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Would be interesting to see alpha zero trained on 2048, conv nets seem well suited for this kind of game.

Here’s a very simple but clever 2048 game playing AI: https://ronzil.github.io/2048-AI/

This is likely to be a piece of cake for alpha zero given the number of states are lot less than Go.

I would like to see how high it could get to, how much higher than 2048 could it go?

I assume you are talking about the highest tile value, I think in 4x4 game the highest possible tile value should be 2^16 or 2^(16+1)