Archive for June 13th, 2009

Even though I’m too sloppy/lazy/uneducated to work out the details of complicated problems, I’m quite interested in the mathematics of poker. I feel like I do have a broad grasp of the game theory that underlies many situations and can use that to aid in my decision-making. Recently, I’ve been curious about how to quantify exactly the value of seemingly abstract concepts like position and implied odds. I think I may have come upon a sketch of how to work some of it out, though I doubt I’ll ever follow up on it.

We start with the “exploitability”, the idea that there is something about how you play that an opponent could potentially take advantage of. Conversely, “unexploitable” means that there is nothing an opponent could do to take advantage of how you play. Importantly, unexploitably is not always the most profitable way to play. Often, you will do something exploitable in order to exploit something exploitable an opponent is doing.

Suppose that you hold AQ in the big blind in a $1/$2 NLHE game. The action folds to the SB, who open shoves for $20. If you know that this opponent will only shove JJ+ and AK, you can fold your AQ. Though itself exploitable, this fold exploits your opponent’s excessively tight shoving range.  Read the complete post...