[Retros] FW: FW: Distance-PG

[Francois Labelle]

On 31/08/16 04:59 AM, Yoav Ben-Zvi wrote:
> Verification must wait for a full search of all sound SPGs in 6.0.

Actually, about 5 years ago I did a full search of all sound checkmate 
PGs up to 6.0 moves. Luckily I found my old files containing those PGs, 
so I'm able to give examples with maximum geometric length.

Nicolas's 52.142136 = (38,10,0) in 5.5 moves is optimal, congrats!

Here are the records from 4.0 to 6.0 moves:

4.0 moves: 32.970563 = (16,12,0)
1. d4 e5 2. Qd3 Ba3 3. Qxa3 Qg5 4. Qh3 Qxc1#
second place: 31.970563

4.5 moves: 37.526912 = (5,23,0)
1. e3 b5 2. Qh5 Bb7 3. g4 Bxh1 4. Bc4 Bb7 5. Bxf7#
second place: 37.035058

5.0 moves: 41.698485 = (12,21,0)
1. c4 e5 2. Qc2 Qh4 3. Qxh7 Qxc4 4. Qe4 Ba3 5. Qxb7 Qxc1#
second place: 41.455844

5.5 moves: 52.142136 = (38,10,0)
1. e4 h5 2. Qxh5 a5 3. Qxa5 Rxh2 4. Qh5 Ra3 5. Bc4 Rah3 6. Bxf7#
1. e4 h5 2. Qxh5 a5 3. Qxa5 Rh3 4. Qh5 Rxa2 5. Bc4 Rha3 6. Bxf7#
1. e4 h5 2. Qxh5 a5 3. Qxa5 Rxh2 4. Bc4 Rh8 5. Qh5 Rxa2 6. Bxf7# (Nicolas)
1. e4 h5 2. Qxh5 a5 3. Qxa5 Rxh2 4. Qh5 Rxa2 5. Bc4 Ra8 6. Bxf7#
second place: 51.142136

6.0 moves: 56.142136 = (42,10,0)
1. a4 e5 2. Ra3 Qh4 3. Rh3 Qxa4 4. Rxh7 Bc5 5. Rh3 Qh4 6. Ra3 Bxf2#
second place: 55.183766

It turns out that the records are all unique except for length 5.5! So 
using the second place lengths, I can formulate the following 
composition challenge:

Compose a sound checkmate PG...
a) in 4.0 moves with total move length > 32.0
b) in 4.5 moves with total move length > 37.1
c) in 5.0 moves with total move length > 41.5
d) in 6.0 moves with total move length > 55.2


As for Dominique's challenge of the type "checkmate (0,b,c)", some 
optimal problems are

5.5 moves: 33.444893 = (0,11,8)
1. Nf3 Nc6 2. Ne5 Nd4 3. Nxd7 Nxe2 4. Ne5 Nf4 5. Bc4 Bh3 6. Bxf7#
[5 more problems]

6.0 moves: 36.273320 = (0,13,8)
1. Nc3 Nf6 2. Nd5 Ne4 3. Nxe7 Nxd2 4. Nxc8 Ne4 5. Bg5 Bc5 6. Bxd8 Bxf2#
[4 more problems]

but those are not as good as the claimed 39.694106 = (0,17,7) in 6.5 
moves, even if we compare the average distance per ply, which I compute 
to be

(0+17*sqrt(2)+7*sqrt(5))/13 = 3.053393/ply (not 2.5117/ply ?).

     François