Ever wonder how the
video poker experts decide on the best playing strategy for any particular
game? Yeah, I know, they use computer-derived strategies, but haven't
you ever wondered how a programmer tells the computer to go about deriving
When I first learned
to play video poker, I had never heard of Bob Dancer or Dan Paymar or
John Grochowski, but I did have a subscription to Casino Player Magazine.
And buried within that magazine every month was a one-page video poker
article, written by Lenny
Frome, the guy who popularized video poker and made gamblers realize
that it can be a predictable and therefore profitable game.
had written a book entitled Winning
Strategies for Video Poker. Catchy title, isn't it? There were 55
games in it with pay tables, frequency tables, percentage payback and,
most importantly, 55 strategy charts or "ranking tables."
The far right column of each ranking table was a list of Expected Values,
I had not a clue
as to what those EVs meant, but I didn't need to. Just give me the chart
itself, the ranking of pre-draw hands.
Then I discovered
a video, Winning
at Video Poker, by Frome.
It was a great learning tool and helped me visualize concepts that I
had read about but could not quite fully grasp.
Turns out that the
math that VP experts use is not very complicated at all. A little multiplication,
then some addition and finally some division. Tedious, yes, but that's
what computers are for.
Let's take the same
example that the film used. Say you're playing at a 7/5 Jacks or Better
game, and you're dealt a 7d, 8c, 8d, 10h, 9d. There are three reasonable
ways to play the hand: hold the pair of 8s, hold the three diamonds,
which make a 3-card straight flush, or hold the 7-8-9-10, which make
a 4-card straight. A lot of people say to go for the straight flush
because it pays back 50 coins for every coin played. A straight will
give you only four coins, and the lowly pair gives you nothing.
But the obvious
answer is not always the correct one.
If you discard one
of the 8s, you'll be drawing to the 4-card straight. There are 47 cards
remaining in the deck and eight of them, the four 6s and the four jacks,
will produce a winning hand, a straight. All other cards drawn leave
the hand a loser. The expected value is determined by taking the total
sum of all the payouts from winning hands. In this case, it would be
eight straights, each paying four coins for a total of 32 payouts. Divide
32 by the possible 47 draws, and you have an expected value of 0.68.
I won't detail the
math of the other two possibilities in this example, but if you go for
the straight flush and hold the three diamonds, there is a total of
595 potential payouts. Divide that by the 1,081 possible draws, and
you're left with an EV of only 0.55.
If you hold the
pair of 8s and draw three cards, there are 16,215 possible draws, with
the potential winners giving you 13,026 payouts and an EV of 0.80.
Surprised that such
a lowly pair can give you so much potential? But remember, a low pair
has the potential of 45 four-of-a-kinds, 165 full houses, 1,854 triplets
and 2,595 two pair.
It also works out
the same way with the more respectable game of 9/6 Jacks: a pre-draw
3-card straight flush is ranked below a straight, which in turn is ranked
below a low pair.
Now think of going
through these steps in order to rank not three ways to play a particular
hand but 36 possible ways in order to come up with a ranking table.
And that's for just one game. Multiply those calculations times thousands
of different pay tables. Makes you a little grateful for computers,
Until next time,
aces and faces to you.