Puzzle 22: Can Oleg beat Erdös?

Oleg and (the ghost of) Erdös play the following game. Oleg chooses a non- negative integer a1 with at most 1000 digits. In Round i the following happens:
Oleg tells the number ai to Erdös, who then chooses a non negative integer bi, and then Oleg defines ai+1 = |ai − bi| or ai+1 = ai + bi. Erdös wins if a20 is a power of 10, otherwise Oleg wins.

Who is the winner, Oleg or Erdös?




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