Poker Theory Problem (crosspost from poker theory forum)

[inlemur]

I am crossposting this from the poker theory forum because it seems like it could be a fun problem for some of the mathier folks. If this is an out of line thing to do, please let me know and I'll contact a mod to lock the thread.

I apologize if this is an old question, because it seems like the kind of thing that has probably been posed several times, but it can't really be searched for.

Suppose I design a robot that plays poker, and you are going to play a heads-up NL hold-em tournament with it. The robot's strategy is to push all in with any two cards without even looking at them.

What strategy should you adopt to maximize your equity? That is, what hands should you call with? How does this change as a function of the blind structure of the tournament? Finally, what is your equity against the robot assuming perfect play?

Calling with any favored hand does not seem correct unless each player has a very small number of BBs. For example, many hands are slightly +EV against a random hand but if it costs very little to wait for a hand with a larger +EV vs random, then it seems correct to do so. But how can you relatively accurately calculate your equity as a function of the structure?

This is a summarization of a question a friend asked while I was teaching them how to play poker. I was trying to explain that unlike say, basketball, where I would lose to LeBron 100% of the time, in poker, even a two line program could win a heads up game against Phil Ivey some percent of the time. I could not, however, come up with that percent chance of winning figure, though I suspect it's around 20% for most reasonable blind structures.

Thanks for any replies.