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Subject: Endgame speed and evaluation

Author: Omid David Tabibi

Date: 17:29:54 01/16/03


[D] 4k3/8/8/p1p1p1p1/PpPpPpPp/1P1P1P1P/8/4K3 w - - 0 1

At the above position, some programs (e.g. Fritz, Hiarcs, Crafty) reach their
maximum depth in a second or two (see the Crafty analysis below), while others
(e.g. Tiger, Shredder) need more time as they search deeper (Tiger for example
quickly reaches depth 20, and then slowly goes deeper and deeper, see the Tiger
analysis below. For Genesis it takes about 4 minutes to reach depth 60). What is
different in the former class which enables them to quickly reach the max depth?

Another interesting point is that Crafty (and many others) gradually reduce the
score as they searches deeper (in the below log you can see that at depth 47
Crafty gives the score 0), while some others like Tiger, remain with their fixed
score (-0.24 in the log below). Based on what factors is the score reduced in
Crafty?

==============================================================================

Analysis by Crafty 19.01:

1.Ke2
  µ  (-1.10)   Depth: 1/2   00:00:00
1.Ke2 Kd7
  µ  (-1.30)   Depth: 2/2   00:00:00
1.Ke2 Kd7 2.Kd2
  µ  (-1.30)   Depth: 3/3   00:00:00
1.Ke2 Kd7 2.Kd2 Kd6
  µ  (-1.40)   Depth: 4/4   00:00:00
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2
  µ  (-1.40)   Depth: 5/5   00:00:00
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke6
  µ  (-1.40)   Depth: 6/6   00:00:00
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke6 4.Kd2
  µ  (-1.40)   Depth: 7/7   00:00:00
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke6 4.Kd2 Kd6
  µ  (-1.40)   Depth: 8/8   00:00:00  1kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2
  µ  (-1.40)   Depth: 9/9   00:00:00  1kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6
  µ  (-1.40)   Depth: 10/10   00:00:00  2kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2
  µ  (-1.40)   Depth: 11/11   00:00:00  3kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke6
  µ  (-1.40)   Depth: 12/12   00:00:00  3kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2
  µ  (-1.30)   Depth: 13/13   00:00:00  4kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6
  µ  (-1.30)   Depth: 14/14   00:00:00  6kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6
  µ  (-1.30)   Depth: 15/15   00:00:00  7kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6
  µ  (-1.30)   Depth: 16/16   00:00:00  8kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6 6.Kd2 Ka6 7.Ke2 Kb7 8.Kd2 Kc6
9.Ke2
  µ  (-1.30)   Depth: 17/17   00:00:00  9kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6 6.Kd2 Ka6 7.Ke2 Kb7 8.Ke1 Kc8
9.Ke2 Kd7
  µ  (-1.30)   Depth: 18/18   00:00:00  10kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6 6.Kd2 Kc6 7.Ke2 Kc7 8.Ke1 Kd6
9.Ke2
  µ  (-1.30)   Depth: 19/19   00:00:00  12kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6 6.Kd2 Kc6 7.Ke2 Kc7 8.Kd1 Kb7
9.Ke1 Kc8 10.Ke2 Kd7
  µ  (-1.30)   Depth: 20/20   00:00:00  13kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke1 Kc6 4.Kd2 Kc7 5.Ke2 Kb6 6.Kd2 Kc6 7.Ke2 Kc7 8.Kd1 Kc8
9.Ke1 Kd8 10.Ke2 Ke7 11.Kd2
  µ  (-1.30)   Depth: 21/21   00:00:00  14kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kf6 6.Ke1 Kg6 7.Ke2 Kf7 8.Kd1 Kg7
9.Kd2 Kf8 10.Ke2 Ke8 11.Kd2 Kd7
  µ  (-1.30)   Depth: 22/22   00:00:00  19kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kf6 6.Ke1 Kg6 7.Ke2 Kf7 8.Kd1 Kg7
9.Kd2 Kf8 10.Ke2 Ke8 11.Kd2 Kd7 12.Ke2
  µ  (-1.30)   Depth: 23/23   00:00:00  20kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kf6 6.Ke1 Kg6 7.Ke2 Kf7 8.Kd1 Kg7
9.Kd2 Kf8 10.Ke2 Ke8 11.Ke1 Kd8 12.Ke2 Ke7
  µ  (-1.30)   Depth: 24/24   00:00:01  21kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc8
9.Ke2 Kc7 10.Kd2 Kb7 11.Ke2 Kb6 12.Kd2 Kc6 13.Ke2
  µ  (-1.30)   Depth: 25/25   00:00:01  24kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Ke2 Kc8 12.Ke1 Kd8 13.Ke2 Ke7
  µ  (-1.30)   Depth: 26/26   00:00:01  25kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Ke2 Kc8 12.Ke1 Kd8 13.Ke2 Kc7 14.Kd2
  µ  (-1.20)   Depth: 27/27   00:00:01  28kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Kd1 Kc8 12.Ke2 Kb8 13.Kd2 Ka7 14.Ke2 Kb6
  µ  (-1.20)   Depth: 28/28   00:00:01  29kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Kd1 Kc8 12.Ke2 Kc7 13.Kd2 Kd7 14.Ke2 Kc6 15.Kd2
  µ  (-1.30)   Depth: 29/29   00:00:01  34kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Kd1 Kc8 12.Ke2 Kc7 13.Kd2 Kb6 14.Kd1 Kb7 15.Ke2 Kc6
  µ  (-1.30)   Depth: 30/30   00:00:01  35kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Kd1 Kc8 12.Ke2 Kc7 13.Kd2 Kd7 14.Ke2 Ke6 15.Kf2 Kd7
16.Ke2
  µ  (-1.30)   Depth: 31/31   00:00:01  37kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke2 Kd6 6.Kd2 Ke7 7.Ke2 Kd8 8.Ke1 Kc7
9.Ke2 Kb6 10.Kd2 Kb7 11.Kd1 Kc8 12.Ke2 Kc7 13.Kd2 Kb6 14.Kd1 Kb7 15.Ke2 Kc8
16.Kd2 Kd7
  µ  (-1.30)   Depth: 32/32   00:00:01  38kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kc8
9.Kd2 Kd7 10.Ke2
  µ  (-1.30)   Depth: 33/33   00:00:01  42kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kc8
9.Kd2 Kd7 10.Ke2 Ke6 11.Kf2 Kf7 12.Ke2 Kf8
  µ  (-1.30)   Depth: 34/34   00:00:01  43kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kc8
9.Kd2 Kd7 10.Ke2 Kc6 11.Kf2 Kc7 12.Ke2 Kb7 13.Kd2 Kc8 14.Ke2 Kb8 15.Kd2 Ka7
16.Ke2 Ka6
  µ  (-1.10)   Depth: 35/34   00:00:01  47kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kc6
9.Kf2 Kd7 10.Ke2
  µ  (-1.20)   Depth: 36/36   00:00:01  54kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kc6
9.Kf2 Kd7 10.Ke2
  µ  (-0.80)   Depth: 37/37   00:00:01  57kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kb8
9.Kd2 Kc7 10.Kd1 Kb6 11.Kd2 Ka6 12.Kc1 Kb7 13.Kd2
  µ  (-1.20)   Depth: 38/38   00:00:01  65kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Kd8 5.Ke2 Kc7 6.Kd2 Kb6 7.Kd1 Kb7 8.Ke2 Kb8
9.Kd2 Kc7 10.Kd1 Kb6 11.Kd2 Ka6 12.Kc1 Kb7 13.Kd2
  µ  (-0.80)   Depth: 39/39   00:00:01  71kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf6 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
  µ  (-1.20)   Depth: 40/40   00:00:01  79kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf6 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Kf1 Kc7 10.Ke2 Kc8 11.Kf1 Kd8 12.Ke2 Ke8
  µ  (-1.20)   Depth: 41/41   00:00:01  80kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf6 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kf7
9.Kd1 Kg6 10.Ke2 Kg7 11.Kd2 Kf8 12.Ke2 Ke8
  µ  (-1.20)   Depth: 42/41   00:00:01  83kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7
  µ  (-1.20)   Depth: 43/42   00:00:01  85kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7
  µ  (-0.80)   Depth: 44/42   00:00:01  87kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7
  ³  (-0.41)   Depth: 45/42   00:00:01  93kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7
  =  (-0.02)   Depth: 46/46   00:00:01  98kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 47/46   00:00:01  104kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 48/48   00:00:01  105kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 49/48   00:00:01  106kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 50/48   00:00:01  107kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 51/48   00:00:01  108kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 52/48   00:00:01  109kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 53/48   00:00:01  110kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 54/48   00:00:01  110kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 55/48   00:00:01  111kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 56/48   00:00:01  112kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 57/48   00:00:01  113kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 58/48   00:00:01  114kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 59/48   00:00:01  115kN
1.Ke2 Kd7 2.Kd2 Kd6 3.Ke2 Ke7 4.Kd2 Ke6 5.Ke1 Kf7 6.Kd2 Ke7 7.Ke1 Ke6 8.Ke2 Kd6
9.Ke1 Kc7 10.Ke2 Kd6
  =  (0.00)   Depth: 60/48   00:00:01  116kN

(David Tabibi, Tel-Aviv 17.01.2003)

==============================================================================

Analysis by Chess Tiger 14.0:

1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd6 6.Ke2 Ke7 7.Kd2 Kf6 8.Ke2 Kf7
9.Kd2 Ke6
  =  (-0.24)   Depth: 19   00:00:00  158kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd6 6.Ke2 Kc6 7.Kd2 Kd7 8.Ke2 Ke7
9.Kd2 Kf6 10.Ke2
  =  (-0.24)   Depth: 19   00:00:00  195kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd6 6.Ke2 Kc6 7.Kd2 Kd7 8.Ke2 Ke7
9.Kd1 Kf6 10.Ke2 Ke6
  =  (-0.24)   Depth: 20   00:00:01  552kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Kc8 7.Kd2 Kd8 8.Ke2 Ke7
9.Kd2 Kf7 10.Ke2 Kf6
  =  (-0.24)   Depth: 21   00:00:02  921kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Kd2 Kf8 8.Ke2 Kf7
9.Kd2 Kg7 10.Ke2 Kf6
  =  (-0.24)   Depth: 22   00:00:04  1759kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Ke1 Kf7 8.Kd1 Kg6
9.Kd2 Kh6 10.Ke2 Kg7
  =  (-0.24)   Depth: 23   00:00:08  3424kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Kd1 Kf6 8.Ke2 Kg7
9.Kd2 Kf8 10.Ke2 Kg8
  =  (-0.24)   Depth: 24   00:00:17  6771kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Kd2 Ke8 8.Ke2 Kf7
9.Kd2 Kg6 10.Ke2 Kh6
  =  (-0.24)   Depth: 25   00:00:35  13930kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Kd1 Kf8 8.Kd2 Ke8
9.Ke2 Kf7 10.Kd2 Kg6
  =  (-0.24)   Depth: 26   00:01:09  26869kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kd7 6.Ke2 Ke7 7.Kd2 Kf7 8.Ke2 Kf8
9.Kd2 Kg7 10.Ke2 Kh6
  =  (-0.24)   Depth: 27   00:02:13  50982kN
1.Kd2 Ke7 2.Ke2 Kd6 3.Kd2 Kc6 4.Ke2 Kc7 5.Kd2 Kb6 6.Ke2 Kc6 7.Kd2 Kd7 8.Ke2 Ke7
9.Kd1 Kf7 10.Ke2 Kg6
  =  (-0.24)   Depth: 28   00:03:37  84351kN

(David Tabibi, Tel-Aviv 17.01.2003)




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