[eastbay]

Warning: probably only potentially interesting to math geeks

At the end of a tournament, it's common to be in a (mostly) all-in or fold situation. When you're on the big blind, what should you be calling all-in with? It seems clear that the answer depends on the size of the blinds relative to the stacks (how long can you wait?), and also to a great extent what your opponent is pushing with.

To make things real simple as a first experiment so that we can work some numbers, what if we presume heads-up, initially equal stacks, a big blind that is 10% of the stack, and a maniacal opponent who is going to push all-in on every single hand.

Also assume that when you're on the button, your play is dead even, so we're only going to look at a series of plays with you on the big blind, deciding whether or not to call.

What hands would you call with?

I wrote a computer model that uses something like a genetic algorithm to search out the best set of calling hands for this situation. The answers are approximate, taken from samples of 20,000 tournaments played out until somebody wins, using trial sets of calling hands (a population), choosing the sets that give the best results, discarding the rest (survival of the fittest), and using those best sets to generate some new alternatives (mating and mutation), and repeating until changing your strategy tends to make the results worse and not better.

Before I share the results, anyone care to make a guess at the answer? Maybe expressed as a percentage of hands ranked in order of their win rates against a randomly chosen hand. Another interesting question is: how much of an edge can you get over your opponent when he uses this strategy, if you make the best choice for calling hands? Can you destroy him by making the best choices, or is he actually playing decently to push in from the button every single time?

Results to come.

These calculations are expensive. It's basically an overnight run to look at one set of parameters. Once I am satisfied with the "push on every hand" answers, I would like to try some different opponent strategies, and apply the same model to compute the best counter strategy. If your opponent is only going to push, say, Sklansky hand groups 1&2, and fold everything else, what changes in the optimal set of calling hands? Groups 1-4?

Looking at this from the other direction, if the big blind is playing an optimal calling counter strategy, how tight should the small blind be with pushing? What push hands give the smallest edge to the big blind if he is going to play a perfect counter strategy?

Before you launch into some big rant about how this is at best loosely related to real poker, save your effort. I understand that. But to me, this kind of exploration is fun and also potentially useful in that some basic concepts and trendlines might come out of it that might be worth keeping in mind.

eastbay