# Problem 436: Unfair wager
Julie proposes the following wager to her sister Louise. She suggests
they play a game of chance to determine who will wash the dishes. For
this game, they shall use a generator of independent random numbers
uniformly distributed between 0 and 1. The game starts with S = 0. The
first player, Louise, adds to S different random numbers from the
generator until S > 1 and records her last random number 'x'. The
second player, Julie, continues adding to S different random numbers
from the generator until S > 2 and records her last random number
'y'. The player with the highest number wins and the loser washes the
dishes, i.e. if y > x the second player wins. For example, if the
first player draws 0.62 and 0.44, the first player turn ends since
0.62+0.44 > 1 and x = 0.44. If the second players draws 0.1, 0.27 and
0.91, the second player turn ends since 0.62+0.44+0.1+0.27+0.91 > 2
and y = 0.91. Since y > x, the second player wins. Louise thinks
about it for a second, and objects: "That's not fair". What is the
probability that the second player wins? Give your answer rounded to 10
places behind the decimal point in the form 0.abcdefghij