a simple 3 player game

here's a simple math problem that more people have probably thought of.

3 people (A, B, and C) are playing a simple game. in turn, each one chooses a real number between 0 and 1. afterwards, a random number N is picked between 0 and 1. the person who picked the number closest to N wins. what number should each person play? who is most likely to win?

i have absolutely no clue what the answer is. however, one of you might! because of this, i've left a little form for you to fill out in case you have any idea. if someone has a good idea i'll put it in the post.

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