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Sorry guys, but I won the 3x3 to 1024 on the first attempt, so the next 99 of you will only see losses. ;) > We can also see it being ‘lazy’ — even when it has
by ballenf 9y ago
Sorry guys, but I won the 3x3 to 1024 on the first attempt, so the next 99 of you will only see losses. ;)
> We can also see it being ‘lazy’ — even when it has two high value tiles lined up to merge, it will continue merging lower value tiles. Particularly within the tight constraints of the 3x3 board, it makes sense that it will take the opportunity to increase the sum of its tiles at no risk of (immediately) losing — if it gets stuck merging smaller tiles, it can always merge the larger ones, which opens up the board.
One flaw in the strategy I noticed was failure to prioritize getting higher values together when board space is scarce. That is, it seems to employ the same strategy regardless of board free space. (Maybe they addressed this, admittedly didn't read all.) Or maybe that is better than my strategy.
- tpolzer 9y agoIt's better than your strategy.
- htgb 9y agoCare to elaborate?
- empath75 9y agoThat’s what optimal means.
- jdleesmiller 9y agoStrictly speaking, all we can say is that the optimal strategy used in my post is no worse than ballenf's. It's possible that ballenf's strategy is also optimal --- i.e. that they are equally good. :)
- tialaramex 9y agoYes! Optimal strategies for playing a game too complicated to reason out completely in your head, or which has some random element often aren't unique. Cepheus http://poker.srv.ualberta.ca/ http://poker.srv.ualberta.ca/ is a Heads Up Limit Texas Hold 'Em strategy (two players, no betting strategy needed beyond whether to fold / call / raise) that is proved to be approximately optimal. There absolutely must be other strategies that are similar, and in particular circumstances one would dominate another, it's just that since they're all optimal if they played random hands over time they'd all break even.
- static_noise 9y agoSeparate but equal. There can be different strategies that are exactly equal in terms of some performance measures.
- fjsolwmv 9y agoAre you sure? Maybe it delays moving large tiles together until the last moment before it risks being impossible to combine then.
- jameshart 9y agoBoardspace creates uncertainty - on a wide open board there are more places the new tiles can appear. It seems possible that controlling the amount (or, more precisely, the position) of boardspace helps reduce the odds of new tiles appearing in unhelpful places, so prematurely combining tiles could be an antistrategy.