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.)
Alice: "I just flipped a coin [large number] times. Here's the sequence I got:
(Alice presents her sequence.)
Bob: No, you didn't. The probability of having gotten that particular sequence is 1/2^[large number]. Which is basically impossible. I don't believe you.
Alice: But I had to get some sequence or other. You'd make the same claim regardless of what sequence I showed you.
Bob: True. But am I really supposed to believe you that a 1/2^[large number] event happened, just because you tell me it did, or because you showed me a video of it happening, or even if I watched it happen with my own eyes? My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?
Alice: Someone usually wins the lottery. Should the person who finds out that their ticket had the winning numbers believe the opposite, because winning is so improbable?
Bob: What's the difference between finding out you've won the lottery and finding out that your neighbor is a 500 year old vampire, or that your house is haunted by real ghosts? All of these events are extremely improbable given what we know of the world.
Alice: There's improbable, and then there's impossible. 500 year old vampires and ghosts don't exist.
Bob: As far as you know. And I bet more people claim to have seen ghosts than have won more than 100 million dollars in the lottery.
Alice: I still think there's something wrong with your reasoning here.