It is a mind game, but not the one you’re claiming imo. Probabilities are a game about choices, aka co-products. There are lots of ways to specify the alternatives in a co-product. And once you’ve done so, you can create an instance of that co-product by injecting one of its constructors. A co-product is a type, and its constructors create instances of that type. So frequentists count up the instances and then compare the relative frequency. Your mind games are just silly ways of defining different co-products using hypothetical knowledge or not. Differences in knowledge imply different definitions of alternatives (“Knowing” something subtracts the alternatives), which defines different types. But obviously you don’t actually need silly anecdotes about what somebody knows or doesn’t know to define different co-products. You could do it with toothpicks of different lengths, or the color of balls, or whatever.
It is a mind game, but not the one you’re claiming imo. Probabilities are a game about choices, aka co-products. There are lots of ways to specify the alternatives in a co-product. And once you’ve done so, you can create an instance of that co-product by injecting one of its constructors. A co-product is a type, and its constructors create instances of that type. So frequentists count up the instances and then compare the relative frequency. Your mind games are just silly ways of defining different co-products using hypothetical knowledge or not. Differences in knowledge imply different definitions of alternatives (“Knowing” something subtracts the alternatives), which defines different types. But obviously you don’t actually need silly anecdotes about what somebody knows or doesn’t know to define different co-products. You could do it with toothpicks of different lengths, or the color of balls, or whatever.