Quote:
Originally Posted by ChrisV
Gonna try one more tack. If the bot knew before it acted that we had JJ, would it alter its strategy? Yes, right? It'd just fold most of its range preflop. You agree with that, right?
But your contention is that it doesn't matter whether WE put in more money or not. How can both things simultaneously be true? How can the bot react to the news that we have JJ by wanting to wager less money, yet when we find out we have JJ, it doesn't matter at all whether we wager more money or not?
This is getting ridiculous.
Suppose A and B are NLHE players that are in equilibrium, I.e., they are both playing GTO strategies.
Suppose A's strategy includes 3betting JJ 90% of the time and flatting 10% of the time.
By definition, this means that for player A, when playing against player B, that EV(3Betting JJ)=EV(flatting JJ). Suppose this isn't true. Let's say EV(3betting JJ)>EV(flatting JJ). Then A would choose to 3bet JJ more often, and therefore it would not be in equilibrium at the 90, 10 frequencies.
The EVs are the same because in order to get to equilibrium, B has adjusted its strategy to make A indifferent between the two. A, however, must choose the exact frequencies to minimize B's EV. In this case, A found that 90,10 minimize B's EV.
However, now that it's in equilibrium, if we fix B's strategy, then A can choose any frequencies it wants to. It's only if B is allowed to exploit A that A would have to retain the 90,10 frequencies.
I don't know how else to make this any clearer. Maybe post a link to this in the poker theory forum or something; perhaps somebody there can explain better.