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The Black Ghost. Black gets a teleporting Ghost piece that can not capture to balance White's first move advantage. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
H. G. Muller wrote on Sun, Oct 23, 2022 10:56 AM UTC:

To get a reasonable value for the gost I had to adapt the way the Diagram calculates piece values; the usual formula M*(33+0.7*M) for a piece with M moves values it more than a Queen even when I do count non-captures only for 1/3 (and captures for 2/3) as I did. But it turns out that (0.11*N+0.89*C)*(22+0.7*N), with N the number of non-captures and C the number of captures, gives exactly the same result when C = N (as it is for non-divergent pieces), and puts more emphasis on captures. And it still predicts the same devaluation when a piece with 24 moves gets one captures or non-captures removed, from which I concluded that captures were worth twice as much as non-captures.

This still predicts a value of about a Rook, though. I guess the problem here is that non-captures contribute a lot through future mobility, where you can go after 2, 3, 4... moves. But for a Universal Leaper this provides no extra value, as it can get anywhere in a single move anyway. I now made the hack to discount the number of non-captures above 1/3 of the board area by a factor 10. That still makes the Ghost worth more than a Pawn. But some comments below claim it is worth more than Betza thought, so perhaps this is correct. In any case the Diagram would not sacrifice a minor for the Ghost now.