[pzhon]

IIRC, Turmel was a borderline crackpot in other contexts. He proclaimed that control of the world financial systems should be turned over to engineers because engineers understand feedback systems, or something like that. It's interesting to see him turn his "insights" to poker theory.

The idea he points out is that if you know your edge is small, and your opponent knows your edge is small, it takes an overbet to force your opponent out.

In practice, you don't know exactly what your edge is. If you overbet with what you think is a small edge, say with 55 against overcards, you will get called when you were horribly wrong, and the cost of this is prohibitive.

You also have to take into account implied odds and bluffing.

I think it is better to imagine a market whose consumers are the different hands your opponent could have, weighted by likelihood. As a simple approximation, if there can be no raises, and no betting on future streets, then each hand may have a maximum amount it is willing to call. If you bet too much, only the strong hands will call, and you may lose more from those times than you gain from buying many pots. If you bet too little, you will get called by more hands, but you might leave too much money on the table. The profit-maximizing bet sizes depend on the distribution of calling thresholds.