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Perft, (performance test, move path enumeration)
a debugging function to walk the move generation tree of strictly legal moves to count all the leaf nodes of a certain depth, which can be compared to predetermined values and used to isolate bugs. In perft, nodes are only counted at the end after the last makemove. Thus "higher" terminal nodes (e.g. mate or stalemate) are not counted, instead the number of move paths of a certain depth. Perft ignores draws by repetition, by the fifty-move rule and by insufficient material. By recording the amount of time taken for each iteration, it's possible to compare the performance of different move generators or the same generator on different machines, though this must be done with caution since there are variations to perft.

Perft function

A simple perft function in C looks as follows:
typedef unsigned long long u64;
 
u64 Perft(int depth)
{
    MOVE move_list[256];
    int n_moves, i;
    u64 nodes = 0;
 
    if (depth == 0) return 1;
 
    n_moves = GenerateMoves(move_list);
    for (i = 0; i < n_moves; i++) {
        MakeMove(move_list[i]);
        nodes += Perft(depth - 1);
        UndoMove(move_list[i]);
    }
    return nodes;
}

Bulk-counting

Instead of counting nodes at "depth 0", legal move generators can take advantage of the fact that the number of moves generated at "depth 1" represents the accurate perft value for that branch. Therefore they can skip the last makemove/undomove, which gives much faster results and is a better indicator of the raw move generator speed (versus move generator + make/unmake). However, this can cause some confusion when comparing perft values. Assuming the above code used a legal move generator, it would only need the following modification:
...
//__/* DELETE: if (depth == 0) return 1; */__//
 
n_moves = GenerateMoves(move_list);
 
__if (depth == 1) return n_moves;__
...

Hashing

Perft can receive another speed boost by hashing node counts, with a small chance for inaccurate results. Sometimes this is used as a sanity check to make sure the hash table and keys are working correctly.

Perft History

Supposable, perft was first implemented within the Cobol program RSCE-1 by R.C. Smith, submitted to the USCF for evaluation, and subject of an 1978 Computerworld article [1]. RSCE-1's purpose was not to play chess games, but position analysis, to find forced mates, and to perform a move path enumeration of up to three plies, with the perft(3) result of 8,902 from the initial position already mentioned [2]. Ken Thompson may have calculated perft(3) and perft(4) earlier than this date with Belle. Steven Edwards was the first to compute perft(5) through perft(9), and has since been actively involved in Perft computations.

In December 2003, Albert Bertilsson started a distributed project [3] to calculate perft(11) of the initial position, taking over a week to calculate [4]. Exact Perft numbers have been computed and verified up to a depth of 13 by Edwards and are now available in the On-Line Encyclopedia of Integer Sequences [5], and are given under Initial Position Summary. A so far unverified claim for perft(14) of 61,885,021,521,585,529,237 was given by Peter Österlund in April 2013 [6], while Daniel Shawul proposed Perft estimation applying Monte carlo methods [7] [8].

See also


Publications


Perft in other Games


Forum Posts

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External Links


References

  1. ^ Written in Cobol - Program Written as Chess Buff's Research Aid by Brad Schultz, Computerworld, April 17, 1978, Page 37
  2. ^ Perft(3) from 1978, with a twist! by Steven Edwards, CCC, December 08, 2011
  3. ^ Distributed perft project by Albert Bertilsson, CCC, December 09, 2003
  4. ^ Distributed Perft Project
  5. ^ A048987 from On-Line Encyclopedia of Integer Sequences (OEIS)
  6. ^ Re: Perft(14) estimates thread by Peter Österlund, CCC, April 02, 2013
  7. ^ MC methods by Daniel Shawul, CCC, April 11, 2013
  8. ^ Daniel S. Abdi (2013). Monte carlo methods for estimating game tree size. pdf
  9. ^ Re: MC methods by Daniel Shawul, CCC, April 13, 2013
  10. ^ Perft, search the CCC Archives
  11. ^ Written in Cobol - Program Written as Chess Buff's Research Aid by Brad Schultz, Computerworld, April 17, 1978, Page 37
  12. ^ ankan-ban/perft_gpu · GitHub
  13. ^ Fast perft on GPU (upto 20 Billion nps w/o hashing) by Ankan Banerjee, CCC, June 22, 2013

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