Can't We Just Flip A Coin?

Albert and Bradley can't decide who will get the ball first in a game of basketball. Cathy decides to step in and tell them to pick an integer between \(1\) and \(100,\) inclusive. Whoever is closer to the number Cathy randomly picked will get the ball first.

Albert randomly guesses the number \(37.\) Bradley then picks a number that will maximize his chances of winning. What number did Bradley pick?

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