Single Comment

Sac Chess. Game with 60 pieces. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]

💡📝Kevin Pacey wrote on Sun, Dec 20, 2015 11:48 PM UTC:

Thought I'd give the wikipedia link below, discussing the value of the Archbishop (Princess) fairy chess piece:

https://en.wikipedia.org/wiki/Princess_(chess)#Value

I'd note wikipedia mentions that computer self-play studies were used to establish a sort of value for this piece that Muller gave (though he nor anyone else seems to be credited for the computer studies, as far as I've read). Note also that links concerning the Chancellor (Empress) and Amazon are given by wikipedia.

Regardless of arguments about what the Archbishop's value might be in a particular chess variant, I'd note that wikipedia mentions that the computer studies led to the conclusion that the Archbishop increased its relative value (in comparison to that of a queen) on an 8x10 board, as opposed to the smaller 8x8 board. Without bringing in any notion of synergy necessarily, I can give one possible reason (or contributing reason) why that conclusion might be correct, in case no one has mentioned it. 

Namely, whereas on an 8x10 board the rook component of a queen benefits the queen as a piece by 2 extra squares covered (on an empty board) at all times, not depending at all on the location of the square, note that the knight component of the Archbishop has many more available squares to it (than on an 8x8 board) where it benefits the Archbishop as a piece, by up to 4 extra squares covered more than from a less favourable square nearby that a knight might have to settle for on the smaller 8x8 board.

I can note that on a 10x10 board (such as for Sac Chess), the rook component for a queen would by similar reasoning pick up 4 extra squares covered on an empty board (than if on an 8x8 board) whereas the knight component for an Archbishop often allows it to pick up up to (still) just 4 extra squares coverage for the Archbishop (than if on an 8x8 board), suggesting to me that a 10x10 board might not benefit an Archbishop like an 8x10 board apparently did, in terms of its value to that of a Queen. Perhaps inconclusive and murky pondering on my part, I'll admit, but it gave me pause.