Was Justice Served in This Video Poker Case?
by Lenny Frome

In the book "Statistics and the Law", one of the authors, Joseph B. Kadane presents a chapter which Video Poker players can really appreciate. He records the case of the Commonwealth of Pennsylvania v. Electro-Sport Draw Poker Machine, Serial No. 258. In 1980 the state charged the manufacturers of a video poker machine with selling a gambling device. The keystone of the accusation was the state's contention that video poker is primarily a game of chance and does not require skill to play. Mr. Kadane was an expert witness for the defendants. The case was decided for the defendants in the Alleghany Court of Common Pleas, then again in the Superior Court, but was reversed on appeal to the Pennsylvania Supreme Court.

In the lower courts, Mr. Kadane's argument that the use of a smart strategy produced much better results than a dumb strategy won the day in proving that a high degree of skill is needed to play successfully. Although Mr. Kadane did not have the benefit of sophisticated high-speed computer simulations of Video Poker, he was able to draw very astute conclusions about the stats of the game. The machine in question had a pay table:

Straight Flush50
Four of a Kind25
Full House10
Flush8
Straight5
Three of a Kind3
Two Pairs2
Pair Aces1


The maximum theoretical payback from this game is 90.7%. Mr. Kadane played 128 games and attained a return of 159 skill points with his smart strategy and only 34 with his dumb strategy. These numbers were offered to show that skill produced a better than 4 to 1 improvement in results, or "skill factor". The dumb strategy called for standing pat on all hands. The smart strategy kept winners and made "common-sense" decisions based on Mr. Kadane's knowledge of statistics, which he teaches at the highly respected Carnegie-Mellon University. Obviously, Lady Luck was smiling on Mr. Kadane when he drew cards, giving him a return exceeding 125% for his sample, but his argument would have been just as effective with a 90% return producing a skill factor of only 3.5 to 1.

In the Supreme Court's reversal of the earlier decisions, we are told that the court simply found that chance played a more important part than skill in determining the outcome. They believed that skill could affect whether the player won and how much the player won, but chance determined what cards were dealt to the player and what was drawn.

What might have caused the Supreme Court to see it that way is moot, but the book continues with a Commentary by one of Mr. Kadane's colleagues at CMU, Mr. John Lehoczky, who discusses the question of establishing a skill vs. chance criteria. He creates a fairly realistic model of various "common-sense" strategies, working upward from Mr. Kadane's "dumb" strategy to a set of 5 rules for holding/discarding. Using these rules he arrives at paybacks ranging from 24% (Kadane's dumb strategy) to 85.7% for his most astute strategy namely:


Since Mr. Lehoczky considers these rules to involve no skill, being simple common sense, he concludes that since these simplistic rules attain virtually the maximum return, which he accurately estimates at slightly over 90%, one can conclude that Video Poker is primarily a game of chance.

Now 16 years and Pentium light years ahead of the courts, the lawyers and the expert witnesses, we can define the optimal strategy for the game, as follows:



A review of this strategy show numerous refinements (conflicts) with the "common sense" strategy and it surely makes one recognize that just interpreting what a player sees in the pre-draw hand and cataloging it properly requires considerable skill, even if one had the entire strategy in sight while playing. But today is now and 1981 was an eternity ago. With a 90% return, it really is tough to win on a machine, even today --as many folks in Oregon and other jurisdictions have found out, as a consequence of their legislators mandating such ridiculous low maximum paybacks.

Too bad the defendants didn't have the sense to create a 99% return pay-table or even a positive return for skilled players. Their expert witness(es) would have been able to show that skill is the single most important factor that determines whether one wins or loses, as well as how long one can be entertained by the machine. That's what works for Video Poker aficionados in Nevada.