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# Gaming Guru

### Video Poker Sure Isn't Poker

3 February 2002

I have several friends who are regulars in private Poker games in my region. Of these, a few make regular trips to Foxwoods Casino in Ledyard, Connecticut to play in the Poker games there. All of these pals have at one time or another tried to entice me to join one of their games or one of their Poker trips and I have always refused. Why? Because I am well aware of my Poker skills or lack thereof. I usually just tell them that I am "happy playing Video Poker." "Oh yeah," they'll say, "I'll have to give that a try someday." "Well, make sure you talk to me before you do," I tell them. I hope they will take my advice seriously because if they don't, Video Poker is going to be a rude awakening for them.

The fact is that the only things Poker and Video Poker have in common are the names of the hands and their ranks. A skillful Poker player who tries to use his knowledge of Poker to play Video Poker will suffer the same fate I would if I joined my friends' private Poker games. Let me show you why.

Consider a game of Five Card Draw with guts to open. You are dealt the following hand: AC, KS, QD, 8C, 5H. With guts to open this is a fair hand. Suppose that the betting round before the draw leaves only you and one other player in the game. He draws first and calls for three cards. You are most likely facing a pair. What do you do? Good question; the answer isn't that obvious. If you knew he had a low pair you would keep only the Ace. On the other hand, if he had a pair of Jacks you would keep the Ace, King, and Queen. The only way to resolve the issue is to take a weighted average of the win probabilities over all possible opponent pairs and obtain the overall win rate for each drawing scenario. It turns out that the win rate is 28.4% holding the AKQ and 29.4% holding the Ace alone. So the correct draw (ignoring any psychological effects your draw might have) is to only hold the Ace.

In a Jacks or better game it is unlikely that you would stay in for the draw with the above hand although it is not impossible. If the opponent with the pair sandbags and bets low, you would stay in if the bet was less than one fifth of the pot minus your ante. In this case holding the AKQ is the better move and the win rate is 21.9%.

The above numbers are really irrelevant but I calculated them just because I was curious about the way to play such a situation. The point here is that no matter how you decided to play the hand you would never, never throw away that Ace.

Now let us suppose you are playing 9/6 Jacks or better Video Poker and you get dealt the exact same hand, namely AC, KS, QD, 9C, 5H. What is the correct draw? Well, there are several rational choices: discard the 9 and 5 and then either hold a single, hold a pair, or hold all three. In each case you have to calculate the expected return that results from your action. Here are the results assuming that 5 coins are played:

 Hold Expected Return KQ 2.4172 AK 2.3383 AQ 2.3383 AKQ 2.2803 Q 2.2768 K 2.2541 A 2.2264

So you see, the correct play is to toss the Ace, something a dyed-in-the-wool Poker player would probably have trouble doing. In fact, I imagine that most people, Poker players or not, would probably hold onto that Ace. Bad move!

There are many other plays like this that exhibit the difference between Poker and Video Poker but I'm sure this example makes the point. In Video Poker your opponent is not another player but the pay table listed on the front of the machine. Your decisions should be based on this pay table, and this alone, and not on other factors--especially your intuitive feeling for the right play. When you are in a casino, beware of your intuition.

Speaking of intuition, next month I'll have an article that deals with exactly that issue. See you then.

Video Poker Sure Isn't Poker is republished from Online.CasinoCity.com.
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Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers