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Dmitry Eskin wrote on Tue, Dec 10 12:42 AM UTC in reply to Dmitry Eskin from Mon Dec 9 10:08 PM:

According to my theory of ranks, the values ​​for slow pieces like the Yawn or Maw are as follows:

The Yawn has almost the same activity as the Ferz in terms of reaching enemy ranks. Thus, it reaches the 6th rank as quickly as the Ferz. But from there, the Ferz attacks squares 7+7+5+5 = 24 points, while the Yawn attacks 7+7+5 = 19 points. Thus, the Yawn should be worth 19/24 of the Ferz, or 1.2 pawns.

The Maw is an improved Wazir that lacks its slowness. While the Maw reaches its best, the 7th rank, the Ferz will only end up on the 4th. On the 4th rank, the Ferz would be worth 5+5+3+3 = 16 points, while the Maw on the 7th attacks 8+7+7+6 = 28 points. Thus, the maximum value of Maw = 28/16 of the value of the Ferz = 28/16 1.5 = 1.75 1.5 = 2.625 pawns. The practical value of Maw will be slightly lower, since from the 4th rank the Ferz can improve its position further, and Maw on the 7th has already reached its best position. However, its value should be higher than 2 pawns (even in comparison with the Ferz on the 5th rank, Maw on the 7th will show 28/20 * 1.5 = 2.1 pawns). So I think Maw is about 2.1 pawns.

Also, my theory explains why the Queen is stronger than the sum of a Rook and a Bishop, compared to a Rook, the Queen occupies more active ranks much earlier, and thus the orthogonal squares attacked by the queen matter much more than the orthogonal squares attacked by the rook.

Similarly to the Queen, the Chancellor (Rook + Knight) is active in orthogonal directions much earlier than the rook (but the Knight is able to attack the most valuable squares later than the Bishop - thats why Queen is stronger than Chancellor).

As for the Archbishop (bishop + knight), there is maximum synergy, since diagonal moves allow the relatively slow knight to be strengthened as quickly as possible. To attack the 7th rank with a knight move, the knight needs 2 moves, while the archbishop does it in 1, with a simple diagonal move.


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