Symmetry arguments in maths can be misleading. When a magazine published the optimal strategy for the Monty Hall TV game, angry professors wrote in saying it was nonsense, then had to eat humble pie because their intuition had let them down. Now there’s a whole book on the problem, and it starts with convincing explanations of why that strategy really is optimal. In fact the author’s ambition is to use it as a way in to all the main branches of statistics: hence ‘Bayesian Monty’, ‘Monty Meets Shannon’ and so on. And there a few more general insights along the way, eg that frequentism bars irrational numbers from being probabilities (obvious once pointed out) and that, empirically, people better judge the success of different strategies if they’re couched in terms of numbers - - say, 1000 attempts - - rather than probabilities, which I imagine could be important for Bayesian prior elicitation.