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in reply to @hthrflwrs's post:

Fascinating to consider that if we were actually picking "random positive numbers" (and assuming an reasonably defined even distribution, to the extent that is a concept that makes any sense in that context) we should expect all but an infinitesimal part of the votes to be for the last poll option

oh. well. our methodology was that we "randomly" picked 13, 18, and 11, and computed 13 * 18 mod 11, which is 8, unless we got it wrong in our head. this is just a way of making sure we pick a number that isn't 3 or 7, because our brain tends to be highly predictable.

so we were always going to be in your first bracket. oops. bad assumption in how we did it! :D

(before doing that, we "randomly" picked 7, 13, and 8, which was a little easier to do the math with, but that gave us 3. so we decided it wasn't random enough and did it again. yeah, our methodology is really, really bad.)

this is fascinating to me because for some reason i didn't even for a second consider going higher than 10. I guess the question made me think of picking a number between 1 and 10 even though that is very much not what was asked.