Maybe references could be the votes. Like, if someone links an old post by someone else in their post or comment, every upvote on the new post could turn into "stock" votes on the old post, or something.
I guess it's might not be technically part of the quantum mechanics sequence, but this one still has a broken image.
There are still lots of broken images in the rest of the sequences, for example here.
I think I found a way to do slightly better than .69 for 2 and .31 for 3 when cooperating with yourself:
Play 1 with probability .12, 2 with .60, and 3 with .28. If you played the same number, repeat. If you played different numbers, the higher one can play a 3 and the lower one can play a 2 (or whichever cooperating pattern you choose), and they can start alternating from there.
If my calculations are correct, this only loses 2.10 points on average from the maximum possible, which seems to be the best you can do. The goal of the randomization is to pick a different number than your opponent so that you can start cooperating, so the reason this does better is that by picking out of 3 numbers, you have a higher change of not picking the same number.
Oh my gosh this sounds really fun.
Are programs allowed to have either a way to differentiate themselves from each other (like one program gets a 1 and the other gets a 0 for each game) or a source of randomness? Because otherwise it doesn't seem possible to cooperate with yourself.
It would be so cool if someone organized a game of this here or something...
You saying that will just make other people try to figure it out...