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Dmitry Eskin wrote on Mon, Dec 9 10:08 PM UTC in reply to H. G. Muller from Wed Mar 6 2013 07:01 PM:

A very interesting comparison of the ferz and the wazir.

Theoretically, the ferz should be weaker due to the color weakness.

However, in practice I would draw the following conclusions:

  1. The color weakness does not matter at all as long as the piece's range of movement is low, like the ferz. What difference does it make that the ferz cannot reach 50% of the board squares if it cannot reach 90% of the board squares due to its slowness?

  2. Slowness is the key parameter why the ferz is much stronger than the wazir, and why the wazir on 2 ranks is much stronger than the wazir on 1.

In my model, different ranks have different values. For convenience, consider the white pieces. The first rank will be worth 1 point, the second - 2, and so on, up to 8 - eight points. These numbers show that there is a much higher chance of capturing an enemy piece on the 7th and 8th ranks than on the 1st and 2nd, because they start on the 7th and 8th ranks, and they have a long way to go to 1st and 2nd.

While the wazir from the 1st rank will go to 4th, the ferz will have time to go from 1st to 6th.

Thus, the wazir from the 4th rank will attack 1 square of the 5th rank (5 points), 2 squares of the 4th rank (4+4 = 8 points) and 1 square of the 3rd rank (3 points), a total of 5+8+3 = 16 points.

While the ferz from the 6th rank will attack 2 squares of the 7th rank (7+7 = 14 points) and 2 squares of the 5th rank (5+5 = 10 points), a total of 14+10 = 24 points.

These numbers perfectly explain why the wazir on the 1st rank is worth 1 pawn, and the ferz is worth 1.5 (24/16), that is, 1.5 times stronger.

At the same time, the wazir on the 2nd rank will be 25% more valuable (1.25 pawns), because in the example above it will have time to reach the 5th rank instead of the 4th, and will score 6 + 10 + 4 = 20 points.

I predict that the ferz on the 2nd rank will also be stronger than on the 1st, and the difference will be the same 0.25 pawns (1.75 instead of 1.5).

It also follows from this model that a double pawn move (from the starting position) has a huge significance (up to 0.25), since it allows you to attack more valuable ranks earlier, compared to a slow single move.


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