# Video poker is as plain as the nose on your face

Jun 28, 2011 3:00 AM

I have frequently stated in my column the biggest difference between slots and video poker is that in video poker "everything is known."

What does this mean? Well, it does not mean that anyone knows exactly which cards are about to be dealt or drawn. What it does mean is because the cards are random, we know what will happen over the long run and we know the probability of winning hands forming. Thus, we are able to create a strategy that maximizes the amount of money we can win by using these probabilities and the payouts of these winning hands.

When you walk up to a roulette wheel, everything is known also – and it’s fairly simplistic. If you bet a single number (assuming a single zero wheel), you have a 1-in-37 chance of winning. If you bet "Odd" or "Black," you have an 18-in-37 chance of winning.

If you sit down at a blackjack table you know the probability of you getting a blackjack is about 4.75%.

This information is all known because you’re dealing with real life objects that have a clear probability and are completely random.

The same is true of video poker. The fact that it is a digital deck does not change the randomness. Everything about the game would be the same if you could somehow play it with a real deck of cards.

The overall math is a bit more complex than figuring out the probability of a single number in roulette or of getting a blackjack, but the concepts are the same.

Let’s start with a simple example. Let’s say you are dealt the following:

3 (heart) 4 (diamond) 5 (club) 6 (spade) 10 (heart)

The play is fairly obvious. Discard the 10 and go for the straight. What is the probability of drawing the straight? There are eight cards that will complete it, with 47 possible cards to be drawn. Thus, the probability is 8/47 or about 0.17. With a payout of 4, we multiply this by the probability to arrive at the Expected Value (EV) of this hand of 0.68.

What if we make the hand a bit more complex? What if the 10 was another 6? Now there are two possible plays. We can do as we did before and go for the straight or we can discard the 3-4-5 and hold the low pair.

We don’t have to guess what the right play is. While the specific result for a single hand will be determined by the random number generator of the machine, we can look at every possible outcome of each situation and determine which results in the higher Expected Value.

When we look at all the possible draws or use some combinatorial math, we find that starting from a low pair and drawing three cards (16,215 possible outcomes) will result in 45 quads, 165 full houses, 1,854 trips, 2,592 two pairs and 11,559 losing hands.

When we multiply each of these by the payouts of each hand, and divide the total by the total possibilities, we come up with our EV of a low pair, which is 0.82.

This is considerably higher than the EV of the four-card straight (0.68). Thus, the proper play is to hold the low pair. By looking at every possible (2,598,960) way of playing each one (32) and every possible draw for each of these ways (varying depending on how many cards are drawn), we can figure out the probability of absolutely everything that can happen in video poker.

In total, we have to look at more than 675 billion combinations of deals/draws. Fortunately, with the help of today’s computers, this really isn’t all that daunting of a task (and there are some shortcuts to help!).

The important thing to realize is there is no guesswork here. There is hard, cold and very precise math based on a 52-card deck and the idea that the probability of any card appearing is the same as every other card.

A long time ago, I saw someone suggest the way to tell if a slot machine is a "good one" is to play 20 times and count the number of winners. A machine set to pay more will have a higher win frequency than one set lower (I can’t even verify this much!), so based on how many winning hands you have in the 20 times gives you an idea if the machine is a good payer or not!

Huh?

Show me a video poker machine’s paytable and I’ll tell you the win frequency and the payback in a matter of minutes. (Okay, if it’s something new, it might take a bit longer!) This can be done because there is nothing hidden in video poker. The payback is known. The hit frequency is known. The strategy is known. Everything is known!

If you’d like to know more, one of the best ways to learn about video poker is from my father’s book Video Poker: America’s National Game of Chance. It is 200 pages of dozens of some of my father’s best articles about video poker, all geared to teaching you how to play in a more laid back way.

It retails for \$19.95, but for a limited time I’m making it available for \$6 each or two for \$10, which includes first class shipping and handling. Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, N.J. 07603.

If you have a chance, head over to my blog at gambatria.blogspot.com to read more of my columns.