Practice

According to our quantitative experiments with razor margin = queen val, limited razoring at pre-pre-frontier nodes exhibits no measurable loss in tactical strength as compared with extended futility pruning alone. Yet it shrinks the search trees by additional 5%-15% on average at fixed search depths > 10 plies. Table 1.2 lists the according performance data as obtained by searching all 2180 positions of the ECM, WAC, and WCS test suites to fixed depths of 8, 10, and 12 plies with the 1997 WMCC version of DARKTHOUGHT (see Appendix 1.3.8 for a detailed description of the exact experimental setup). The data shows that limited razoring hardly influences searches of fixed depths  <= 10 plies but then really takes off at fixed depth of 12 plies. We observe even greater savings (10%-15%) in other test positions with deep solutions which need search depths  >= 13 plies to be found.

 
Table 1.2: Performance of Extended Futility Pruning vs. Added Razoring.
Test Extd. Extd. +Razor +Razor  
Suite #Nodes #Solved $\Delta$Nodes $\Delta$Solved (No.)
ECM-08 1,085,889,029 542 / 879 -0.91% +0.92% (+5)
ECM-10 7,640,512,567 636 / 879 -1.50% 0.00% (0)
ECM-12 69,508,462,114 696 / 879 -9.64% -0.43% (-1)
WAC-08 125,494,781 285 / 300 -0.21% 0.00% (0)
WAC-10 753,895,911 294 / 300 -1.93% 0.00% (0)
WAC-12 6,308,884,467 296 / 300 -3.87% 0.00% (0)
WCS-08 661,758,996 837 / 1001 -2.41% -0.24% (-2)
WCS-10 4,469,041,033 863 / 1001 -2.54% +0.23% (+2)
WCS-12 38,766,902,141 876 / 1001 -6.68% +0.11% (+1)
Sum-08 1,873,142,806 1664 / 2180 -1.39% +0.18% (+3)
Sum-10 12,863,449,511 1793 / 2180 -1.89% +0.11% (+2)
Sum-12 114,584,248,722 1868 / 2180 -8.32% 0.00% (0)
 

Last but not least, we like to highlight the synergetic performance of both extended futility pruning and limited razoring combined. Table 1.3 presents the according data by comparing the normal version of DARKTHOUGHT (see Section 1.3.5) with one that is identical except for the addition of extended futility pruning and limited razoring.

 
Table 1.3: Performance of Normal vs. Extended Futility Pruning + Razoring.
Test Normal Normal Ex.+Rz. Ex.+Rz.  
Suite #Nodes #Solved $\Delta$Nodes $\Delta$Solved (No.)
ECM-08 1,232,004,798 552 / 879 -12.66% -0.91% (-5)
ECM-10 8,823,781,692 642 / 879 -14.71% -0.94% (-6)
ECM-12 83,443,531,950 704 / 879 -24.73% -1.28% (-9)
WAC-08 146,094,041 285 / 300 -14.28% 0.00% (0)
WAC-10 946,867,509 296 / 300 -21.92% -0.68% (-2)
WAC-12 8,998,551,515 296 / 300 -32.60% 0.00% (0)
WCS-08 750,804,397 841 / 1001 -13.98% -0.71% (-6)
WCS-10 5,398,696,585 866 / 1001 -19.32% -0.12% (-1)
WCS-12 52,801,555,626 874 / 1001 -31.49% +0.34% (+3)
Sum-08 2,128,903,236 1678 / 2180 -13.24% -0.66% (-11)
Sum-10 15,169,345,786 1804 / 2180 -16.81% -0.50% (-9)
Sum-12 145,243,639,091 1874 / 2180 -27.68% -0.32% (-6)
 



Created by Ernst A. Heinz, Thu Dec 16 23:28:11 EST 1999