It's not like the Archbishop's value drops off that much later in the game. He's similar to the Knight in that regard.
But the way it seems to me:
In the opening:
Knight > MoaFerz or MaoWazir
SkiBishop > AlfilFerz > Bishop
Rook < SkiRook or FlyingRook
Knight > Bishop > Rook
Archbishop > Chancellor > Queen
In the middlegame:
Knight < MoaFerz or MaoWazir
SkiBishop < AlfilFerz < Bishop
Rook = SkiRook or FlyingRook
Knight = Bishop < Rook
Archbishop < Chancellor = Queen
In the endgame:
Knight < MoaFerz or MaoWazir
SkiBishop < AlfilFerz < Bishop
Rook > SkiRook or FlyingRook
Knight < Bishop < Rook
Archbishop < Chancellor < Queen
The starting value of the pieces is determined by the sum of their influence in the opening, then the middlegame, then the endgame (so knight = bishop).
But the exchange value of the pieces is determined at the moment of their exchange, that is, usually it is the sum of their influence in the middlegame + endgame (so bishop is slightly stronger than knight).
I would like to check all these estimates with the help of precise digital estimates of Fairy Max, but it will take a lot of time anyway. The maximum speed that can be achieved is 6 thousand games per day (24 hours), which gives an error of about 1% in the win rate (or less than 10% of the pawn).
Another thing I'd like to find out:
Does SkiBishop really have such a low starting value as a 2/3 Bishop? Or is it because he was in a worse position on b1/g1 when he was tested (it was many years ago, I don't remember exactly)?
Perhaps MoaFerz is slightly stronger than MaoWazir precisely because of his position on c1/f1 (he currently has a classic position on b1/g1)?
Although MoaFerz has a lot of advantages:
- MoaFerz has checkmate potential, while MaoWazir does not
- MaoWazir must alternate square colors, while MoaFerz does not
- MoaFerz is generally more active than MaoWazir, since Ferz is faster than Wazir, and has 2 frontal directions instead of 1
However, MaoWazir has the following advantages:
- MaoWazir is stronger than MoaFerz on the edge of the board, since Wazir has more moves there than Ferz
- MaoWazir attacks more new squares on its move than MoaFerz (alternating square colors gives this advantage)
How does the balance of power change between SkiRook and FlyingRook? FlyingRook has a double jump, so in theory it should have an advantage in the opening. The SkiRook often behaves like a line piece, so it should ideally have an advantage in the endgame. However, both of these Rooks should eventually tend towards 2/3 of the Rook, by which time their jumps will no longer matter due to the small number of pieces.
Another interesting thing is that Interactive Diagram often trades SkiRook for MaoWazir in the second half of the game. Perhaps the trade value of these pieces is really close, like Knight and Bishop? Despite the fact that SkiRook's starting value is a whole pawn higher.
Personally, I noted that closer to the endgame I tend to trade the Skirook for the FlyingRook. Despite the fact that the SkiRook has a linear component, it feels like this figure is more static and less convenient to move than the FlyingRook (while in the endgame mobility is especially in demand, since individual pieces move more often than in the opening or middlegame). It has a weakness in close combat, which is easier to exploit than the FlyingRook's lack of range. Even checkmating with FlyingRook does not cause any problems, but in case of SkiRook you need to learn (the difficulty is close to checkmating with Bishop and Knight). If the Rook or FlyingRook moves to take a stronger position, many of the SkiRook's endgame moves are simply trying to hold the line by eliminating a near-field weakness.
It's not like the Archbishop's value drops off that much later in the game. He's similar to the Knight in that regard.
But the way it seems to me:
In the opening:
Knight > MoaFerz or MaoWazir
SkiBishop > AlfilFerz > Bishop
Rook < SkiRook or FlyingRook
Knight > Bishop > Rook
Archbishop > Chancellor > Queen
In the middlegame:
Knight < MoaFerz or MaoWazir
SkiBishop < AlfilFerz < Bishop
Rook = SkiRook or FlyingRook
Knight = Bishop < Rook
Archbishop < Chancellor = Queen
In the endgame:
Knight < MoaFerz or MaoWazir
SkiBishop < AlfilFerz < Bishop
Rook > SkiRook or FlyingRook
Knight < Bishop < Rook
Archbishop < Chancellor < Queen
The starting value of the pieces is determined by the sum of their influence in the opening, then the middlegame, then the endgame (so knight = bishop).
But the exchange value of the pieces is determined at the moment of their exchange, that is, usually it is the sum of their influence in the middlegame + endgame (so bishop is slightly stronger than knight).
I would like to check all these estimates with the help of precise digital estimates of Fairy Max, but it will take a lot of time anyway. The maximum speed that can be achieved is 6 thousand games per day (24 hours), which gives an error of about 1% in the win rate (or less than 10% of the pawn).
Another thing I'd like to find out:
Does SkiBishop really have such a low starting value as a 2/3 Bishop? Or is it because he was in a worse position on b1/g1 when he was tested (it was many years ago, I don't remember exactly)?
Perhaps MoaFerz is slightly stronger than MaoWazir precisely because of his position on c1/f1 (he currently has a classic position on b1/g1)?
Although MoaFerz has a lot of advantages:
- MoaFerz has checkmate potential, while MaoWazir does not
- MaoWazir must alternate square colors, while MoaFerz does not
- MoaFerz is generally more active than MaoWazir, since Ferz is faster than Wazir, and has 2 frontal directions instead of 1
However, MaoWazir has the following advantages:
- MaoWazir is stronger than MoaFerz on the edge of the board, since Wazir has more moves there than Ferz
- MaoWazir attacks more new squares on its move than MoaFerz (alternating square colors gives this advantage)
How does the balance of power change between SkiRook and FlyingRook? FlyingRook has a double jump, so in theory it should have an advantage in the opening. The SkiRook often behaves like a line piece, so it should ideally have an advantage in the endgame. However, both of these Rooks should eventually tend towards 2/3 of the Rook, by which time their jumps will no longer matter due to the small number of pieces.
Another interesting thing is that Interactive Diagram often trades SkiRook for MaoWazir in the second half of the game. Perhaps the trade value of these pieces is really close, like Knight and Bishop? Despite the fact that SkiRook's starting value is a whole pawn higher.
Personally, I noted that closer to the endgame I tend to trade the Skirook for the FlyingRook. Despite the fact that the SkiRook has a linear component, it feels like this figure is more static and less convenient to move than the FlyingRook (while in the endgame mobility is especially in demand, since individual pieces move more often than in the opening or middlegame). It has a weakness in close combat, which is easier to exploit than the FlyingRook's lack of range. Even checkmating with FlyingRook does not cause any problems, but in case of SkiRook you need to learn (the difficulty is close to checkmating with Bishop and Knight). If the Rook or FlyingRook moves to take a stronger position, many of the SkiRook's endgame moves are simply trying to hold the line by eliminating a near-field weakness.