The fact that it becomes very slow to get arena matches when your team reaches high rating is an issue because a lot of those players want their farming bonus as much as their arena rating. An NPC match that wouldn't give rating but gave bonus (if won) would be an interesting compromise.
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Computing the probability that at least one of the following events will occur:
P(a or b ... or z) = 1  P(!a and !b ... and !z)
Probability
