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Larry Smith wrote on 2008-11-11 UTC
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.

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