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 in no
limit poker.
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.
You can calculate your poker odds automatically when
playing online as well with the
Calculatem Pro program which will automatically read
your hands and give you your starting hand percentage,
how many outs your have, and even read your pot odds for
you.
Andy Bloch
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