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Hi, I have a question bothering me. Let's say I have a decent preflop solution with full starting ranges for both OOP and IP. As I understand it guarantees me that my opponent can not increase his EV by changing his own preflop strategy.
This is true assuming exploitability is 0. If exploitability is X then your opponent can increase their EV by X per hand at most assuming they play alternating sides (one hand IP, one hand OOP).
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But preflop solution is based on numerous postflop solutions. Let's say we are pretty sure that our opponent is not playing optimally. So his starting ranges for postflop spots will be drastically different. It is clear that this fact doesn't scare our preflop strategy, but what about postflop spots?
They can play better postflop with a different range than the solution but they can make up at most what they have lost altering their EV preflop if it wasn't the case then the optimal solution preflop would be different.
This is relatively obvious when you ask the same question for flop and altering turn ranges. Unfortunately preflop we don't represent the whole game but only a part of it. We took care to provide flop subsets which are possibly close to the whole game so in general the mechanism applies unless the opponent can find a specific weakness of flop subset used and exploit that. The bigger the subset the less it's possible and less EV can be "leaked" that way.
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So, the question is - does preflop solution guarantee an unexploitability for each postflop spot as well?
It would guarantee it if run on all 1755 flops. As it is it almost guarantee it where almost is caused by imperfection of flop subsets.
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And in other words, does it make sense to study postflop spots using optimal ranges if we are sure our opponent does not play optimally (and so his range in the root of postflop scenario is different every time)?
It does make sense as you can't be sure what your opponent is really doing preflop and it makes sense to know what optimal strategy is assuming they are doing well. Now it also makes sense to know what to do if you can pinpoint their exact postflop range but you are guaranteed to do at least decently if you follow one against optimal range.
The main point here is that if it was possible for the opponent to gain more EV on later streets than they lose by altering their strategy on earlier streets then that change would increase their overall EV and it would cause the solution to be different in the first place. Exploitability is calculated across the whole tree so there is no possible way for the opponent to do something clever as we already calculate the best possible exploitive strategy for them.