Thursday, March 18, 2010

Winning by Losing in Poker

I haven't played poker much the last month, except for a few online tournaments.  However, I sat down and played a bar poker tournament a few days ago.  There was a particular hand that I want to share - it involved pot odds.  I may not have the details correct in my memory, but the pot odds principle is there.

To be honest, I wasn't really playing at first.  I was running a tournament that started small and an extra player was needed at the table.  So I sat down and played.  Without any real desire to win, I just bleed chips to the other players until almost all of mine were gone.

Then I realized, why not?  I should go on and win this thing.  So, I started playing in earnest.

A pivotal moment came where I was the big blind for 4,000 chips.  A guy in middle position raised to 8,000.  There were three players who called.  It was on me. My cards really weren't that good.  I didn't even need to be in the hand.

The pot was now 36,000; I had to call 4,000.  That gave me 9:1 pot odds.  With those pot odds, I really wanted to call, so I pushed in my extra 4,000 in chips.  The flop came.

I almost laughed.  The pot was 40,000.  I had just flopped an open ended straight  My odds of catching one of my four outs was 31.5%, or about 1:2.  Trying to keep a straight face and failing, I blurted out to the original raiser "There is nothing you can bet that will not give me good pot odds."

After the flop, you want to make a big bet that destroys a person's pot odds and keeps him out of the hand when he has a draw.  On a 40,000 pot I'd call 100 (an impossible bet here) even if I had nothing at all and no chance for a draw.  40:1 pot odds would be too much enticement.  But even if he had 40K in chips, I'd have to call - that would give me 2:1 pot odds, a break even point.  If someone else called, my pot odds woudl be even higher.

So the original raiser opened for 10K.  That gave me 4:1 pot odds, and since two more players went in, it gave me a 70K pot I needed 10K to call.  With 7:1 pot odds, and 1:2 odds of making my hand the "pot odds" were dictating that I call.

Work it out.  Over time I will lose two out of every three hands like this I play.  So I am far more likely to lose than to win.  But by playing a hand that loses, my chip stack will grow.  If I play the hand 100 times, at a cost of 10,000 to call on the flop, it will cost me 10K * 100 = 1,000K chips.  If I win 1/3 of the time, I win one third of 80K * 100, or about 8,000K / 3 = 2,666K chips (the actual amount is 8,000K * 31.5% = 2,520K chips)

For 100 such hands, my win of 2,520 chips, less my cost of 1,000K chips equals a profit of 1,520K chips, or 15K chips per hand.  To put in terms of mathematical expectation, I "expect" to win 15K in chips every hand, whether I win the pot or not.  How can I not call?

This is what pot odds are and how they are played.

Just to note, since this would have bankrupted me if I had lost, which I was favored to do in a one hand situation, stack management is important to consider as well as pot odds.  Always call when in a cash game, but for tournaments it is a gamble.  But I gambled, and won.

Just remember, it is important to know the math.

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