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?
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.
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?
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.)
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.
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.