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The birthday paradox kicks in when you have a set of objects, and a collision between any pair is interesting. Here, only a collision with 0 is interesting.

Suppose that the sequence of values you have after each ack is A, B, C, D, E (five acks total). So long as A, B, C, and D are all nonzero, we're OK. With the birthday paradox, we'd be looking at A=B, A=C, A=D, A=E, B=C, B=D, etc. -- many more combinations.

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