Purposefully throwing matches is very much against the rules and people have been banned for it. In your scenario, if you did actually lose every single match it would not end up technically hurting anyone, but allowing people to purposefully lose matches opens the door to abuse by taking it a step further and actually beating people who you dislike if you recognize them, thus skewing the results of the arena.
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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
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