I don't see why this can't be solved (approximated) recursively. If I know the EV of 1 and 2 choices, then the 3 number situation is the same as whatever weigh

I don't see why this can't be solved (approximated) recursively. If I know the EV of 1 and 2 choices, then the 3 number situation is the same as whatever weight I assign to choosing the first number multipled by Ballmer's strategy multiplied by the EV of the 1 case when I pick 2, and the 2 case if I pick 1 or 3. Run this as a Counter Factual Regret minimization problem for each value from 3 through 100 with some sort of error threshold and you have a good enough answer. I'm not 100% sure of that though. Perhaps there's a dependency in the two steps that confounds this approach?