Computers Determine Best Video Poker Playing Strategy

Ever wonder how the video poker experts decide on the best playing strategy for any particular game? Yeah, I know, they use computer-derived strategies, but haven’t you ever wondered how a programmer tells the computer to go about deriving that strategy?

When I first learned to play video poker, I had never heard of Bob Dancer or Dan Paymar or John Grochowski, but I did have a subscription to Casino Player Magazine. And buried within that magazine every month was a one-page video poker article, written by Lenny Frome, the guy who popularized video poker and made gamblers realize that it can be a predictable and therefore profitable game.

Frome had written a book entitled "Winning Strategies for Video Poker." Catchy title, isn’t it? There were 55 games in it with pay tables, frequency tables, percentage payback and, most importantly, 55 strategy charts or "ranking tables." The far right column of each ranking table was a list of Expected Values, or EVs.

I had not a clue as to what those EVs meant, but I didn’t need to. Just give me the chart itself, the ranking of pre-draw hands.

Then I discovered a video, "Winning at Video Poker," by Frome. It was a great learning tool and helped me visualize concepts that I had read about but could not quite fully grasp.

Turns out that the math that VP experts use is not very complicated at all. A little multiplication, then some addition and finally some division. Tedious, yes, but that’s what computers are for.

Let’s take the same example that the film used. Say you’re playing at a 7/5 Jacks or Better game, and you’re dealt a 7d, 8c, 8d, 10h, 9d. There are three reasonable ways to play the hand: hold the pair of 8s, hold the three diamonds, which make a 3-card straight flush, or hold the 7-8-9-10, which make a 4-card straight. A lot of people say to go for the straight flush because it pays back 50 coins for every coin played. A straight will give you only four coins, and the lowly pair gives you nothing.

But the obvious answer is not always the correct one.

If you discard one of the 8s, you’ll be drawing to the 4-card straight. There are 47 cards remaining in the deck and eight of them, the four 6s and the four jacks, will produce a winning hand, a straight. All other cards drawn leave the hand a loser. The expected value is determined by taking the total sum of all the payouts from winning hands. In this case, it would be eight straights, each paying four coins for a total of 32 payouts. Divide 32 by the possible 47 draws, and you have an expected value of 68 percent.

I won’t detail the math of the other two possibilities in this example, but if you go for the straight flush and hold the three diamonds, there is a total of 595 potential payouts. Divide that by the 1,081 possible draws, and you’re left with an EV of only 55 percent.

If you hold the pair of 8s and draw three cards, there are 16,215 possible draws, with the potential winners giving you 13,026 payouts and an EV of 80 percent.

Surprised that such a lowly pair can give you so much potential? But remember, a low pair has the potential of 45 four-of-a-kinds, 165 full houses, 1,854 triplets and 2,595 two pair.

It also works out the same way with the more respectable game of 9/6 Jacks: a pre-draw 3-card straight flush is ranked below a straight, which in turn is ranked below a low pair.

Now think of going through these steps in order to rank not three ways to play a particular hand but 36 possible ways in order to come up with a ranking table. And that’s for just one game. Multiply those calculations times thousands of different pay tables. Makes you a little grateful for computers, doesn’t it?

Until next time, aces and faces to you.