# Holding high cards

Aug 31, 2004 4:25 AM

There are many people out there who like to tell us that video poker is all intuitive. Look at any dealt hand, and you can figure out how to play that hand very easily. Quite frankly, that’s probably how most players play.

Unless they’ve studied the game, how would anyone know how to play the following hand?

Jd,  Qd,  Kc,  4h, 7s

I think if you asked any "intuitive" player, they would tell you to hold the three high cards. After all, you’ll have some chances to draw the straight, and most importantly, you’ll have two draws at one of the other picture cards. It seems so simple.

Well, I’ll admit I was as surprised as anyone about 15 years ago when my dad discovered that it wasn’t so simple after all. I say discovered because all he really did was calculate the expected value. Fifteen years ago, it was the gaming equivalent of sliced bread. Today, it seems kind of routine.

As always, to calculate the expected value, we simply have to look at all the possible draws based on what we choose to hold. In this case, our choices would appear to be limited to two:

”¡ Hold the J-Q-K

”¡ Hold the 2-card royal

Let’s look at the possible results for a full-pay jacks or better machine, as reflected in the accompanying chart.

 Hold J-Q-K Hold 2-Card Royal Royal Flush 0 1 Straight Flush 0 2 Four of a Kind 0 2 Full House 0 18 Flush 0 162 Straight 32 157 Three of a Kind 9 281 Two Pairs 27 711 Jacks or Better 348 4,914 Non-Winners 665 9,967 Total Unique Draws 1,081 16,215 Total coins returned 557 9,711 Expected Value 0.5153 0.5989

When all the numbers are out on the table, we realize that what looked intuitive only a few minutes ago, looks like a really bad play now. The expected values aren’t even close. There really is no statistic that can be pointed at to say the three high cards is a better play.

The win frequency (% of winning hands) is virtually identical. While you’ll get a few more pushes with the three high cards and certainly more straights, this is completely offset (and then some) by the increase in the number of two pairs, trips and flushes. Not to mention, you still give yourself a chance at the royal.

Of course, the skeptics will tell you that it’s this one-in-16,215 chance that accounts for the increased expected value. While it’s true this accounts for about half of the increase, it’s the increase chance at the two pairs, trips and flushes that makes this play counter-intuitive and yet 100% correct.