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Lenny Frome Gaming GuruThe Predictability of Video Poker5 May 2006
By Lenny Frome 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! Avoid the Tourist Traps5 October 2005
The occasional Video Poker players, such as the tourists who visit Nevada casinos just a few times a year, usually have a totally different way of looking at the game, from the way regular players, who attain high levels of expertise, view it. The tourist feels much more limited time-wise but usually has more money ready to risk. ... (read more)
Less Glitz, More Payola28 April 2005
Nearly 30% of the hands we're dealt contain a low pair and are designated LPR
in our table of rankings. The expected value (average return if each possible
draw occurs once) of LPR is a healthy .82, so we can expect to recover 82% of
our wagers on these hands.
It is very important that we do not ... (read more)
Holding Kickers is Never Correct in Video Poker30 March 2005
One of the biggest advantages of gambling with Video Poker is that every bit of
statistical data about the game is known in advance. In table poker, only the
rudimentary probabilities can be expressed in absolute terms. For example, nobody
knows for certain what advantage (or disadvantage) can be ... (read more)
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