How much of Video Poker is Luck and how much Expertise?

Video poker is a combination of luck, expertise, and more luck. Luck helps in the initial hand dealt. Expertise improves your prospects by dictating the cards to hold or dump. Then, assuming you do draw, luck aids in productively replacing your discards.

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

Favorable hands (descending from best)	expected value
"made" royal flush	800.000
"made" non-royal straight flush	50.000
"made" four-of-a-kind	25.000
four-card possible royal	18.708
"made" full house	9.000

Unfavorable hands (ascending from worst)	expected value
garbage (whenever expert strategy is to dump all five)	0.359
three-card double inside straight flush, no high cards	0.439
one high card	0.476
suited K-10, Q-10, or J-10	0.477
two unsuited high cards	0.478

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

Most likely starting hands (descending order)	probability
low pair	20.20898 %
one high card	15.64872 %
two unsuited high cards	15.04894 %
high pair	12.98458 %
two pair	4.75390 %

Least likely starting hands (descending order)	probability
"made" royal	0.00015 %
"made" non-royal straight flush	0.00138 %
"made" four of a kind	0.02401 %
four-card possible royal	0.03601 %
suited J-10-9	0.03878 %

On the average, a quarter of all starting hands have positive expectation -- are favorable or guarantee a return. Of these, 0.75 percent require no draw. The rest are mainly no-brainers -- four- or three-card possible royals, four-card possible straight flushes, four-card flushes, triplets, two pairs, and high pairs.

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,
Still take their chances but lessen the danger.