[Edit: Intro + fixed link + emphasizing key text]
I may be incorrect. That has happened before. But if I am correct, then I am correct by quite some margin. It would be nice if some guru could have a look at the article and the rest of my post.
[End Edit]
The subject refers to this article: http://www.pokerstrategy.com/strategy/fixed-limit/1289/2
I believe that there is an error in the section "When exactly is a river bet profitable?". In particular, when we are out of position, the logic fails a bit in my opinion.
The context: We are out of position.
Our read (read 1) is that if we check, then our opponent will bet if and only if he has us beat.
The question: Is a bet better than a check-fold?
The article claims that the anwer depends on the calling range of the opponent.
I too claim that the anwer depends on the calling range of the opponent, so all is well so far.
The article then claims that if the opponent calls and then loses with a probabiliy p that greater than (bet size/pot size in bets), then we should bet.
Our read is this (read 2): He will call with every hand (b of those) that he would have bet with had we checked. He will also call with c of the hands that he would have checked behind had we checked.
Moreover (read 3): Our opponent will not raise if we bet period.
I claim that our bet is profitable in this situation if and only if the probability p as defined above is greater than 1/2.
Statement: We beat the c hands and lose to the b hands.
[You can't argue with this. It is consistent with our original read 1 and read 2 about what happens if we check.].
My claim: We should bet if and only if c>b. The size of the pot is irrelevant in this situation.
It is a different matter when our bet will make hands fold that would originally have bet (or more generally hands that beat us) but this simply is not the case here.
One could speculate about the origins of the reasoning in the article (or better, ask cornolio). From the opponents perspective, the pot size is involved. He should base his call decisions based on the pot size. We should still ignore the pot size since we are not bluffing here. We are making a thin value bet.
To be specific: The article presents an example where we have KK oop. There is an A on the board. The action goes bet-call (flop), bet-call (turn).
In the article it is estimated that the opponent will call with all Ax remaining in his range (AQ+), and also with QQ. [He will also bet all A if we check and check worse hands if we check.] The article says (correctly probably) that we lose 4/5 if we bet, but maintain that the bet is correct because the pot is large.
Sure, betting is better than checking and calling. But checking and folding is best given our reads.
/Johan = 
