I think the argument is that if the stakes are high enough people's betting patterns create a zero expectation on the bit itself. This seems wrong on the face of it. It assumes that the bettors on the chess match are perfectly evaluating their skills at making perfect bets with expectation of zero, that there is no skill in determining the bet. Thus with an expectation of zero, the winner of the bet is determined by luck.

This becomes more absurd in the poker game. The difference in skill of betting for action is a large part of the game. Most poker books try to teach it. Most people can't do it.