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Matthew_Opitz comments on What's wrong with this picture? - Less Wrong Discussion
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An analogous question that I encountered recently when buying a powerball lottery ticket just for the heck of it (also because its jackpot was $1.5 billion and the expected value of buying a ticket was actually approaching a positive net reward) :
I was in a rush to get somewhere when I was buying the ticket, so I thought, "instead of trying to pick meaningful numbers, why not just pick something like 1-1-1-1-1-1? Why would that drawing be strictly more improbable than any other random permutations of 6 numbers from 1 to 60, such as 5-23-23-16-37-2? But then the store clerk told me that I could just let the computer pick the numbers on my ticket, so I said "OK."
Picking 1-1-1-1-1-1 SEEMS like you are screwing yourself over and requiring an even more improbable outcome to take place in order to win...but are you REALLY? I don't see how....
I'm sure if 1-1-1-1-1-1 were actually drawn, there would be investigations about whether that drawing was rigged. And if I won with ANY ticket (such as 5-23-23-16-37-2), I would start to wonder whether I was living in a simulation centered around my life experience. But aren't these intuitions going astray? Aren't the probabilities all the same?
Nitpick: Balls are drawn without replacement in the Powerball lottery, so 1-1-1-1-1-1 is not a possible winning combination. 1-2-3-4-5-6 is, though.
The probabilities are all the same. But you are probably screwing yourself over (above and beyond the screwage of buying a ticket in the first place, at least if wealth is your goal) if you pick 1,2,3,4,5,6 or something of the kind -- because more other people will have picked that than 1,4,5,18,23,31 or some other random-looking set, so if you win you'll have to share the prize with more people. (Assuming that that's what happens when there are multiple jackpot winners. It usually is.)
I treated the ticket as an experiment into the question of whether or not I'm living in a simulation, treating it as weak evidence against an already weak hypothesis.