Copyright 2005 Full
Tilt Poker
August 15, 2005
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Poker Lesson: No-limit
by the Numbers
Author: Andy Bloch
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.
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