Comments/Ratings for a Single Item

On an 8x10 field.

White: Ke3 Rj1
Black: Ke5

Mate in 15.

White: Ke3 Big1
Black: Ke5

Mate in 28.

So the Rook appears almost twice as efficient compared to the Bison in this particular scenario. If the Rook is valued at 5, then the most the Bison can be valued is 3. To be considered a 4, it would need to mate in less than 20.

Although a Bison has twice the number of potential cells than a Knight, it also has a larger footprint. With leapers, a larger footprint can actually be a negative factor, particularly on small playing fields. They must operate closer to the center of the field to exercise all their potential moves during play.

And though the Rook and Bison both have the potential of 16 cells on the 8x10 field, only the Rook is able to exercise all its potential cells no matter what position it occupies on the field. The Bison loses potential cells below the fourth rank and file. And so only excercise its full potential when located on 2x4 central cells of the field. In the corner cell of the field it is only able to exercise the potential of four cells. And an average of less than eight cells for the overall field. Thus in this scenario it is half the value of a Rook.

Compare this to a Knight which only begins to lose potential cells below the third rank and file and thus maintains a higher average of its moves on the overall field.

What if we add the Knight moves to the Bison? Is there already a piece like this? If not, I lay claim to it. ;-)

It would have both a 50% increase in potential cells, but also the ability to exercise a smaller footprint. As a conditional piece it may even approach the value of a Rook.

I will work up some code with this particular piece, making the Knight leap also conditional.

This piece is in the Piececlopedia under the name 'Buffalo'.

8x10 = 8 files and 10 ranks, and you start counting ranks at 1? This indeed is a mate in 28, with white to move.

But I don't think you can derive the value of a piece from how long it needs to checkmate a bare King. Indeed, there are pieces that cannot mte  bare King at all, and yet are worth more than a Rook. A Nightrider, for instance. A more obvious case would be a piece that moves like a King, but captures to any square of the color it is on. I am pretty sure this must be worth more than a Queen.

The Bison must be stronger than the Falcon, but I did not develop a etup to play-test it yet. If you start with a conventional array (pawns on 2nd and 7th rank), Bisons make it into a highly tactical position, as they can fork lots of trapped or undefended pieces on the back rank, before you have tme to develop them. Grasshopper play-testing also suffered from this, but after some experimenting, it turned out that starting all Pawns on 3rd and 6th rank was a very good remedy against it. I guess that for Bisons this should work too, but I haven't tried it yet.

My guess would be that the Bison would gain 100-200 centiPawn compared to the Falcon, as the latter is not that easy to block. This would put it at 6-7 pawns.

On an 8x10 field.

The Buffalo averages more than 18 potential cells, better than the Rook.

White: Ke3 Bug1
Black: Ke5

Mate in 15. Same as the Rook.

With K+Bu versus K+R, it appears the same draw condition(not conclusive).
Though the Buffalo is able to perpetual check.

Zillions values this piece at 10033, with conditionals. thus it might be
as high as 20000 without such. I'll test this out.

If conditionals were applied to the Buffalo, we might call it a
Hartebeest(that is, if this name has not already been taken). It would
make a great asset, without being too powerful in the opening and
mid-game.

Zillions evaluates the Buffalo at 18340, higher than the Rook.

All evaluations should be taken in the context of the parameters examined. Thus when a piece is evaluated in its relation to mating, that is strictly within that parameter. The same goes with the evaluation of the average potential moves on a field. And Zillions definitely cannot be considered the final arbitrator of pieces evaluation, since it is a generic game engine and not specificly programmed for a particular piece or game.

But if the various evaluations begin to show a trend, the examiner might take notice.