[pavlov]

It's kind of a given that you can't use the proposed mixed strategy for a single game, because it expects you to draw one of the patterns at the start of the game.

And some of the patterns are just obviously suboptimal if this is your only chance:

> With probability 0.9686%: Binary search, first guess is 1.

(I wonder what Ballmer would think that, when proposed to play this game, you first manually throw dice to draw a random number in the range 1 - 1,000,000 and if it's 9,686 or less, you start your binary search at 1. He might be impressed by your dedication to the mixed strategy.)