# Problem 298: Selective Amnesia
Larry and Robin play a memory game involving of a sequence of random
numbers between 1 and 10, inclusive, that are called out one at a time.
Each player can remember up to 5 previous numbers. When the called
number is in a player's memory, that player is awarded a point. If it's
not, the player adds the called number to his memory, removing another
number if his memory is full. Both players start with empty memories.
Both players always add new missed numbers to their memory but use a
different strategy in deciding which number to remove: Larry's strategy
is to remove the number that hasn't been called in the longest time.
Robin's strategy is to remove the number that's been in the memory the
longest time. Example game:Turn Callednumber Larry'smemory Larry'sscore
Robin'smemory Robin'sscore 1 1 1 0 1 0 2 2 1,2 0 1,2 0 3 4 1,2,4 0 1,2,4
0 4 6 1,2,4,6 0 1,2,4,6 0 5 1 1,2,4,6 1 1,2,4,6 1 6 8 1,2,4,6,8 1
1,2,4,6,8 1 7 10 1,4,6,8,10 1 2,4,6,8,10 1 8 2 1,2,6,8,10 1 2,4,6,8,10 2
9 4 1,2,4,8,10 1 2,4,6,8,10 3 10 1 1,2,4,8,10 2 1,4,6,8,10 3 Denoting
Larry's score by L and Robin's score by R, what is the expected value of
|L-R| after 50 turns? Give your answer rounded to eight decimal places
using the format x.xxxxxxxx .