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I have decided. Out of all the pieces in infinite chess, I am representing... THE GUARD!!! In general, this guy is underrated, even in bulldog. If you'll look at me v. AidenB1, the second his guard fell, his king side defense was immediately compromised, he started to have many soft pawns with not many defensive measures
I haven't played evert, only hitthepin and pixelbypixel.
The guard is an excellent defensive piece and will be huge in endgame, but when it comes to middlegame attacks, I can't see the guard doing much.
@CaptainTugwash is leaning towards 7/8 or even higher. I feel that it is only 5/6, but can still be a useful piece.
I value it when developed early more than anything other than the chancellor and queen, so I suppose 7-8, but I recognise its value will decrease as pawns are exchanged, while the rook (the next best piece) will increase in value, so I expect in endgame the rook to be better.
The hawk is an interesting piece.
I do realize how it's important for hawks to get out early, but their points are slightly to high. BTW, I am arguing with the rook/chancellor. I refer to the useless space far away as "Nowhere" i.e. a space outside the board where queen only hits 1 piece. capitalized N. Q/R/C are the only ones who can effectively reach Nowhere, and it's there just for kicks. So, a rook can actually reach about 40 useful squares, and a chancellor can reach 48.
It's not often in infinite one goes Q(999999999999999999999999999999999999999999999999999999999999999,999999999999999999999999999999999999999999999999999999999) That space is "useless"
Perhaps the value of a piece is some function on the number of moves..?
HGMuller made a formula to estimate piece value based on how many squares it attacks. But it is only valid for pure-jumpers (like knight), and he also said for "short-range" jumpers. The formula is:
value (in centipawns) =33(N) + 0.6875(N)^2 N = number of squares attacked.
For example, these pieces are jumpers, and their value is estimated as follows:
knight: 8 squares, value = 308 (3 points) guard: 8 squares, value - 308 (3 points) hawk: 16 squares, value - 704 (7 points)