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# Gaming Guru

### The Predictability of Video Poker

5 May 2006

Because the payback of conventional reel slot machines cannot be known to the players without analyzing the exact distribution of the symbols on the reels, many novice players naturally assume that Video Poker must similarly be a "pig in a poke" game.

Nothing could be further from the truth. With the pay-table in view and the deck's composition identified, we can determine all the stats governing the game, including the percentage payback and the frequency of all winning hands assuming expert play. In fact, we can also calculate the harmful effects of non-expert play on these parameters.

Note that we said calculate, which is much more exact than simulating play. To our knowledge, even though Blackjack has been under the scrutiny of mathematicians for over 30 years, nobody has determined the basic strategy and payback except by programming a computer to play many hands of Blackjack and then establishing the strategy by comparisons of alternatives. Then, using that strategy to play many millions more hands, gave the payback.

Even the card-counting systems and the estimated win-rates were derived by simulation of many millions of Blackjack hands. Yet, with all these years of simulation, there is still a raging controversy about whether the stats of Blackjack can be trusted because the methods of shuffling, riffling and cutting are now believed to influence the results significantly.

Therefore, the analysts of Video Poker and more important, the players can be more confident of their figures, derived in just the past three years, than their Blackjack colleagues with some 30 years extra time to get that job done. Let's get some insight into why this is so true.

In Video Poker analysis, our strategy table is primarily a list of "playable hands" which can be dealt from the deck, ranked in order of their "win-power" which is determined by calculation. To illustrate, in Jacks or Better (full-pay, five coins) there are 36 types of playable hands which can be dealt to a player. The top hand is of course a Royal Flush, which has an Expected Value of 800, since we'll always stay pat and get 800 for 1 on our bet. The bottom of the list is a completely useless hand with no high cards, no possible 3-card straight flush and no sequential 4-card straight. If we toss all five cards away, the Expected Value of the replacement hand will be 0.36, meaning that for every 100 times we draw 5 new cards we will have an average return of 36 bets. Of course, some of the replacement hands will be Royals (only 4 out of 1.5 million, unfortunately) and some will be all other kinds of winners, but still the Expected Value (EV) will be only 0.36.

In between are 34 other playable hands, 4-card inside straights, 3-card straight flushes, 2-card Royals, one, two or three high cards, etc. ranging in EV from 0.44 (3-low-card Straight Flush missing two inside cards) to 50 (Straight Flush). The EV of each is relatively easy to calculate. Every possible draw is considered and the collective value of all the resulting winners is divided by the number of draws. For example, there are 16,215 unique draws to a low pair and the resultant winners will pay out 13,356 so the EV of any low pair is 0.8236 and this ranks it as number 16 in this specific game's ranking table of strategy.

We can use a computer to examine each of the 2,598,960 unique hands (order is immaterial, except when sequential Royals are in the pay-table), and determine what type of playable hand it is. Obviously, when a hand fits more than one category, our computer identifies it as the highest ranking, since that is the way an expert player would want to draw to it.

With this program, the exact number of each type is found, and since we already know the EV of each type, it is a simple matter to get the cumulative payouts. For full-pay Jacks or Better, the average payouts will be 2,588,324, which is a 99.6 percent payback.

This illustrates why the stats of the many versions of Video Poker are currently available, providing players with the winning strategies and reliable figures about the paybacks. And without having to wait 30 years!

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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.

www.vpheaven.com