Results.


Here are showed the results in simulating in a PC a large number of chess games choosing the next movement at random among all the possible movements at each turn according to the rules of this game.

  1. Table 1. Partial and accumulated facts obtained after simulating 2.000.000 games.
  2. Table 2. Results of the previous simulation when it was included the 50 movements rule, which didn't turned out to be significant since from the 264.831 draws resulting from it , 247.354 had also been it without the rule application.
  3. Table 3. The percentage of times that each kind of pieces appears in the winner ban's final position (Of course in not drawn games).
  4. Table 4. It shows the number of squares that are averagely attacked by each piece during de development of the games. As it is well known this is a measure of each piece's power.
  5. Table 5. This list contains different information from the previous ones. It shows the results in simulation series from initial positions which just contain the matter form elemental mates. It collects the results of five sessions of 4.000.000 games each one. In the first session the initial position just contains both kings and a white queen, in the second one instead of the queen there is a white rook, in the third one the kings and the white bishops, in the fourth one a white bishop and a white knight and finally the kings with two white knights.

Table 1. Results for the first 1.000.000 of games

  MATE MATE STALEMATE STALEMATE OTHERS MATE MATE STALEMATE STALEMATE OTHERS
GAMES WHITE BLACK WHITE BLACK DRAW WHITE BLACK WHITE BLACK DRAW
250,000 24,812 25,160 17,924 18,103 163,984 9.9% 10.1% 7.2% 7.2% 65,6%
250,000 25,250 25,061 17,889 17,972 163,818 10.1% 10.0% 7.2% 7.2% 65.5%
250,000 25,039 25,280 17,829 18,131 163,708 10.0% 10.1% 7.1% 7.3% 65.5%
250,000 24,974 24,947 17,761 18,144 164,155 10.0% 10.0% 7.1% 7.3% 65.7%
1,000,000 100,075 100,448 71,403 72350 655,665 10.0% 10.0% 7.1% 7.2% 65.6%

Results for the next 1.000.000 of games.

  MATE MATE STALEMATE STALEMATE OTHERS MATE MATE STALEMATE STALEMATE OTHERS
GAMES WHITE BLACK WHITE BLACK DRAW WHITE BLACK WHITE BLACK DRAW
1,000,000 100,469 100,465 71,366 71,956 655,692 10.0% 10.0% 7.1% 7.2% 65.6%

Table 2. Results if it is taken into account the 50 movements rule.

(For 1.000.000 of games)

Table with the 50 movements rule : 264,831

Without the 50 movements rule, 264,831 of the previous games will also be drawn.

  MATE MATE STALEMATE STALEMATE OTHERS MATE MATE STALEMATE STALEMATE
GAMES WHITE BLACK WHITE BLACK DRAW WHITE BLACK WHITE BLACK
1,000,000 1,590 1,673 7,020 7,142 247,354 0.2% 0.2% 0.7% 0.7%

Table 3. Presence in the winner ban's final position.

PIECE WHITE BLACK TOTAL
262.53% 261.52% 262.02%
71.74% 71.18% 71.46%
78.87% 78.63% 78.75%
104.22% 103.97% 104.10%
103.55% 103.43% 103.49%
100.00% 100.00% 100.00%

Table 4. Average of squares attacked by each piece.

PIECE WHITE BLACK

PIECE

WHITE BLACK
a 0.82 0.82 = 18.55 18.59
b 1.11 1.10 = 20.12 21.14
c 1.10 1.10 = 20.75 20.75
d 1.13 1.13 = 21.08 21.07
e 1.13 1.13 = 21.32 21.30
f 1.10 1.10 = 21.32 21.33
g 1.10 1.10 = 21.61 22.41
h 0.82 0.81 = 0.00 0.00
b 3.97 3.97 g 3.96 3.96
c 4.73 4.73 f 4.72 4.72
a 5.64 5.65 h 5.58 5.59
8.60 8.63 5.62 5.62
PIECE WHITE BLACK
MEDIA 3.78 3.78

Table 5. Elemental mates king and piece/s against king.

Simulated games

MATES

STALEMATES

Draws
REYES

% MATES

% STALEMATES

% Total

4.000.000

30.978

222.886

3.746.136

0,774

5,572

6,347

4.000.000

27.754

9.699

3.962.547

0,694

0,242

0,936

4.000.000

2.361

52.217

3.945.422

0,059

1,305

1,364

4.000.000

227

27.950

3.971.823

0,006

0,699

0,704

4.000.000

140

19.128

3.980.732

0,004

0,478

0,482