What's Your Starting Hand Really
Worth?
Pro Poker Tips - Steve Brecher
Most players know that pre-flop
position is important in hold 'em. The earlier your position, the more
players there are behind you and, unless you hold pocket Aces, the
bigger the chance that one of them will have a hand better than yours.
There is another aspect to position: It's better to act after your
opponent(s) rather than before. But for this tip, I'm going to
investigate the chances that a player behind you will have a better
hand.
There is no universal definition of what "better" means when comparing
hold 'em starting hands. For this article, I needed some reasonable,
quantifiable criterion. So in the following, I'm assuming that one
hand is "better" than another if its showdown equity is greater. A
hand's showdown equity against another hand is the average portion of
the pot it will win across all possible combinations of board cards.
This is similar to the percentages that TV poker programs display next
to player hands when the players are all-in. If you're interested in
investigating this for yourself, there are several free computer
programs and websites which calculate the showdown equities of
user-specified competing hands.
For example, Ah 2d all-in pre-flop against Kc Qc will, over all
possible boards, win an average of 53.9% of the pot. So the A-2 is the
"better" hand against K-Q suited by our definition. Obviously, it is
not better for all purposes; at a full table I'd usually open-raise in
early position with K-Q suited, but toss A-2 offsuit.
Given some specific hand category – such as K-Q suited – we'll need to
know the chance that a random hand dealt from the remaining 50 cards
will be "better." This requires that we have a showdown equity
calculation for each of the 1,225 possible opposing hands and tabulate
against how many of them the K-Q suited has the worse (less than 50%)
equity. It turns out that 238 of the 1,225 possible opponent hands are
"better" in this sense. So we say that the chance of a random hand
being better than K-Q suited is 238/1,225 or 19.4%; conversely, the
chance that a random hand will not be better is 80.6%. This tabulation
would be too tedious to do by hand. For the example results below, I
developed some simple software to do the calculations.
Suppose that you are considering an opening bet pre-flop. There are
players yet to act behind you. I'll denote the number of hands to play
behind you as N. For example, if you're on the button, then there are
two hands - the blinds - behind you, and N would be equal to 2. What
is the probability that none of some number of random hands will be
better than yours? It is the chance that one random hand will not be
better than yours multiplied by itself N-1 times, which is the same as
saying it's that probability raised to the Nth power. For example, if
there's a 40% chance that a random hand won't be better (i.e., a 60%
chance it will be better), then the chance that none of three random
hands will be better is 40% x 40% x 40%, or 0.4 to the 3rd power,
which equals 0.064. Hence, the chance that at least one of the three
hands will be better is 1.0 - 0.064 or 0.936 or 94%.
I think the most interesting thing
about these numbers is the difference between earlier and later
positions. This is something to consider when you're thinking of
open-raising in early position.
Steve Brecher
These pro poker tips are brought to you
by the professionals at
FullTilt Poker.
More Pro
Tips
|
