Say that in each case where a Beauty and a Visitor meet each other, a wild Bookmaker appears and offers each of them a chance to bet on what was the outcome of the coinflip. If they have different subjective odds then they will choose to make different bets (depending on the odds offered) and one will be more profitable than the other—so in that sense at least one of them is wrong. Or am I missing something?
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.
Say that in each case where a Beauty and a Visitor meet each other, a wild Bookmaker appears and offers each of them a chance to bet on what was the outcome of the coinflip. If they have different subjective odds then they will choose to make different bets (depending on the odds offered) and one will be more profitable than the other—so in that sense at least one of them is wrong. Or am I missing something?
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.