# Showcase Showdown

This week’s Fiddler is based on “Showcase Showdown” on the game show “The Price is Right”.

Suppose we have some number of players. Player A is the first to spin a giant wheel, which spits out a real number chosen randomly and uniformly between 0 and 1. All spins are independent of each other. After spinning, A can either stick with the number they just got or spin the wheel one more time. If they spin again, their assigned number is the sum of the two spins, as long as that sum is less than or equal to 1. If the sum exceeds 1, A is immediately declared a loser.

After A is done spinning (whether once or twice), B steps up to the wheel. Like A, they can choose to spin once or twice. If they spin twice and the sum exceeds 1, they are similarly declared the loser. This continues until all players are done. Whoever has the greater value (that does not exceed 1) is declared the winner.

Assuming all players play the game optimally, what are player A’s chances of winning?

My solution:
[Show Solution]