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ewang comments on Nonmagical Powers - Less Wrong Discussion
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But next time one person, knowing what you did and figuring out your secret weakness, will put 3^^^3 or some other barely-finite-and-yet-nowhere-near-transfinite number to disrupt your 'powers'.
One amazing power we have is being able to use formulas to find equations that fit any data. Dangerously deceptive.
I've used this strategy before. A common way of dealing with this is simply to throw out any obvious outliers. Note that most people who do that sort of thing aren't doing it to disrupt the average, but rather just to be "funny" and so are more likely to just put down a 1 with a lot of zeros, or a long string of 9s.
Assuming you have enough entries, you can simulate a probability distribution way too far to either direction. However, assuming that same thing, you can also just guess everything and actually win.