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Okay, I play a lot of CSGO, which is notorious for cheating. I have encountered 7,836 unique players, and 447 of those people have been banned after I played against them for cheating. Coming out to roughly 5.7% of players I've played with or against have been banned.

If there are 10 people, including myself, per game what is the probability of having a game with a cheater in it?

If anyone could calculate this for me, I would greatly appreciate it!

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Probability of a given person *not* being a cheater: 94.3% = 0.943

Probability of 9 people all not being cheaters (I’m assuming your not being a cheater is a given): 0.943^(9), approx 59%

So the probability of “9 people all not being cheaters” being false, ie the probability of at least 1 cheater, is 1 - 0.943^9 = approx 0.41 or 41%

Of course this is just the ones who get caught
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The probability of not having a cheater after 1 player is .943

Probability of not having a cheater after 9 players i .943\^9 = 0.589 or 58.9%.

Is this right? Is this just a simple binomial probability?
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The probability of someone not cheating is then (100-5.7)% = 94.3%, or 0.943. Assuming you are not cheating then the chance of 9 other people not cheating is 0.943^9 = 0.590 (3s.f.). This means the chance of having at least one cheater is 1-0.590 = 0.410 or 41%.

Of course this has neglected any cheaters who have not yet been banned so the real number may be slightly higher.

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