Qg2#, not Qb2# (typo)

I believe that instead of "Should you pay $1 for this box?", the question should be "Should you pay $1 for each use of this box?". Otherwise, I believe I can just cut the island in half, go back and forth between the sides a billion billion times and keep pressing the button and look for bias in the responses. Then throw away the worse half of the island and repeat