Suppose you play with a Nash equilbirum strategy in a heads up NLH match, can you play every equal situation in the same way? (Equal in the sense of the same cards on the board and in your hand and the same bet sequence). Or do you have to roll a dice and play different ways some percent of the time?
I am wondering if there is a proof or disproof of this, if not is there a good arguemnt for or against?
My question is, is there a pure (not mixed) nash equilbirum strategy in poker? Ie such that you dont loose money against a mixed nash strategy?