playBunny: Too many in this context simply meant the number that starts to affect your ability to keep up. If I play 10 games I may do all my moves quickly, going to 20 may be the same (I just play 2x as many moves to make up for the extra games), however if I go to 1000 games it's unlikely I'll be moving 100x faster to compensate.
I may move a little faster though, which is why the average can't be over too long a time.