Aart's Computer Checkers Page
Ongoing thoughts related to chess, checkers, or reversi programming can
be found at Aart's blog.
Discussions related to checkers can be found at the
World Draughts Forum.
Aart also wrote the UCI chess engine BikJump.
Checkers Engine: BikMove
Aart implemented an 8x8 straight checkers engine called
BikMove that can be plugged into Martin Fierz' excellent
CheckerBoard
application. To install BikMove v1.0,
download the following package, unzip
it in the checkboard engines directory, and then import
the engine through the Engine=>Select menu.
All C++ source code of the checkers engine BikMove
has been written by Aart Bik
(except the endgame databases probing code, which is used with
kind permission of Martin Fierz).
The main features of BikMove are listed below.
- Checkerboard compliant checkers engine.
- Iterative deepening with alpha-beta pruning.
- Ability to query endgame databases during search.
Perft for Checkers
The perft method originated in
the chess programming community as a way to verify the move generator of an engine. The
method traverses the game tree up to various, increasing depths to count all leaf nodes
at each given depth. These results are compared with pre-computed values to isolate bugs
and timings can be used to analyze the performance of the move generator. The perft
method can be applied to other game engines as well, such as
perft for reversi or,
as done on this page, perft for checkers. Below, perft numbers from the start
position are given using the move generator of BikMove on a
2.2 GHz Core 2 Duo (optimized with "bulk counting").
perft(1) = 7 in 0 ms.
perft(2) = 49 in 0 ms.
perft(3) = 302 in 0 ms.
perft(4) = 1469 in 0 ms.
perft(5) = 7361 in 0 ms.
perft(6) = 36768 in 1 ms. 36,768.0 KN/s
perft(7) = 179740 in 5 ms. 35,948.0 KN/s
perft(8) = 845931 in 23 ms. 36,779.6 KN/s
perft(9) = 3963680 in 86 ms. 46,089.3 KN/s
perft(10) = 18391564 in 398 ms. 46,210.0 KN/s
perft(11) = 85242128 in 1821 ms. 46,810.6 KN/s
perft(12) = 388623673 in 8395 ms. 46,292.3 KN/s
perft(13) = 1766623630 in 37182 ms. 47,512.9 KN/s
perft(14) = 7978439499 in 174947 ms. 45,604.9 KN/s
perft(15) = 36263167175 in 808155 ms. 44,871.5 KN/s
perft(16) = 165629569428 in 3767118 ms. 43,967.2 KN/s
perft(17) = 758818810990 in 17317695 ms. 43,817.5 KN/s
perft(18) = 3493881706141
perft(19) = 16114043592799
perft(20) = 74545030871553
Aart implemented a distributed version to compute perft(18) through perft(20) on a cluster
of machines. The breakdown per move (a must-have feature for debugging a move generator)
for these depths is shown below.
move divide(18) divide(19) divide(20)
------------------------------------------------------------
0 : 12-16 : 550829166472 2517202147314 11531470109861
1 : 11-16 : 566149929068 2564849953998 11736729175821
2 : 11-15 : 435063007630 2041959240377 9515983205474
3 : 10-15 : 472279451484 2180656975018 10055597639275
4 : 10-14 : 402570639569 1859042884028 8600202424158
5 : 9-14 : 441590753001 2068865301476 9698986164172
6 : 9-13 : 625398758917 2881467090588 13406062152792
------------------------------------------------------------
3493881706141 16114043592799 74545030871553
Thanks to Martin Fierz, Ed Gilbert, and Ed Trice for
verifying various perft numbers with their own move generators.
Checkers for Android
Checkers for Android is a simple standalone 8x8 straight checkers
application for the Android phone. The application is available for free
at the Android Market
and consists of a checkers engine (a Java version that evolved into
BikMove) together with a GUI that accepts moves through the touch screen
or trackball. More information can be found at
Aart's Android page.
Please note that this page is privately maintained by
Aart Bik.