt three high cards where two of them are of the same suit, play the two-card royal over the three high cards.

Maybe it’s as easy as one, two, three after all!