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.
|-||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 1e-9.|
|-||R will be between 0 and 5,000, inclusive.|
|-||B will be between 0 and 5,000, inclusive.|