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Andy Bloch
August 15, 2005
I get asked a lot of poker strategy
questions, from beginner to advanced.
Some are easy, but some involve the
kind of math I can't always do off the
top of my head. When that happens, I
rely on one of a number of free tools
to calculate the probability of
winning the hand.
Here's an example based on a hand
posted on a website I run:
Our hero was playing at a small
stakes No-Limit table online, with
$.25-$.50 blinds. At the start of the
hand, he had $44. He was dealt Ad-Td
and raised to $2. Both blinds called.
The flop was Kd-Jd-2c, giving our hero
a royal flush draw. The big blind bet
$2, hero raised $2 more, the next
player called, and the big blind (with
more chips than our hero) re-raised
all-in.
Should our hero call with his last
$38? Let's assume the third player
will fold. If our hero were to call
and win, he'd be up to $94 (the $18 in
the pot, plus his $38 and his
opponent's $38). If he wins the hand
four times out of 10, on the average
he'd have $37.60 after the hand ($94
multiplied by four, and divided by
10). In poker, it's the long run that
matters, so he should only call if his
probability of winning is greater than
40%. Now he needs to figure out the
probability he'd win the hand.
The first step is to put his
opponent on a range of hands.
Sometimes, you can figure out exactly
what your opponent must have by the
betting or tells. Most of the time,
you're left to guess a little. In this
situation, the other player probably
has a very strong hand, but there's a
chance he's bluffing or even
semi-bluffing.
The strongest hand our hero could
be facing is three kings. He has 11
outs to win the pot - every diamond
but the 2d, and three queens. But even
if our hero makes his flush or
straight, his opponent could still win
by making a full house or quads on the
last card. I could calculate the
probability by hand, but I don't need
to.
Instead, I head to the Internet and
one of the many free poker odds
calculators, such as the one at
twodimes.net. Enter "Kd Jd
2c" in the box labeled
"Board" and "Ad
Td" and "Ks Kc" under
"Hands", and click submit.
The result says that Ad-Td wins under
34% of the time - less than the 40+%
that would make a call the right play.
If our hero knows that his opponent
had three kings, he should fold. The
probabilities for the other possible
three-of-a-kinds are the same.
But what if he's up against two
pair - kings and jacks? Using the
poker calculator again, his
probability of winning would be 44%.
That's enough to make calling correct.
Our hero might also be against other
two pairs, which he'd beat a little
less often (42%), or A-K (46%). He
might even already be ahead if he's
against an aggressive player who would
semi-bluff with something like Q-T
(81%) or Qd-9d (82%).
Having calculated the probabilities
of winning, our hero is now left with
the subjective part of the answer,
guessing the probabilities of what the
other player has. I would guess that
it's more than twice as likely that
the player has two pair, or A-K, or
even some weaker hand than that he has
three of a kind. And I would guess
that maybe 5% to 10% of the time,
Ad-Td is actually ahead. I told our
hero that, based on the numbers, I
would have called.
Our hero did call, and the other
player had K-J, giving our hero a 44%
chance of winning the hand. The turn
card was the 2d, but the river was a
jack and our hero's flush lost to a
full house. The river card was a tough
break, but playing by the numbers, he
still made the right play.
It's good to know the numbers, but
it's equally important to know how to
get them. And if you use the available
tools whenever you aren't sure, you'll
start to remember them when they come
up at the table. In poker, every tool
in your toolbox brings you one step
closer to mastery of the game.
Andy Bloch
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