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Charles Gilman wrote on Wed, Aug 25, 2010 06:28 AM UTC:

You know how the Queen and Gnu and Cardinal and Canvasser are worth more than the sum of their parts because the unbound component unbinds the bound one? Well that led me to wonder about compounds whose diagonal or Camelwise move remains restricted to squares of a single colour. There could be a Queen that can move as a pale-square Bishop but not a dark-square one. Three questions strike me about such pieces:
1 Are they closer to being worth the sum of their parts? For example, is the restricted Queen described above worth a Rook plus a Bishop, or is it worth less because it can find itself on squares where it is temporarily only a Rook? How does it compare in strength to an Ajax or Ajaxrider Rook?
2 Are they worth cataloguing in my Man and Beast series? There are already two such pieces in use, the Korean pieces that are partway from General/Wazir to King/Prince, but they are something of a special case as they are further restricted to not leaving the Fortress. Can anyone see themselves using such pieces more widely?
3 If they are worth cataloguing, has anyone any ideas about how they should be named? I did have a brief idea for square-cell pieces, but thought better of it as I would prefer something more widely applicable. Should all pieces moving along the same subset of diagonals have the same prefix(es) or suffix(es), or should they be named according to whether the subset includes their own starting cell? What about the three colours of the hex board, and the overlapping Bishop and Unicorn bindings on a cubic board? What would you call a Governor restricted to Bishop moves including its starting cell but Unicorn ones not including it? How would you distinguish between a Waffle whose Elephant moves are confined to an entire Bishop binding, and to a mere Elephant one?

Claudio Martins Jaguaribe wrote on Wed, Aug 25, 2010 07:08 AM UTC:

Dear Charles:

I believe that my Mega Doom Chess Has a lot to do with you and your ideas.

Would you care to take a look, and, who knows, promote it?

Hugs.

H. G. Muller wrote on Wed, Aug 25, 2010 06:49 PM UTC:

> There could be a Queen that can move as a pale-square Bishop
> but not a dark-square one. Three questions strike me about
>  such pieces:
> 1	Are they closer to being worth the sum of their parts?
> For example, is the restricted Queen described above worth
> a Rook plus a Bishop, or is it worth less because it can
> find itself on squares where it is temporarily only a Rook?

My estimate is that it would be worth way less than the sum of its parts. A
simplistic guess would be that it is just the average of R (500) and Q
(950), or 725 centi-Pawn. This, however, is probably an under-estimate,
because in actal ply you would favour position where it is on a 'good'
square. But you are unlikely to be able to always put it there. More likely
seems that you can do that 66% of the time. Thus weighting the average
would bring you to 800 cP. Note that an average Bishop is worth 350 (325
for the first, and 375 for the second, completing the pair). So the sum of components would be 850 cP.

Btw, it is not always true that compounds earn a synergy bonus. An Amazon,
for instance, exactly balances a Queen plus a Knight, in opening value.

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