Bag of Mice Game

A bag contains w white mice and b black mice. Two players take turns drawing mice from the bag at random without replacement. If a player draws a white mouse, they win immediately and the game ends. If a player draws a black mouse, the turn passes to the next player. Additionally, after each black mouse is drawn, a random mouse from the remaining mice escapes from the bag (is removed at random). Both players play optimally. Calculate the probability that the first player wins.

Examples
Input: [1,0]
Output: 1
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Bag of Mice Game

A bag contains `w` white mice and `b` black mice. Two players take turns drawing mice from the bag at random without replacement. If a player draws a white mouse, they win immediately and the game ends. If a player draws a black mouse, the turn passes to the next player. Additionally, after each black mouse is drawn, a random mouse from the remaining mice escapes from the bag (is removed at random). Both players play optimally. Calculate the probability that the first player wins.