Hey, Doc, I just wanted to say thanks for this very educational post. I'm still thinking about it, days later. Part math, part psychology, and a great lesson in thinking rationally.
Here's how the psychology of variance works.
The situation: you work for one hour and get nothing, then you work another hour and get double of normal pay.
People perceive this in different ways.
Overly negative person (very common): "OMG! I worked a whole hour and got nothing!". Those people can earn millions and still feel they are losing, because there was that one little thing which was not perfect. That's why they paid a 10% fee to mine PPS at Deepbit. After months of mining it felt like nothing had gone wrong, there was not a single moment with horrible pay. That was their only focus and they were happy. Overall they got the lowest mining payouts in the history of Bitcoin.
Overly positive person (common with gamblers): "I got double pay! I really hit the jackpot this time!". These people can gamble away their entire life savings and still feel that they are winning, as long as they get a small win every once in a while in between the huge losses. That's how casinos make a lot of money. They let players win small sums frequently. That keeps them hooked and makes them gamble away all the money they can get their hands on. Even the casino making it look like the player "almost won" counts as a win in the head of some players.
The reality? Overall you got average pay. This is where rational thinking is, and this is where you want to be.
Notice how those other two people looked at only part of the picture and then got very emotional about it, while you looked at the whole picture and stayed rational. This difference is important. There are entire businesses built around taking advantage of the psychological weaknesses of those other two people.