I have a complete solution that solves this problem in just 2 questions a third of the time, and at most 3 questions.

http://sadowl.com/Three-Idols-Solution.html

anthonylo221: See my solution. I think it makes a lot more sense.

@ahaselhu: Random doesn’t randomly determine whether or not to answer yes or no, he randomly determines whether to tell the truth or lie. Whether he does one or the other, his answer is still no.

A simpler case is the question “Are you lying?” A truth teller will say no, and a liar will also say no.