Each of them gets most expected profit when betting on their own odds. My python code snippets are about basically this scenario.
When a Beauty meets a Visitor in Room 1 she is right about coin being heads 2⁄3 of times. But Visitor meeting Beaty in Room 1 can guess Heads only 1⁄2 of times. That’s because on a repeated experiment, Visitor meets Beauties (there are two of them on Tails) more often than any specific Beauty meets Visitor—they have different possible outcomes, thus different probability estimates and different favourable betting odds.
We can, in principle, make a betting scheme to which only the Visitor’s (or, likewise, only the Beauty’s) probability estimate is relevant. I’ll talk more about it in the next post.
Each of them gets most expected profit when betting on their own odds. My python code snippets are about basically this scenario.
When a Beauty meets a Visitor in Room 1 she is right about coin being heads 2⁄3 of times. But Visitor meeting Beaty in Room 1 can guess Heads only 1⁄2 of times. That’s because on a repeated experiment, Visitor meets Beauties (there are two of them on Tails) more often than any specific Beauty meets Visitor—they have different possible outcomes, thus different probability estimates and different favourable betting odds.
We can, in principle, make a betting scheme to which only the Visitor’s (or, likewise, only the Beauty’s) probability estimate is relevant. I’ll talk more about it in the next post.