It's been too long since I've done probability or statisitcs, so I'm looking for a bit of help on this subject. I hope that my title is actually what I'm about to talk about :tongue: . Basically, we always seem to assume that everything evens out in the long run so that no one really experiences 'luck.' But I think that we should in fact expect some people to be 'lucky' or 'unlucky' in the long run. I'm just having some trouble with the math:(adsbygoogle = window.adsbygoogle || []).push({});

Let's say we have this guy named Jason (that's me!) who flips a coin N times (I hope we're able to keep N variable, but if you must choose a value for it, just make it something really really big). We expect that Jason gets some proportion of heads to tails that only insignificantly deviates from 1:1. However, even with a fair coin, we expect with probability P that Jason will get some deviation from the expected values that is of statistical significance.

I'm pretty sure I can prove that last sentence, which is important to be true. With probability 1/(2^N), Jason will flip all heads. With N big enough (I'm recalling N>10, but this could be wrong), this would be a statistically significant deviation from the expected probabilities and we'd assume an unfair coin even though it's fair. When N is much larger, we don't need to flip all heads for this to work out, so finding the value of P is slightly more work. ----How do I find P here?----

Also, let's say that we attribute heads to winning, and tails to losing. This means that with probability P, Jason will appear to be very lucky or very unlucky. (Note that if either P or the size of our coin flipping population were big enough, we'd even expect 1 or more Jasons to exist!). Now remove the coins and give everyone a deck of cards and some poker chips. We now expect with probability Q that any given individual will appear to be lucky or unlucky IN THE LONG RUN (because N is big enough). Again, if Q and/or our poker playing population is big enough, we actually can expect these lucky/unlucky people to exist.

This is a much more open ended question, but how would one go about determinging Q here?

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# Expectations for Type I Error

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