The question I asked last time was, if you are facing a pot-sized bet on the river, how often do you need to have the best hand to call profitably?
As a couple commenters pointed out, the correct answer is more than 1/3 of the time. To see why, we have to consider the possible scenarios. The value of folding is 0. We don’t put any more money in and we don’t get anything back.
For calling to be better than folding, the expected value of calling must be more than 0. If we call and lose, we lose a pot-sized bet. If we call and win, we win two times the pot: our opponent’s bet plus the pot. Every time we win, that balances out two times we lose. We only need one win for every two losses to break even. Since 2/3 is twice 1/3, the break-even point is 1/3. If we have the best hand exactly 1/3 if the time, it doesn’t matter whether we call or fold. Any less than 1/3 and we should fold; any more and we should call.
This does not seem to be intuitive. Most people would like to be more confident that they have the best hand in order to call. The most common answer I got was more than half the time.
It also highlights how emotional reinforcement in poker is not always aligned with making the best plays. If you are consistently calling in situations where you have the best hand 40% of the time, those are good calls, but you will still feel the embarrassment of paying off a worse hand 60% of the time.
In a sense, the most important point is implied in the question itself. Namely, that you should answer in terms of probability. This is not most people’s first instinct. They think of whether the guy is trying to bluff them, how it will feel if they lose, and so on.
The next obvious question is how do you know if you have the best hand 1/3 of the time? That’s a much more difficult question. It relies on everything that’s happened in the hand, your opponent’s style, what he thinks of you, etc. etc. etc. Think of it like you’re a sharpshooter: there’s a lot that goes into improving your accuracy, but if you don’t know the odds, you don’t even know where the target is.