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2048x4

So there's this hot new game, 2048. First I said I wouldn't be part of the craze. But then I was.

Stage 1: I went on an intuition of combining numbers as opportunistically as possible. This got me to 512 and 5000ish points on my first attempt, 7 or 8k points on the 2nd, but getting past 512 seemed really hard; the board fills up with disjoint numbers.

Stage 2: In a comment thread I saw someone's simple algorithm for an AI:
go up if possible
if not, go left or right, depending on which consumes more numbers after an 'up' followup.
if all else fails, go down. Commentary was that you never want to go down if you can avoid it; logic wasn't given.

Spamming that got me to 13,000 points on the first use, and probably 1024. I know I've seen 1024, and I think the 10th Doctor on a Doctor Who clone (definitely the 9th, but that's like 512.) Further scores tended to be lower, around 7000, though having a dumb algorithm beat me was humbling. Couldn't get past 1024.

Then I thought about it again, inspired by a diagram I'd seen. And this works, so if you want to figure it out on your own, shoo.


The diagram was of a high number in the corner, and then halves trailing and wrapping around, e.g.
256 128 64 32
2 4 8 16
blah blah
blah

I got the logic, if you can build up such a sequence then you can cascade up to 512, like falling dominos. But how to get such a sequence? I tried fixing the high number in a corner and not budging it. So if 256 is in the upper left, you only use up and left until the top row is filled with unique numbers, allowing you to go right safely. (Otherwise a 2 might drop into the corner, and that gets messy. I've recovered from such, but it's a fight.) And then merge numbers, but not just anywhere; aim for building up doubles along the top row, then back around. You don't have to be precise about it; 256 2 32 2 is a valid top row; you'll just want to concentrate on keeping the first 2 column clear, so you can merge other 2s with it, then 4s, and such. The big thing is not having a small number locked into the top row, inaccessible.

I know that's not very precise, but hey, that's why it feels good -- human judgement, not a simple algorithm!

A big problem was going down accidentally and having to deal with a spoiler piece, but I got better.

Sometimes you have to go right without a full row, and you get a spoiler. Sometimes I was able to work around that, sometimes I just gave up. So there's some luck involved, and some selection of my results. Nonetheless:



With that I quickly got 2048. I don't remember if it was on the first attempt, but soon. Then again, and again, and again. Not quite in a streak, but close enough that it's not a fluke nor a mining of many attempts. Scores ranging from 22516 to 32908. 4096 seems a long way off, though.

Feels a bit like my nethack ascension. Played for years, then Ascended, then Ascended again. Something had clicked.

See the comment count unavailable DW comments at http://mindstalk.dreamwidth.org/389547.html#comments

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Damien Sullivan
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