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Fridolin comments on Crazy Ideas Thread, Aug. 2015 - Less Wrong Discussion
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What are the meanings of these symbols "EX", "P(X>a)"?
X is a random variable, E is expected value (a.k.a. average), P is probability. For example, if X is uniformly distributed between 0 and 1, then EX=0.5 and P(X>0.75)=0.25.
Sarunas is saying that some action might not affect the average value, but strongly affect the chances of getting a very high or very low value ("swing for the fences" so to speak). For example, if we define Y as X rounded to the nearest integer (i.e. Y=0 if X<0.5 and Y=1 if X>0.5), then EY=0.5 and P(Y>0.75)=0.5. The average of Y is the same as the average of X, but the probability of getting an extreme value is higher.
This is probably obvious for others, but it wasn't obvious for me that by paying 0.1 to go from the first game to the second one you both decrease your average earnings and increase the probability of high earnings.