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Bishop vs Rook: Why They Differ in Value

Another way to test board geometry is to consider different board shapes, such as hexagonal chess, cylinder chess, and billiards(?) chess (the variant where pieces can bounce off the edges of the board).

Another way to test board geometry is to consider different board shapes, such as hexagonal chess, cylinder chess, and billiards(?) chess (the variant where pieces can bounce off the edges of the board).

Yes, that's true. Unfortunately Fairy-SF doesn't really support different geometries, so I can't easily test it.

The only thing it can do is to change geometry by excluding squares, so I did in fact test troitzky chess, but the fact that it also reduces effective board size makes direct comparison hard as I would perhaps need to start making up a similar sized rectangular board variant and compare against that, but the post already was a bit lengthy at that point.

Yes, that's true. Unfortunately Fairy-SF doesn't really support different geometries, so I can't easily test it. The only thing it can do is to change geometry by excluding squares, so I did in fact test troitzky chess, but the fact that it also reduces effective board size makes direct comparison hard as I would perhaps need to start making up a similar sized rectangular board variant and compare against that, but the post already was a bit lengthy at that point.

What if the board were something like 12x12 or 15x15, with the same starting pieces (but more distance between White and Black)?

What if the board were something like 12x12 or 15x15, with the same starting pieces (but more distance between White and Black)?

I don't understand the analysis well enough, but I'm curious if the drop in bishop value with increased range could be real.

It feels like covering more squares must be better, but my dark square bishop covering more squares also means your dark square bishop is covering more squares, and increased range of both our dark square bishops means more overlap in coverage that could neutralize their strengths.

I don't understand the analysis well enough, but I'm curious if the drop in bishop value with increased range could be real. It feels like covering more squares must be better, but my dark square bishop covering more squares also means your dark square bishop is covering more squares, and increased range of both our dark square bishops means more overlap in coverage that could neutralize their strengths.

@WWWWWWWWWMWWWWWWWWWW said in #5:

What if the board were something like 12x12 or 15x15, with the same starting pieces (but more distance between White and Black)?

Good question, but hard to tell. If you increase the board size without increasing the range of the pieces (e.g., a range 7 bishop and rook) I think they would get closer in strength. But if they are unlimited range, I think it would be a fairly similar situation as in the 8x8 case. However, many factors could make a difference, like the smaller relative occupancy if you increase the board but keep the number of pieces, which would very likely favor rooks.

@ColdBrewPlz said in #6:

I don't understand the analysis well enough, but I'm curious if the drop in bishop value with increased range could be real.

It feels like covering more squares must be better, but my dark square bishop covering more squares also means your dark square bishop is covering more squares, and increased range of both our dark square bishops means more overlap in coverage that could neutralize their strengths.

I doubt it. If both sides have the same number of pieces of a type that cancels out and has no impact on the piece value calculation. It simply is hard to completely eliminate such fluctuations when differences get small. One could train a neural network evaluation on these piece types, let the engine run longer, or collect more data to reduce uncertainty there, but I already let 10 threads run for about 20 hours to get that data so I thought it would be overkill to do even more, especially given the general trend for the main question seemed quite clear.

@WWWWWWWWWMWWWWWWWWWW said in #5: > What if the board were something like 12x12 or 15x15, with the same starting pieces (but more distance between White and Black)? Good question, but hard to tell. If you increase the board size without increasing the range of the pieces (e.g., a range 7 bishop and rook) I think they would get closer in strength. But if they are unlimited range, I think it would be a fairly similar situation as in the 8x8 case. However, many factors could make a difference, like the smaller relative occupancy if you increase the board but keep the number of pieces, which would very likely favor rooks. @ColdBrewPlz said in #6: > I don't understand the analysis well enough, but I'm curious if the drop in bishop value with increased range could be real. > > It feels like covering more squares must be better, but my dark square bishop covering more squares also means your dark square bishop is covering more squares, and increased range of both our dark square bishops means more overlap in coverage that could neutralize their strengths. I doubt it. If both sides have the same number of pieces of a type that cancels out and has no impact on the piece value calculation. It simply is hard to completely eliminate such fluctuations when differences get small. One could train a neural network evaluation on these piece types, let the engine run longer, or collect more data to reduce uncertainty there, but I already let 10 threads run for about 20 hours to get that data so I thought it would be overkill to do even more, especially given the general trend for the main question seemed quite clear.

Have you done similar value analysis on piece combos?

I.E. I've seen people say that bishop+rook is better than bishop+knight; queen+knight is better than queen+bishop.

And obviously bishop+bishop is better than bishop+knight or knight+knight.

But does the stockfish regression analysis agrees with those patterns? And if yes, then how big is the difference between the piece combos.

Have you done similar value analysis on piece combos? I.E. I've seen people say that bishop+rook is better than bishop+knight; queen+knight is better than queen+bishop. And obviously bishop+bishop is better than bishop+knight or knight+knight. But does the stockfish regression analysis agrees with those patterns? And if yes, then how big is the difference between the piece combos.

The analysis incredible, but, what is the final practical value of your research then ? what we can applied during a chessgame?

The analysis incredible, but, what is the final practical value of your research then ? what we can applied during a chessgame?

That was a really interesting read -- nice work!

That was a really interesting read -- nice work!