Puzzle: probability to guess one number given a second number...

[Bomb#20]

Suppose the numbers are x and y, with x < y. Choose your favorite probability distribution supported on the whole real line, let's say N(0,1), and sample a random value z from it. If the number you see is greater than or equal to z, guess it is the larger of the two

Brilliant! I was wrong.

One quibble — you can’t actually sample N(0, 1) or any other distribution supported on the whole real line in finite time. But that isn’t a necessary feature of the algorithm — any dense distribution will serve. For example, roll a die and write a minus sign if even. Roll a pair of dice repeatedly. Subtract 2 and write the digit, over and over, until you roll double sizes. Write a decimal point. Do the same thing again, only this time write a 0 when you get double sixes, and you’re done.

 

[fromderinside]

Substitute P for N and you've fixed it. Of course you still need a set of real numbers, I suggest N(0,n), from which to sample.