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.

**Play Online Poker**

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