Sunday, May 27, 2007

Poker Math I

Poker is a game of strategy based on mathematics and psyhcology. In order to be a winning player you should have a firm grasp of the math involved in poker. when i became interested in poker the first thing i did was to research the rules of games, followed by learning hand rankings and the basic hand & pot odds. That is basically as far as i have gone in terms of the math of poker. I've picked up on implied odds from reading the forums but have not studied it myself. I have never sat and done an EV calculation in my life! This will change shortly but first i will address hand odds & pot odds.

Hand Odds & Pot Odds

There is a long drawn out method to calculating you're hand odds but i will not get into that. Instead i will give you the short and sweet method that i initially learned.

[Total outs x 2]+ 2 = percentage to make hand from turn
[Total outs x 4] = percentage to make hand from flop

Inside straight drw [4outs x 4] = 16%
Two overs [6outs x 4] = 24%
OESD [8outs x 4] = 32%
flush drw [9outs x 4] = 36%
flush drw + Gutshot [12outs x 4] = 48% (actually 45%)
flush + straight drw [15outs x 4] = 60% (actually 54%)

As you can see this method gives you a rough estimate and can be off by a few percentage points... especially with the combo drws. But it is good enough to use at the tables.

Convert percentages to odds as follows

Odds = [100 / whole percentage]- 1

e.g
Odds of making OESD = (100/32)-1 = 2:1

2:1 odds mean you can expect to make your drw 1 out of 3 times.

Pot odds are the ratio of the amount of money in the pot to how much it cost to call.
If there is 100.00 in the pot and its 10.00 for you to call then you're pot odds are 100:10 or 10:1. The higher the ratio the better you're pot odds. If you were to make this call, you must make your hand 1 out of 11 times just to break even! The thinking is that if you make this play 11 times it will cost you 110.00, but when you win once you will get 110.00 back.

While at the tables you compare your pot odds to the hand odds to make the most profitable play. So id there is 35.00 in the pot and its 10.00 for you to call with a flush draw the pot is laying you 45:10 or 4.5:1 odds. You must win this hand 1 out of 5 times to break even, but the odds of winning with the flush draw is 1 out of 3 times.

Net cost to play = 100 hands x 10.00 to call = -1000.00
Pot value = 35.00 + 10.00 bet + 10 call = 55.00

Odds to win = 2:1 or 35% (from flop)
Total hands won = 100 x 35% = 35

Net profit = Cost to play + [Total times won x Pot value]
= -1000.00 + (35 * 55)
= -1000.00 + 1925.00
= \$925.00

If your Pot Odds are greater than your Hand Odds, then you are making profit in the long run!

This is pretty basic and straight forward stuff but its good to go back over it. I very rarely think about this at the tables in this form, I just try to ensure that i'm getting at least 4:1 or better to call. If its close then i decide if i will be able to get more money if i hit my hand. I will be progressing through more complicated examples, Implied odds, reverse implied odds and eventually EV calculations.

ps. just want to add that i'm referencing various books and internet sources for my info... which i read, think about then post here as i understand it. I'm no math whiz, far from it, but i think going through this process will help me. 