https://docs.google.com/spreadsheets/d/e/2PACX-1vThljkK2nUIL...
I find it interesting: it is definitely symmetrical, but I did not expect that in the final result 1/98 could be more important as a starting value, while 2-17/82-97 are not used at all.
The initial set of strategies wasn't very diverse and compensated for the binary search "weaknesses" on the ends of the spectrum by sometimes guessing 1 and 98.
But after adding some more pure strategies to the set, we've got a far better mixed strategy that prefers the numbers between 28-70 as the first pick: https://github.com/gukoff/ballmer_puzzle#winning-strategy
> Avg win if Ballmer chooses randomly: $0.16247848000093376
> Win if Ballmer chooses adversarially: $0.14657033010415976