Then I apologise for thinking it had been you. I’m going to sound very arrogant but: I don’t need to set up the scenario you describe because optimal strategie

Then I apologise for thinking it had been you. I’m going to sound very arrogant but: I don’t need to set up the scenario you describe because optimal strategies in identical games have been proven since the 1940s when Oskar Morgenstern and John Von Neumann published their seminal Theory of Games and Economic Behaviour (1944). If you are getting results that are in conflict with that which is mathematically proven (provided certain circumstantial criteria are met), then you can be sure that you have not exactly matched the circumstantial criteria assumed as a perquisite for the proof. So basically you’re in another situation where the theorem makes no claim to hold and, unsurprisingly, doesn’t.