H. G. Muller wrote on Mon, Dec 10, 2018 09:17 AM UTC:
I think the term you are looking for is 'color alternator'. I don't think there isn't much consequence of being a color alternator for the piece value, though. It merely means that there are some squares where you could not go in an even or odd number of moves, but for any piece that is not a 'Universal Leaper' there are always squares where you cannot go in a given number of moves, and it doesn't matter much which color they have. (There are some quirky positions, though, like { white: Ka8, Nh1, Pa7; black Kc8 } which are draw depending on who has the move because of this alternation, but that is just a coincidence, because the defending King here has to keep switching between c8 and c7 to keep up the defense, which happen to be of opposite color.) The significance of 'full' color binding that there are squares you can never go.
Note that 'color binding' is just a special case of 'area binding', more obvious than other forms because in western chess we happen to checker our boards. Pieces that move only in two opposite directions are confined to a single 'ray', and if the opposite steps are equal in size and not minimal, they can even only access part of that ray. If they have two pairs of such moves (like the Alfil) they just sample a subset of the squares in a subset of parallel rays. All point-symmetric pieces with 4 moves suffer from this, except the Wazir (which is the only piece with minimal step in both dimensions, so that it never skips any square). So also left- and right-handed Half-Knights, even though they alternate the 'checkering color' on each move, they still are restricted to 20% of the squares, some light, some dark in the usual checkering. You could paint the board with some 5-colored pattern to make this obvious ('meta-colors'), but the left- and right-handed Half-Knights would need different patterns.
As for the strength of computers: by my standards your rating is very high, and from what you say that you score somewhat below 50% against Fairy-Max in Sac Chess. So why would you consider Fairy-Max' experience considering the value of pieces any less reliable than your own? There is not only the level of play, but also the number of games that constitute this experience. Fairy-Max can play tens of thousands of games in a few months, by just letting a few copies of it run 24/7, you probably did not play more than a hundred in any particular variant. In addition, for determination of piece values I would force Fairy-Max to play with the relevant imbalances from the start, (like Q vs 2R or Q vs 3 minors) rather than just waiting for the small fraction of the games where they occur by coincidence, so that every game is relevant, rather than just some 10%, the other 90% being decided because one of the players gained a Pawn somewhere during the game and could convert that to an end-game (or the game ending in a draw without there ever having been a material imbalance).
Note that Fairy-Max plays variants just as strongy as it plays orthodox Chess. This must be so, because it doesn't have any knowledge specifically pertaining to orthodox Chess. This is why I considered it a good 'test bed' for evaluating values of unorthodox pieces. Also note that for some specific variants much stronger engines are available, and that for determining the value of the Capablanca pieces I used a dedicated Capablanca Chess engine that had a computer rating about 400 Elo above Fairy-Max. (And nowadays engines are available for free download that are 400 Elo stronger still.)
I think the term you are looking for is 'color alternator'. I don't think there isn't much consequence of being a color alternator for the piece value, though. It merely means that there are some squares where you could not go in an even or odd number of moves, but for any piece that is not a 'Universal Leaper' there are always squares where you cannot go in a given number of moves, and it doesn't matter much which color they have. (There are some quirky positions, though, like { white: Ka8, Nh1, Pa7; black Kc8 } which are draw depending on who has the move because of this alternation, but that is just a coincidence, because the defending King here has to keep switching between c8 and c7 to keep up the defense, which happen to be of opposite color.) The significance of 'full' color binding that there are squares you can never go.
Note that 'color binding' is just a special case of 'area binding', more obvious than other forms because in western chess we happen to checker our boards. Pieces that move only in two opposite directions are confined to a single 'ray', and if the opposite steps are equal in size and not minimal, they can even only access part of that ray. If they have two pairs of such moves (like the Alfil) they just sample a subset of the squares in a subset of parallel rays. All point-symmetric pieces with 4 moves suffer from this, except the Wazir (which is the only piece with minimal step in both dimensions, so that it never skips any square). So also left- and right-handed Half-Knights, even though they alternate the 'checkering color' on each move, they still are restricted to 20% of the squares, some light, some dark in the usual checkering. You could paint the board with some 5-colored pattern to make this obvious ('meta-colors'), but the left- and right-handed Half-Knights would need different patterns.
As for the strength of computers: by my standards your rating is very high, and from what you say that you score somewhat below 50% against Fairy-Max in Sac Chess. So why would you consider Fairy-Max' experience considering the value of pieces any less reliable than your own? There is not only the level of play, but also the number of games that constitute this experience. Fairy-Max can play tens of thousands of games in a few months, by just letting a few copies of it run 24/7, you probably did not play more than a hundred in any particular variant. In addition, for determination of piece values I would force Fairy-Max to play with the relevant imbalances from the start, (like Q vs 2R or Q vs 3 minors) rather than just waiting for the small fraction of the games where they occur by coincidence, so that every game is relevant, rather than just some 10%, the other 90% being decided because one of the players gained a Pawn somewhere during the game and could convert that to an end-game (or the game ending in a draw without there ever having been a material imbalance).
Note that Fairy-Max plays variants just as strongy as it plays orthodox Chess. This must be so, because it doesn't have any knowledge specifically pertaining to orthodox Chess. This is why I considered it a good 'test bed' for evaluating values of unorthodox pieces. Also note that for some specific variants much stronger engines are available, and that for determining the value of the Capablanca pieces I used a dedicated Capablanca Chess engine that had a computer rating about 400 Elo above Fairy-Max. (And nowadays engines are available for free download that are 400 Elo stronger still.)