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How do you map the positions to a single number? Are you planning on using a space-filling curve?

23 x 3, you'll want an x,y,z coordinate for each of them.

Can probably get away with 22x2 + 3 as I'm not sure the z coordinate is necessary for the players if you let them carry around a height and vertical attribute

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you probably need the momentum vector of each object too, so 23x6

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