I guess I misunderstood the problem. I thought we knew could beat the game at $20/hr. Your point about uncertainty in win rates is something that I think anyone considering going pro would want to think long and hard about, but I thought we assumed this out of the problem. How do you do this calculation, btw?

Also, I did not think we had the option of building our bankroll for 6 months, since we only were interested in finding the current value of X. Of course, if you have the option of waiting until you have a bigger roll with a buffer to pay bills, you definitely should.

I was imagining a player with closer to 300k hands of history that, for whatever reason, had spent most of the money he made. I also had in mind a player that was playing fewer tables with a win rate around 8ptbb/100. This player is in a vastly different situation than the player you had in mind.