Can't We Just Flip A Coin?

Probability Level 1

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 11 and 100,100, inclusive. Whoever is closer to the number Cathy randomly picked will get the ball first.

Albert randomly guesses the number 37.37. Bradley then picks a number that will maximize his chances of winning. What number did Bradley pick?

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