Friday, February 8, 2008

A thought about odds

PokerOffice displays your odds to improve in green if they are better than your pot odds, indicating that you should call in this case.

This is, of course, nonsense.

To be precise, it only holds in one specific case:
  • your opponent has a made hand
  • you have nothing (well, a draw)
  • if you do not improve, you lose the hand
  • if you do improve, you are guaranteed to win
I guess I was somewhat aware of this already, but I think it is important to write this down. I was given a very clear example of this situation in my latest game: I had 33 and I limped (possibly called a minraise). The flop was 542, and it got checked round to me. I bet out for two thirds of the pot or so, and I got checkraised all-in.

At this point I looked at my odds in PokerOffice. I was not happy about the situation, but the combined odds of making trips and making my straight (1.6:1) were slightly better than the pot odds I was being offered (1.8:1), so I called.

My opponent flipped over 9-8 offsuit for a total bluff. I had not even considered that I might be ahead... I should have though, it was (somewhat) reasonable that he might have AK or something, and figured he had showdown value.


In general of course, deciding whether or not to call should be based on much more than just comparing two numbers (pot odds and your odds to improve).
  • Your opponent may improve. More generally, you might improve but still lose. For example, in the case above, he might have had an Ace, so that a 3 on the turn or river would give me trips but still kill me.
  • You may have implied odds. When you are on a flush draw, you can call against the odds (up to a point!) in the hope that your opponent will put in more money after you make your flush.
The game really is not that simple!

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