H. G. Muller wrote on Fri, Feb 14, 2020 10:28 AM UTC:
Strange anomaly
I have started an attempt to determine piece values on a 12x12 board, about which very little is known. I use Fairy-Max self-play for this. To not make the games too long, the basic start position I use consists of a FIDE army augmented with 4 Pawns (to close the Pawn rank). So the board is pretty thinly popuated. The 4 central Pawns start on 4th rank, to speed up engagement, but the 3 Pawns in each wing start on 2nd rank, to provide some King shelter. The Knights also start in a somewhat advanced position, on 3rd rank behind the central Pawns, as does the Queen (to not have too many unprotected Pawns in the start position.
To determine piece values I delete some pieces from this setup, or sometimes replace them by fairy pieces. The side with the weaker piece can be compensated by giving the opponent Pawn odds, for which I always delete the same Pawn (on the h-file). Such Pawn odds alone results in a 68-70% win of the side with the extra Pawn. I only trust results when the total advantage is closer to equality than Pawn odds.
I don't want to delete more than a single Pawn, because Pawns are highly cooperative pieces, and I cannot be sure that deleting two Pawns gives twice the advantage of deleting a single one. By always granting the same simple Pawn advantage (or none at all), I can get a reliable 'measuring stick' on which the values of other pieces can be mapped. This poses a problem if there is a gap of more than 2 Pawns in the 'piece-value spectrum', though: I cannot play those 1-on-1 without getting an imbalance that is too extreme. I solve that by also introducing fairy pieces with values in the gap, and also determine their value.
I try to avoid Bishops, (and color-bound pieces in general) because of the pair-bonus problem, which would introduce yet another unknown. Which, if not handled properly by the engine, might invalidate the results. So I tried to find a very 'Bishop-like' piece that is not color bound. My first choice was this: to break the color binding of a Bishop, I gave it Wazir moves. To compensate for that (and prevent mating potential), I take away the Ferz moves. But to not affect the more distant B moves, they can still be blocked on the F squares. (So basically this is a Tamerlane 'Picket' + Wazir.)
Such a modified Bishops beats a Knight on 12x12 (as ordinary Bishops also do). The strange thing is that when I then handicap them with Pawn odds, they still beat the Knight, by about the same score. The extra Pawn doesn't seem to help the Knight at all! I have never seen that before; normally deleting a Pawn lowers the score by about as much as the pure Pawn-odds advantage. I watched a few games, and often they end in Knight + Pawns vs modified Bishop + Pawns, where the Knights are still judged by the engine to be ahead (because there are more Pawns on their side). But the Knight then almost always loses. The 'WazirPicket' can easily prevent advance of many isolated Pawns, by guarding a diagonal. And by just stepping in front of a Pawn it attacks as well as blocks it, so that the Pawn easily falls. Even connected passers are easily destroyed this way, if they still have far to go. (And on 12x12 they usually have; I use promotion on last rank only.)
I guess the WazirPicket is just unrepresentatively dangerous to Pawns, in the absence of pieces that can protect those. (And Knights are pitifully slow on 12x12...) So that the value of opposing Pawns shrinks to almost nothing in the late end-game.
My next attempt at a non-color-bound substitute for a Bishop will only change the mF moves of a Bishop to mW, but leaves the captures in place. This will also have the advantage that it cannot be blocked on a square that it doesn't attack, so that it cannot be blocked with impunity (as lame leapers can). Such a piece cannot do more damage to Pawns than ordinary Bishops can, but the mW move does allow it to switch color on non-captures. (Hence I dubbed it Swishop.)
Strange anomaly
I have started an attempt to determine piece values on a 12x12 board, about which very little is known. I use Fairy-Max self-play for this. To not make the games too long, the basic start position I use consists of a FIDE army augmented with 4 Pawns (to close the Pawn rank). So the board is pretty thinly popuated. The 4 central Pawns start on 4th rank, to speed up engagement, but the 3 Pawns in each wing start on 2nd rank, to provide some King shelter. The Knights also start in a somewhat advanced position, on 3rd rank behind the central Pawns, as does the Queen (to not have too many unprotected Pawns in the start position.
To determine piece values I delete some pieces from this setup, or sometimes replace them by fairy pieces. The side with the weaker piece can be compensated by giving the opponent Pawn odds, for which I always delete the same Pawn (on the h-file). Such Pawn odds alone results in a 68-70% win of the side with the extra Pawn. I only trust results when the total advantage is closer to equality than Pawn odds.
I don't want to delete more than a single Pawn, because Pawns are highly cooperative pieces, and I cannot be sure that deleting two Pawns gives twice the advantage of deleting a single one. By always granting the same simple Pawn advantage (or none at all), I can get a reliable 'measuring stick' on which the values of other pieces can be mapped. This poses a problem if there is a gap of more than 2 Pawns in the 'piece-value spectrum', though: I cannot play those 1-on-1 without getting an imbalance that is too extreme. I solve that by also introducing fairy pieces with values in the gap, and also determine their value.
I try to avoid Bishops, (and color-bound pieces in general) because of the pair-bonus problem, which would introduce yet another unknown. Which, if not handled properly by the engine, might invalidate the results. So I tried to find a very 'Bishop-like' piece that is not color bound. My first choice was this: to break the color binding of a Bishop, I gave it Wazir moves. To compensate for that (and prevent mating potential), I take away the Ferz moves. But to not affect the more distant B moves, they can still be blocked on the F squares. (So basically this is a Tamerlane 'Picket' + Wazir.)
Such a modified Bishops beats a Knight on 12x12 (as ordinary Bishops also do). The strange thing is that when I then handicap them with Pawn odds, they still beat the Knight, by about the same score. The extra Pawn doesn't seem to help the Knight at all! I have never seen that before; normally deleting a Pawn lowers the score by about as much as the pure Pawn-odds advantage. I watched a few games, and often they end in Knight + Pawns vs modified Bishop + Pawns, where the Knights are still judged by the engine to be ahead (because there are more Pawns on their side). But the Knight then almost always loses. The 'WazirPicket' can easily prevent advance of many isolated Pawns, by guarding a diagonal. And by just stepping in front of a Pawn it attacks as well as blocks it, so that the Pawn easily falls. Even connected passers are easily destroyed this way, if they still have far to go. (And on 12x12 they usually have; I use promotion on last rank only.)
I guess the WazirPicket is just unrepresentatively dangerous to Pawns, in the absence of pieces that can protect those. (And Knights are pitifully slow on 12x12...) So that the value of opposing Pawns shrinks to almost nothing in the late end-game.
My next attempt at a non-color-bound substitute for a Bishop will only change the mF moves of a Bishop to mW, but leaves the captures in place. This will also have the advantage that it cannot be blocked on a square that it doesn't attack, so that it cannot be blocked with impunity (as lame leapers can). Such a piece cannot do more damage to Pawns than ordinary Bishops can, but the mW move does allow it to switch color on non-captures. (Hence I dubbed it Swishop.)