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?