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.