[vjo]

I did a very similar exercise after reading the original post.

You can get the EV a lot closer to the optimal +0.2 (Although I was unable to prove how close) by dropping the requirement "do not increase worst-case complexity for the binary search" as this is lost with initial guesses outside 36-64 anyway. Deviating at a higher depth makes punishing specific guesses in the tails a lot cheaper, only giving up 1-2 cents of EV.

[gukoff]

Interesting! What about the worst case? And which kinds of strategies did you pick?

[vjo]

Using random strategies with small sub-optimal deviations, I get to about $0.189

Ref. https://pastebin.com/YcRhGpV6