Last ball

A bag is filled with blue and red balls. There are $20$ blue balls and $13$ red balls in the bag. You repeatedly pick out two balls at random, without returning them to the bag. If the two balls are of the same color, you add a blue ball to the bag. If the two balls are of different colors, you add a red ball to the bag. You have an infinite supply of both blue and red balls. If you keep repeating this process until only one ball is left, what color will the last ball in the bag be?