It’d be even more fun if you replaced “1-2-3-4-5-6” with “14-17-26-51-55-36″. (Whenever I play lotteries I always choose combinations like 1-2-3-4-5-6, and I love to see the shocked faces of the people I tell, tell them that it’s no less likely than any other combination but it’s at least easier to remember, and see their perplexed faces for the couple seconds it takes them to realize I’m right. Someone told me that if such a combination ever won they’d immediately think of me. (Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
more likely to happen first
Dunno how you would count the (overwhelmingly likely) case where both Mega Millions and the papacy cease to exist without either of those events happening first, but let’s pretend you said “more likely to happen in the next 10 years”… Event 1 ought to happen 0.6 times per million years in average; I dunno about the probability per unit time for Event 2, but it’s likely about two orders of magnitude larger.
Aren’t you choosing an anti-Schelling point? It seems to me that people avoid playing low Kolmogorov-complexity lottery numbers because of a sense that they’re not random enough—exactly the fallacious intuition that prompts the shocked faces you enjoy.
Choosing something that’s “too obvious” out of a large search space can work if you’re playing against a small number of competitors, but when there are millions of people involved, not only are some of them going to un-ironically choose “1-2-3-4-5-6″, but more than one person will choose it for the same reason it appeals to you.
So whether this choice is Schelling or anti-Schelling depends on reference sets that are quite fuzzy on the specified information, to wit, the set of non-random-seeming selections and (the proportion of players in) the set of people who play them.
I still think many more people pick any given low Kolmogorov-complexity combination than any given high Kolmogorov-complexity combination, if anything because there are fewer of the former. If 0.1% of the people picked 01-02-03-04-05 / 06 and 99.9% of the people picked a combination from http://www.random.org/quick-pick/ (and discarded it should it look ‘not random enough’), there’d still be 175 thousand times as many people picking 01-02-03-04-05 / 06 as 33-39-50-54-58 / 23. (Likewise, the fact that the most common password is password doesn’t necessarily mean that there are lots of idiots: it could mean that 0.01% of the people pick it and 99.99% pick one of more than 9,999 more complicated passwords. Not that I’m actually that optimistic.)
(Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
With this in mind I think I would choose combinations that match the pattern /[3-9][0-9][3-9][0-9][1-6][0-9]/. Six digit numbers look too much like dates!
It’d be even more fun if you replaced “1-2-3-4-5-6” with “14-17-26-51-55-36″. (Whenever I play lotteries I always choose combinations like 1-2-3-4-5-6, and I love to see the shocked faces of the people I tell, tell them that it’s no less likely than any other combination but it’s at least easier to remember, and see their perplexed faces for the couple seconds it takes them to realize I’m right. Someone told me that if such a combination ever won they’d immediately think of me. (Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
Dunno how you would count the (overwhelmingly likely) case where both Mega Millions and the papacy cease to exist without either of those events happening first, but let’s pretend you said “more likely to happen in the next 10 years”… Event 1 ought to happen 0.6 times per million years in average; I dunno about the probability per unit time for Event 2, but it’s likely about two orders of magnitude larger.
Aren’t you choosing an anti-Schelling point? It seems to me that people avoid playing low Kolmogorov-complexity lottery numbers because of a sense that they’re not random enough—exactly the fallacious intuition that prompts the shocked faces you enjoy.
Choosing something that’s “too obvious” out of a large search space can work if you’re playing against a small number of competitors, but when there are millions of people involved, not only are some of them going to un-ironically choose “1-2-3-4-5-6″, but more than one person will choose it for the same reason it appeals to you.
Thank you for that insightful observation.
Just to follow up, army1987′s actual choice is:
So whether this choice is Schelling or anti-Schelling depends on reference sets that are quite fuzzy on the specified information, to wit, the set of non-random-seeming selections and (the proportion of players in) the set of people who play them.
I still think many more people pick any given low Kolmogorov-complexity combination than any given high Kolmogorov-complexity combination, if anything because there are fewer of the former. If 0.1% of the people picked 01-02-03-04-05 / 06 and 99.9% of the people picked a combination from http://www.random.org/quick-pick/ (and discarded it should it look ‘not random enough’), there’d still be 175 thousand times as many people picking 01-02-03-04-05 / 06 as 33-39-50-54-58 / 23. (Likewise, the fact that the most common password is
passworddoesn’t necessarily mean that there are lots of idiots: it could mean that 0.01% of the people pick it and 99.99% pick one of more than 9,999 more complicated passwords. Not that I’m actually that optimistic.)With this in mind I think I would choose combinations that match the pattern /[3-9][0-9][3-9][0-9][1-6][0-9]/. Six digit numbers look too much like dates!