King safety tuning

An important term in the evaluation of an engine is King Safety. This addresses the fact that the game is lost when the own king is mated no matter what. This also allows an engine to consider material sacrifices when the enemy king comes under pressure by them. So without a decent king safety an engine will provide their opponents good chances for some spectacular mate combinations.

A simple approach is just to count the enemy pieces near the own king. The more pieces the more dangerous it is. This ignores the fact that sliders can be very dangerous from a distance. It is better than nothing but usually not good enough.

A more sophisticated implementation counts the attackers and their attacks against the area of the own king. It also considers defenders. Finally the counter is used as a look-up index into a non linear table. So a lone queen or rook attacking the king is not so bad, but if a knight and a rook join into the attack the king safety score jumps up exponentially.  




iCE uses the later approach. So it maintains a counter that is increased if an enemy piece attacks a

square near the king and decreased again if the square is defended by a own piece. The amount of increase and decrease depends on the piece type. In the current release of iCE those values are not tuned. So I just thought of some meaning full values, eg. if the queen attacks increase by 3, if the knight attacks increase by 2, if the pawn defends decrease by 1 etc...

I thought it might make sense to verify that the values I picked here are really good ones. Intuition is usually not the best adviser in chess programming.

I revived my genetic algorithm tuning framework that was responsible for most of the ELO gain of iCE 1.0 and modified it a bit to just tune the king safety counter values and not all the rest of the weights.

I then started an evolution of 1000 generations with a population size of 64, where the fittest individual is determined by a knock-out tournament within the generation. It ran for almost two weeks.

Here are some impressions:

The ranking table of the individuals of the final (1000.) generation. The 32 genoms that did not survive the initial 2-games round are removed from the list. 

 Rank Name     Elo    +    - games score oppo. draws
   1 ice.05   226   59   59   100   64%   131   23%
   3 ice.49   200  116  116    20   53%   191   35%
   4 ice.36   163   95   95    32   53%   154   31%
   5 ice.60   156   56   56   100   50%   164   31%
   6 ice.32   151  169  169     8   56%   127   38%
   7 ice.17   144   72   72    56   54%   123   36%
  10 ice.25   123  125  125    20   58%    96   15%
  12 ice.26   119  169  169     8   44%   152   38%
  13 ice.50   118  174  174     8   56%    96   38%
  14 ice.33   117  169  169     8   44%   158   38%
  16 ice.59   113  115  115    20   48%   131   35%
  17 ice.29   111  197  197     8   50%   146    0%
  18 ice.04    92  121  121    20   50%    97   20%
  20 ice.47    81   93   93    32   53%    65   38%
  21 ice.13    81  168  168     8   56%    61   38%
  24 ice.43    75  167  167     8   44%   103   38%
  26 ice.52    69   90   90    32   47%    89   44%
  28 ice.10    66  113  113    20   55%    35   40%
  30 ice.40    41  175  175     8   38%   103   25%
  32 ice.16    39   78   78    56   51%    47   27%
  34 ice.62    31  163  163     8   50%    38   50%
  36 ice.08     4  178  178     8   50%    19   25%
  37 ice.27   -11  173  173     8   56%   -24   38%
  39 ice.35   -20  118  118    20   45%    14   30%
  42 ice.02   -44  182  182     8   44%    20   13%
  48 ice.41  -102   93   93    32   45%   -73   41%
  49 ice.22  -108  169  169     8   44%   -61   38%
  50 ice.53  -118  120  120    20   45%   -53   30%
  52 ice.00  -127  114  114    20   55%  -147   40%
  54 ice.19  -149  168  168     8   44%  -114   38%
  55 ice.51  -170  162  162     8   50%  -159   50%
  58 ice.48  -187  164  164     8   38%  -135   50%

Here the winner was ice0.5. The final round was played between the individuals ice.05 and ice.60 and it ended 20 - 11 - 13.

Probability Vector after 100 generations. Most bits haven't decided yet whether to converge towards 0 or 1.

Probability Vector after 1000 generations. Most bits are fully converged towards 0 or 1.

The evolution made slow but steady progress. The entropy of the system dropped from 41 to about 10.

Some observations:

My original handpicked values were not so far off in general.

The knight seems more dangerous in attacking the squares in front of the king than the bishop, where as the bishop is a better defender. The most powerful attacking piece is the rook. 

Rook and queen are bad defenders.

The situation becomes more dangerous if the enemy has safe checks available, especially from the sliders (bishop, rook and queen). A safe check from a knight is almost worthless.

The threat of a back rank mate is about as dangerous as an additional attacker.


Result:

I played a final 16k games match between the tuned and the original version. It shows that with a very high statistical confidence the new iCE is stronger. Only 10 (selfplay) ELO, but most patches score muss less and I actually haven't added code. I just modified some values. So I decided to count my little project as a success.

Rank Name      Elo    +    - games score oppo. draws
   1 ice.tuned   5    4    4 16000   52%   -5   36%
   3 ice.base   -5    4    4 16000   48%    5   36%