National Video Poker Day is just three months away. I’m spending the summer writing columns devoted to video poker so you’re ready to celebrate this very special day on Sept. 6 (9/6). The past few weeks I’ve discussed the first leg of Expert Strategy (which games to play), explained what a full-pay machine is and why it’s important to play max-coin, and told you how to figure out what a particular paytable pays if you know what the full-pay payback is. It is time for the second leg of Expert Strategy: knowing how to play the machines you are supposed to play.

I could dive right in and start giving you the strategy, but why should you trust me just like that? I’d rather prove to you why the strategy is what it is. If you know it is based on sound mathematical principles and can be replicated by anyone with a math or computer background, I’d like to think this will make you more likely to stick with the program.

First, a little background. When you deal five cards from a 52-card deck, there are 2,598,960 possible deals. Mathematically, this is called 52 choose 5 or 52C5. The mathematical symbol for this, looks something like this:

To solve this math equation, we also need to know what a factorial is. This is a number with an exclamation point after it. It means that number multiplied by itself and every integer below it down to 1. So, 5! is 5 x 4 x 3 x 2 x 1 = 120. And, 52 choose 5 means 52!/(47! x 5!). When you work with this type of math, you quickly learn some shortcuts. We are able to cancel out most of the multiplication and are actually left with (52 x 51 x 50 x 49 x 48 / (5 x 4 x 3 x 2 x 1), which equals the 2,598,960 I mentioned earlier. If you know how to use Excel or have a scientific calculator you can easily double check my math.

So, now we know there are just under 2.6 million possible deals in video poker. That by itself doesn’t really tell us much. We don’t get to pick our deal. We are given one of these deals and must decide which to hold/discard. This is where the strategy kicks in. In theory, there are 32 ways you can play this deal. Mathematically: 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 or 1 + 5 + 10 + 10 + 5 + 1. We can discard anywhere from 0 to 5 cards. If we discard 0 cards, there is only one way to do this. If we discard one card, there are five ways to do this. Discard two cards, 10 ways, etc.

In total, this adds up to 32. So, on every deal we must determine which of these 32 ways we want to play the hand. The good news is that for most hands, one way is fairly obvious. For the majority of the rest, there are only two or three ways that are seriously considered. This is similar to what happens in blackjack. You need to know whether to hit/stick/split/double/surrender on every hand. In some cases, the choice is not available (you can’t split non-Pair hands). In others, you can quickly eliminate some of the options. Are you really going to double down on a 14? Will you stick on an 8? You’re not going to hit a 19 are you?

The problem comes in with the large number of hands for which there are seemingly multiple reasonable choices. Do you hit or stick on a 12 against a 2? Do you hold the Low Pair or the 4-Card Straight? What about a High Pair and a 4-Card Straight Flush? To answer this question, we use the same mathematical concepts used in blackjack. Which choice provides the highest expected value? We hit a 12 against a 2 in blackjack, because we can expect to win more (or lose less) by hitting vs. sticking. In video poker, the calculation can be a bit more complex, but the concept is the same. Holding the Low Pair or the 4-Card Straight depends on which of these hands has the higher expected value. As in blackjack, “higher” is a relative term and might mean lose less, not win more, but in the long run, both preserve our bankroll.

The critical term here is “in the long run.” On any given hand, the results could be anything. In theory, you might throw away four Aces with a Deuce, holding just a single Ace and wind up drawing a Royal Flush. But, I think we’d all agree, in the long run, this is not a wise move. This is the absolute extreme example of how doing the wrong thing might work out once in a while (a very long while). As my father liked to put it, even a blind squirrel can find an acorn once in a while. But, if a squirrel wants to get through the winter, he’d be better off being able to see and have a plan for how to do it. Next week, we’ll start giving you that plan.