The value of Cylindrical Pieces?

[AdminX]

Hi Ulysses,

Very interesting concept.

[Ovyron]

Hi Ulysses,

Very interesting concept.

Yeah. I also find very interesting that for these pieces the concept of "board center" does not exist.

[Tony]

I actually had a discussion last week with my pupils that rook and king cannot checkmate a cylindrical king.

Tony

Indeed. So perhaps the Rook is highly overestimated above. Currently I favor the theory that a large part of the R-B value is due to mating potential.

Perhaps I should also test the Dragon King (R+K) vs Dragon Horse (B+K) values. (These are two Shogi pieces.) They both have mating potential, but otherwise are pretty close to B and R. Perhaps I should make the difference even smaller by only allowing the 4 extra moves they have to be captures, so that the Bishop look-alike cannot change color that easily.

Not sure.

Is there a big difference between BN and NN ? Or is NN lower than R ?

I think that's the one real difference between Fruit and Rybka. "Own" scores for a lot of different piece configurations.

Tony

[hgm]

So far most measurement of piece values I did were pretty much additive. Main exception I found is the well-known one: the Bishop pair.

There might be an effect of the presence of Archbishop and Chancellor on the value of the Knight.

[hgm]

OK, for those who want to try this game:

I put a version of Fairy-Max that can play it (through adding an extra line for effecting the wrap-around) for download at:

http://home.hccnet.nl/h.g.muller/cylmax.exe

The variant is now defined in the fmax.ini file that also goes with the normal Fairy-Max (which doesn't understand this game, though):

http://home.hccnet.nl/h.g.muller/fmax.ini

The game is listed in the fmax.ini as variant 3checks, so that you can play it in a normal WinBoard (with legality checking off!). I have not changed piece values compared to normal chess; as they are also specified in the fmax.ini file, you can change them if you want.

[hgm]

I started a test on my laptop, giving white two 'cylindrical Knights' in stead of normal ones, against a normal opening setup of FIDE pieces for black. Of course I will have to play with reversed colors later to eliminate the white advantage. (I did not have time to set this up automatically.) So let's see how much advantage the cylinder-Knights offer over normal ones!

[mjlef]

For what it is worth, Zillions of Games piece ratios which is calculate from scratch for cylidrical chess are:

q 9.46
r 5.5
b 4.15
n 3.3
p 1

What kind of calculation does Zillions use to get these values?

For instance, a Queen in normal chess has been found to have a value of about 9.75, so its cylindrical counterpart would be expected to have an even higher value.

Well, that is a trade secret! But basically it looks at things like mobility on an open board, mobility with the board with typical pieces on it, board topology and the goal of the game to determine piece values. Doing this in standard chess comes up with pretty good overall ratios of piece values. It is interesting to see how the ratios change based on board size. For example, a bishop on a larger board becomes worth more than a knight.

Mark

[Ovyron]

So let's see how much advantage the cylinder-Knights offer over normal ones!

Thank you for doing these tests! I am very interested on the results, as cylindrical pieces are my favorite fairy pieces (besides Chancellor and Archbishop.)

[hgm]

After 84 games white (with the cylindrical Knights) was leading by 65%. Now I continue giving the Knights to black. Presumably the score will be somewhat lower then, as the white advantage is usuallyworth close to 4%. Pawn odds gives about 68%.

So in any case the difference between cylindrical and normal Knights is not very spectacular; for two of them the difference seems smaller than a Pawn, perhaps only half of that. So the cylindrical Knight is about 25-30 cP more valuable than a normal one.

I expect the difference to be larger for Bishops.

[Dirt]

After 84 games white (with the cylindrical Knights) was leading by 65%. Now I continue giving the Knights to black. Presumably the score will be somewhat lower then, as the white advantage is usually worth close to 4%. Pawn odds gives about 68%.

So in any case the difference between cylindrical and normal Knights is not very spectacular; for two of them the difference seems smaller than a Pawn, perhaps only half of that. So the cylindrical Knight is about 25-30 cP more valuable than a normal one.

I expect the difference to be larger for Bishops.

Is the normal knight given a bonus for being in the center? Is the cylindrical knight only penalized for being near the top and bottom of the board, but not the edges? I think the difference in the values of the knights may be understated if the positional bonuses are not separately optimized.