But you're playing the house to his Martingale bet, right? If the game was repeated, you should be willing to bet all your money on it, since the odds are in your favor.

I think the question checks your ability to understand the mathematical potential payoff, but also to weigh that against the real-world consideration of risk.

I suppose. But there's a difference between "mathematical potential payoff" and how much I will risk on the flip of a coin. And as far as I can tell, the amount I pay has no effect on the odds or rules. So, three bucks.

Oh, absolutely, and that's the point of the question. My guess is that the answer "three bucks" and the answer "Well, the expected payoff is infinite, but ... three bucks" is the difference between the door and an offer.