Quote:
Originally Posted by Matthew Janda
What EmptyPromises is (correctly) saying is that all that matters for determining the best line is the current state of the game (each player's range, the stack depth, etc). If you and your opponent are playing heads up and find yourselves in a certain situation, it doesn't matter how you got there the optimal lines will be the same.
What you're saying is poker is a multistreet game so the EV of a line has to take those multiple streets into account. So for example, it's not a big deal if someone can make a profitable bluff if they had to risk money to maybe get the chance to make the bluff. This doesn't contradict what EmptyPromises is saying, you're just looking at it in a different way.
Sorry to dredge this back up again, but I finally had a chance to think about it, and I am pretty sure now that what you say in the first paragraph is false.
Again, look at examples 20.1 and 20.2 in TMOP. In the first one, X has a bluffcatcher and Y has 7/8 nuts and 1/8 air, pot size 6 so A calls 6/7 (standard). In Example 20.2, we reach an
identical situation (with identical ranges) on the river but
X only needs to call 1/7. This is not contradictory, because we are maximizing two different things in the two examples, in the first one we wish to find the Nash equilibrium for a one street game, and in the second we want an NE for the entire two street game and dont care about the river in isolation.
I think all this is related to the concept of sub-game perfect equilibria, but it's late and I'm not about to go dig up old classnotes, so if someone who is familiar with that stuff can elucidate that would be great.