Reading about fairy pieces I can see that an amphibian is a type of compound piece that has a larger range than either of it's components. For instance the 3 leaper is restricted to approximately 1/9 of the board, and the ferz is restricted to 1/2 the board, but the compound piece of a ferz and a 3 leaper is able to travel to any square on the board. I understand that the compound of a bishop and rook is usually thought to have a synergy of 1 point as the queen is thought to be 9 points and the rook+bishop is worth 8 points. A non royal king is usually thought to have a synergy of 1 point as the wazir is worth about 1 point and the ferz is also worth about 1 point, but a non royal king is thought to be worth about 3 points. I'm wondering is an amphibian would tend to have a synergy greater than that of other types of compound pieces given that it can cover more squares than the pieces its a combination of combined.
1 Answer
Not just amphibians. Other pieces too!
Note: I'm assuming an 8x8 board. A different board size would have VERY different values!
Let's take the queen as a standard. Queen consists of Rook + Bishop, but is given 9 points, rather than 8. This is due to its ability to switch colours (unlike the bishop).
Another example is the Princess (B+N). It is supposed to be 6, but is reckoned to be ~8 (+2 synergy!). Whereas the Empress(R+N) is reckoned to be only slightly better (5+3 -> 8.5), with only 0.5 synergetic effects!
So, combine a rook with a knight, the synergy is only +0.5, but with a bishop, it is +1!
I think it's more prudent to use the word "restricted piece", as this includes bishops, as when they get unrestricted, they have a lot of synergy. Also, the knight, while being a leaper, doesn't add that much synergy, as it can still traverse every square of the board.
