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Best of Alan Krigman
How much of Video Poker is Luck and how much Expertise?22 November 2006
Initial hands can be ranked two ways. 1) By the chances you'll receive them. 2) By their expected values or, equivalently, the paybacks they average. Results differ among games and machines. They depend on factors such as wild cards, bonuses for special combinations, and returns for specific hands. Plain vanilla Jacks-or-better games with returns of 9-for-1 on full houses and 6-for-1 on flushes are typical and can illustrate the effect.
The first of the accompanying tables shows the five best and five worst starting
hands, ranked by expected value. Data assume a bet of one unit. Values of 1.000
and above indicate advantageous hands, sure or liable to show a profit; those
below 1.000 are underdogs likely although not certain to lose. The break point,
where initial hands go from favorable to unfavorable, is between a four-card
flush and an unsuited K-Q-J-10. Expected values are 1.188 (profit averages $0.188
per dollar bet) for the former and 0.872 (loss averages $0.128 per dollar bet)
for the latter.
Best and worst starting hands ranked by expected value
The second of the accompanying tables shows the five most and five least likely starting hands, ranked by chance of occurrence. The fourth and fifth most probable combinations, high pairs and two pairs, will return minima of 1-for-1 and 2-for-1, respectively. Because of possible improvements in the draw, though, expected value for a high pair isn't 1.000 but 1.537. Similarly, expected value for two pair isn't 2.000 but 2.596.
Most and least likely starting hands, ranked by probability
Expertise comes to the fore in the remaining three quarters of all starting hands. You're an underdog no matter what you do. But skillful solid citizens slim down their dependence on pure luck in the draw to snatch victory from the jaws of defeat.
Do you know, for instance, how best to handle 4-H, 9-S, J-D, Q-D, K-C? Ditching the four is easy enough. But, then what? Holding an unsuited 9-J-Q-K has an expectation of 0.532. Dumping the nine and leaving the unsuited J-Q-K cuts expectation to 0.515. But getting rid of both the nine and the king lifts it to 0.611. So, proficient players would draw three to the suited J-Q. Of course, luck is still needed to upgrade this to a high pair, two pair, triplets, a straight, a flush, a full house, a non-royal straight flush, or -- dare you think it -- a bell-ringing royal.
Louis Pasteur once said "Luck favors the well-prepared." It's more than arguably true in gambling. For, as the bettors' bard, the beloved Sumner A Ingmark, briefed the bucket shop bezonians:
Those to whom study is hardly a stranger,
Best of Alan Krigman