TITLE: Game between Alice and Bob involving extremal numbers
QUESTION [5 upvotes]: Alice generates $4$ numbers in $(0,1)$ independently and uniformly at random. She discloses one of the numbers to Bob, who is requested to guess whether the disclosed number is extremal (i.e. the smallest or the greatest among all generated numbers) or not. Is there a deterministic strategy for Alice to make sure that the chances that Bob is guessing right are at most 50%.

REPLY [2 votes]: I make all 4 numbers in the range (0,1/2] by taking either x or 1-x. The smallest number is trivially extremal. 
The second smallest number is just as likely to have come from (0,0.5] as from [0.5,1). If it came from the same side as the smallest number it isn't extremal, but if it came from the other side it must be extremal.
I submit the (original) value of this number, which has a 0.5 chance of being extremal.