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# Gaming Guru

### Frugal Video Poker

2 February 2004

One of the newer gambling products on the market is the computer program Frugal Video Poker developed by Jim Wolf and highly recommended and marketed by Jean Scott. Jean, as many of you know, is the author of the popular books The Frugal Gambler and More Frugal Gambling, both published by Huntington Press of Las Vegas. I recently saw Jean in Tunica, Mississippi where we were both on the program at Frank Scoblete's Gambler's Jamboree. Jean was kind enough to give me a copy of her Video Poker program to look over and I am glad that she did for I think it is a dandy program.

First of all it has the usual graphics and sound of a tutor program, with a plethora of different versions of Video Poker that one can play, the ability of the user to define a game, warnings when an incorrect play is made, and statistical records of one's play. There is one feature, however, that sets this program apart from other fine Video Poker programs. To adequately explain it I'll need a bit of history.

;In 1992 Lenny Frome published Americas National Game of Chance - Video Poker; his coauthor was Maryann Guberman. This, to the best of my knowledge, was the first book ever written on the subject. The following year Lenny published Winning Strategies for Video Poker. This second book was a collection of strategy tables that provided near optimum strategy for over 50 video poker machines. Let me define what I mean by a strategy table. It is a linear ordering of one, two, three, four, and five-card hands in order of their expected value (EV) in terms of holding them for the draw. For example, in 9/6 Jacks or Better, a 4-card flush is a stronger hand than a 3-card royal, so it appears above the 3-card royal in the list of hands. Thus if we were dealt AH, QH, TH, 6C, 4H the table would tell us that holding the AH, QH, TH, 4H is a better play than holding AH, QH, TH.

Notice in the above paragraph I used the words "near optimum." This is because it is, in general, impossible to linearly order video poker hands. Let me illustrate this with an example. Suppose that in 10/7 Double Bonus Poker we are dealt KH, QH, 3H, 8D, 6C. Should we hold the 2-card royal or the 3-card flush with two high cards? It turns out that with 5 coins played the 2-card royal has an EV of 2.8252 coins and the 3-card flush has an EV of 2.8168 coins; we should hold the 2-card royal. Thus it would seem that KQ royal should appear higher in our strategy table than the 3-card flush with two high cards.

But wait! Suppose that we are dealt KH, QH, 3H, 9D, 6C. Now the KQ3 has an EV of 2.8168 and the KQ has an EV of 2.8005, a bigger difference than the first example. The reason is that by throwing away the 9 we reduce the probability that the KQ will lead to a straight. This is known as straight interference or a penalty card situation. Even though the difference in the EVs is larger in the second example, more hands of the type without straight interference will occur in play, so it really doesn't matter which choice is put above which.

Before I leave this topic I would like to set a record straight. I have seen some writers criticize Lenny for not providing accurate strategies. Lenny and I were friends and collaborators from 1995 until his death in March of 1998. I asked Lenny about the above criticism and on October 10, 1997 he sent me a fax containing the following response: "The nuances cannot be included in a text for 'average players.' Such 'penalty cards' are for consideration by the pros." Lenny knew the correct plays. His goal was to provide strategies for the average player that were easy to understand and would provide them with near optimal results. All of which brings me back to Jean Scott and her Frugal Video Poker program. (By the way, Jean was a close friend of Lenny's as well.)

Jean's program gives the player of any video poker game the option of playing using a strategy table with no penalty card entries. That is to say, rather than providing exact optimal play in terms of either advice or flagging errors, one can choose to only be corrected or given advice based on a simplified strategy table. In my opinion this is a wonderful way to learn the game. One can print out the strategy table for study (in color, no less) and then can play the game according to that strategy. When I play I make my choice and if in doubt I click on the 'Show Best Hand' button to see if I did indeed make the right choice. Once you learn the strategy table, you'll be playing with an accuracy that costs you only pennies per hour at the quarter level. At that point, if you wish to take the time, you can switch to the perfect strategy mode and start learning the exceptions that arise from penalty cards. I think this option in Frugal Video Poker makes it my choice for the best teaching aid that one can buy. Great job, Jean!

See you next month.

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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