Approximating The Odds--Clonie Gowen

I think this sums up the best way, while at the table, to calculate the odds a hand will hit. Came via email from Full Tilt.

By Clonie Gowen


It is very difficult to calculate the exact odds of hitting a drawing hand when you're sitting at the poker table. Unless you're a genius with a gift for mathematics like Chris Ferguson, you will not be able to do it. That leaves two options for the rest of us: The first option is to sit at home with a calculator, figure out the odds for every possible combination of draws, and then memorize them. That way, no matter what situation comes up, you always know the odds. But for those of us without a perfect memory, there's an easier way. Here is a simple trick for estimating those odds.

The first thing you need to do is to figure out how many "outs" you have. An "out" is any card that gives you a made hand. To do this, simply count the number of cards available that give the hand you are drawing to. For example: suppose you hold Ac 8c and the flop comes Qh 9c 4c. You have a flush draw. There are thirteen clubs in the deck and you are looking at four of them -- the two in your hand, and the two on the board. That leaves nine clubs left in the deck, and two chances to hit one.

The trick to figuring out the approximate percentage chance of hitting the flush is to multiply your outs times the number of chances to hit it. In this case that would be nine outs multiplied by two chances, or eighteen. Then take that number, multiply times two, and add a percentage sign. The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.) Now let's say that on that same flop you hold the Jd Th. In this case you would have an open ended straight draw with eight outs to hit the straight (four kings and four eights). Eight outs with two cards to come gives you sixteen outs. Multiply times two and you will hit the straight approximately 32% (31.46% exactly) of the time.

One important thing to keep in mind is that the percentage stated is merely the percentage of the time that you will hit the hand you are drawing to, NOT the percentage of time that you will win the pot. You may hit your hand and still lose. In the first example, the Qc will pair the board and may give somebody a full house. In the second example both the Kc and the 8c will put a possible flush on the board, giving you the straight, but not necessarily the winning hand. Still, knowing the approximate likelihood of making your hand is a good beginning step on the road to better poker.

Heh she hit the nail right on the head when she said she wasnt a genious with the gift of mathematics if she has to multiply by two twice instead of just multiplying by 4

Who cares if she's good at math or not...she's hot AND she likes poker! If she likes wings and beer, she's the perfect woman!!!

You only multiply by two twice if it's from the flop.

If it was on the turn, it'd be outs X 2.

its easy to prove that in your head. say you have 8 outs. you're dealing with roughly 50 cards. so 8 out of 50 make you win. so %'s are out of 100, so doubling gives you 16 out of 100, per card. round up a % or two because its really 47/46 not 50 you're dealing with. multiply by 2 if you're getting multiple cards.

i find these things easiest to remember if you understand why they work.

I've been using this mnemonic for a while. I spent some time writing some MATLAB programs to calculate the percentage of wins, and I found that it essentially boiled down to the same short-hand formula she mentions.

What I've been trying to commit to memory is the percentage of times premium and near premium hands win against multiple opponents.