CasinoCityTimes.com

Gurus
News
Newsletter
Author Home Author Archives Author Books Send to a Friend Search Articles Subscribe
Stay informed with the
NEW Casino City Times newsletter!
Newsletter Signup
Stay informed with the
NEW Casino City Times newsletter!
Recent Articles

Gaming Guru

 

Was Justice Served in This Video Poker Case?

27 February 2004

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:

  • Keep all sure winners
  • Keep all pairs and draw 3
  • Keep a 4-card flush and draw 1
  • Keep any 4-card straight, inside or outside and draw 1
  • Keep an Ace and draw 4

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:

  • Straight Flush
  • 4 of a Kind
  • Full House
  • Flush
  • Straight
  • 4 Card Royal (with Ace)
  • 4 Card Straight Flush
  • 4 Card Inside Straight Flush
  • Two Pairs
  • 4 Card Flush with Ace
  • Pair Aces
  • 4 Card Flush
  • 4 Card Straight (outside)
  • Low Pair
  • 3 Card Straight Flush
  • 3 Card Inside Straight Flush
  • 3 Card Double Inside Straight Flush
  • 4 Card Straight with Ace
  • 4 Card Inside Straight
  • 3 Card Flush
  • One Ace
  • 2 Card Straight Flush
  • 2 Card Inside Straight Flush
  • 3 Card Straight
  • 2 Card Double Inside Straight Flush
  • 2 Card Triple Inside Straight Flush
  • Mid-Size Card
  • Draw 5


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.
Lenny Frome
Lenny Frome spent 40 years in the aerospace engineering business before moving to Las Vegas. During the ensuing 10 years, he became one of the most prolific gaming authors, having written 8 books, countless tip sheets and nearly 1000 articles for a variety of gaming magazines.

Lenny's ground breaking work in the area of Video Poker earned him the title of the 'King of Video Poker'. He also wrote on a variety of other gaming topics including Spanish 21, Let It Ride, Keno and others.

Besides being an author and columnist, Lenny was the premier Gaming Consultant at the time of his passing in 1998. He helped develop paytables for Let It Ride and Three Card Poker, and consulted on literally hundreds of other gaming projects.

His son, Elliot, now follows in his footsteps, as a gaming author, analyst and consultant. Their website, and a complete catalog of all their products can be found at www.vpheaven.com. Feel free to drop Elliot an e-mail at compuflyers@prodigy.net.

Lenny Frome Websites:

www.vpheaven.com
Lenny Frome
Lenny Frome spent 40 years in the aerospace engineering business before moving to Las Vegas. During the ensuing 10 years, he became one of the most prolific gaming authors, having written 8 books, countless tip sheets and nearly 1000 articles for a variety of gaming magazines.

Lenny's ground breaking work in the area of Video Poker earned him the title of the 'King of Video Poker'. He also wrote on a variety of other gaming topics including Spanish 21, Let It Ride, Keno and others.

Besides being an author and columnist, Lenny was the premier Gaming Consultant at the time of his passing in 1998. He helped develop paytables for Let It Ride and Three Card Poker, and consulted on literally hundreds of other gaming projects.

His son, Elliot, now follows in his footsteps, as a gaming author, analyst and consultant. Their website, and a complete catalog of all their products can be found at www.vpheaven.com. Feel free to drop Elliot an e-mail at compuflyers@prodigy.net.

Lenny Frome Websites:

www.vpheaven.com