Problem Statement  
You have a deck that contains R red and B black cards. You are playing the following game: You shuffle the deck, and then begin dealing the cards one by one. For each red card you flip you get a dollar, and for each black card you flip you have to pay a dollar. At any moment (including the beginning of the game) you are allowed to stop and keep the money you have. Write a method that will take the ints R and B, and return the expected amount you will gain if you play this game optimally.  
Definition  
 
Notes  
  During the game, your balance may be negative.  
  We assume that each permutation of the cards in the deck is equally likely.  
  Your return value must have a relative or absolute error less than 1e9.  
Constraints  
  R will be between 0 and 5,000, inclusive.  
  B will be between 0 and 5,000, inclusive.  
Examples  
0)  
 
1)  
 
2)  
 
3)  
 
4)  
 
5)  
