algorithm - 国际象棋:Alpha-Beta 中的错误

Question

我正在实现一个国际象棋引擎，我已经编写了一个相当复杂的 alpha-beta 搜索例程，其中包含静态搜索和换位表。但是，我观察到一个奇怪的错误。

评估函数使用的是方 block 表，就像这个用于棋子的表:

static int ptable_pawn[64] = {  
   0,  0,  0,  0,  0,  0,  0,  0,
  30, 35, 35, 40, 40, 35, 35, 30,
  20, 25, 25, 30, 30, 25, 25, 20,
  10, 20, 20, 20, 20, 20, 20, 10,
   3,  0, 14, 15, 15, 14,  0,  3,
   0,  5,  3, 10, 10,  3,  5,  0,
   5,  5,  5,  5,  5,  5,  5,  5,
   0,  0,  0,  0,  0,  0,  0,  0
};

当轮到黑方时， table 反射(reflect)在 x 轴上。具体来说，如果您好奇的话，查找是这样发生的，其中 A-H 列映射到 0-7，行是从白方开始的 0-7:

int ptable_index_for_white(int col, int row) {
    return col+56-(row*8);
}

int ptable_index_for_black(int col, int row) {
    return col+(row*8);
}

因此，h4(坐标 7、3)上的兵值白棋 3 分(centipawns)，f6(坐标 5、5)上的兵值黑棋 3 centipawns。

整个评价函数目前是 block 方表和 Material 。

在更大的搜索深度下，我的引擎正在选择一些真正可怕的 Action 。考虑从起始位置生成的这个输出:

Iterative Deepening Analysis Results (including cached analysis)
Searching at depth 1... d1 [+0.10]: 1.b1c3 
    (4 new nodes, 39 new qnodes, 0 qnode aborts, 0ms), 162kN/s
Searching at depth 2... d2 [+0.00]: 1.e2e4 d7d5 
    (34 new nodes, 78 new qnodes, 0 qnode aborts, 1ms), 135kN/s
Searching at depth 3... d3 [+0.30]: 1.d2d4 d7d5 2.c1f4 
    (179 new nodes, 1310 new qnodes, 0 qnode aborts, 4ms), 337kN/s
Searching at depth 4... d4 [+0.00]: 1.g1f3 b8c6 2.e2e4 d7d5 
    (728 new nodes, 2222 new qnodes, 0 qnode aborts, 14ms), 213kN/s
Searching at depth 5... d5 [+0.20]: 1.b1a3 g8f6 2.d2d4 h8g8 3.c1f4 
    (3508 new nodes, 27635 new qnodes, 0 qnode aborts, 103ms), 302kN/s
Searching at depth 6... d6 [-0.08]: 1.d2d4 a7a5 2.c1f4 b7b6 3.f4c1 c8b7 
    (21033 new nodes, 112915 new qnodes, 0 qnode aborts, 654ms), 205kN/s
Searching at depth 7... d7 [+0.20]: 1.b1a3 g8f6 2.a1b1 h8g8 3.d2d4 g8h8 4.c1f4 
    (39763 new nodes, 330837 new qnodes, 0 qnode aborts, 1438ms), 258kN/s
Searching at depth 8... d8 [-0.05]: 1.e2e4 a7a6 2.e4e5 a6a5 3.h2h4 d7d6 4.e5d6 c7d6 
    (251338 new nodes, 2054526 new qnodes, 0 qnode aborts, 12098ms), 191kN/s

在深度 8 处，注意黑棋以“... a7a6 ... a6a5”着法开局，根据棋子方格表来看，这一步很可怕。此外，“h2h4”对白棋来说是一个可怕的举动。为什么我的搜索功能会选择如此奇怪的 Action ？值得注意的是，这只会在更深的深度开始发生(深度 3 的移动看起来不错)。

此外，搜索经常会出错!考虑以下位置:

引擎推荐了一个可怕的错误 (3...f5h3)，不知何故遗漏了明显的回复 (4.g2h3):

Searching at depth 7... d7 [+0.17]: 3...f5h3 4.e3e4 h3g4 5.f2f3 g8f6 6.e4d5 f6d5 
    (156240 new nodes, 3473795 new qnodes, 0 qnode aborts, 17715ms), 205kN/s

不涉及静止搜索，因为错误发生在第 1 层 (!!)。

这是我的搜索功能的代码。很抱歉它太长了:我尽可能地简化了，但我不知道哪些部分与错误无关。我假设我的算法在某种程度上是错误的。

实现基于this one来自维基百科，几乎完全一样。 (更新:我已经大大简化了搜索，但我的错误仍然存​​在。)

// Unified alpha-beta and quiescence search
int abq(board *b, int alpha, int beta, int ply) {
    pthread_testcancel(); // To allow search worker thread termination
    bool quiescence = (ply <= 0);

    // Generate all possible moves for the quiscence search or normal search, and compute the
    // static evaluation if applicable.
    move *moves = NULL;
    int num_available_moves = 0;
    if (quiescence) moves = board_moves(b, &num_available_moves, true); // Generate only captures
    else moves = board_moves(b, &num_available_moves, false); // Generate all moves
    if (quiescence && !useqsearch) return relative_evaluation(b); // If qsearch is turned off

    // Abort if the quiescence search is too deep (currently 45 plies)
    if (ply < -quiesce_ply_cutoff) { 
        sstats.qnode_aborts++;
        return relative_evaluation(b);
    }

    // Allow the quiescence search to generate cutoffs
    if (quiescence) {
        int score = relative_evaluation(b);
        alpha = max(alpha, score);
        if (alpha >= beta) return score;
    }

    // Update search stats
    if (quiescence) sstats.qnodes_searched++;
    else sstats.nodes_searched++;

    // Search hueristic: sort exchanges using MVV-LVA
    if (quiescence && mvvlva) nlopt_qsort_r(moves, num_available_moves, sizeof(move), b, &capture_move_comparator);

    move best_move_yet = no_move;
    int best_score_yet = NEG_INFINITY;
    int num_moves_actually_examined = 0; // We might end up in checkmate
    for (int i = num_available_moves - 1; i >= 0; i--) { // Iterate backwards to match MVV-LVA sort order
        apply(b, moves[i]);
        // never move into check
        coord king_loc = b->black_to_move ? b->white_king : b->black_king; // for side that just moved
        if (in_check(b, king_loc.col, king_loc.row, !(b->black_to_move))) {
            unapply(b, moves[i]);
            continue;
        }
        int score = -abq(b, -beta, -alpha, ply - 1);
        num_moves_actually_examined++;
        unapply(b, moves[i]);
        if (score >= best_score_yet) {
            best_score_yet = score;
            best_move_yet = moves[i];
        }
        alpha = max(alpha, best_score_yet);
        if (alpha >= beta) break;
    }

    // We have no available moves (or captures) that don't leave us in check
    // This means checkmate or stalemate in normal search
    // It might mean no captures are available in quiescence search
    if (num_moves_actually_examined == 0) {
        if (quiescence) return relative_evaluation(b); // TODO: qsearch doesn't understand stalemate or checkmate
        coord king_loc = b->black_to_move ? b->black_king : b->white_king;
        if (in_check(b, king_loc.col, king_loc.row, b->black_to_move)) return NEG_INFINITY; // checkmate
        else return 0; // stalemate
    }

    // record the selected move in the transposition table
    evaltype type = (quiescence) ? qexact : exact;
    evaluation eval = {.best = best_move_yet, .score = best_score_yet, .type = type, .depth = ply};
    tt_put(b, eval);
    return best_score_yet;
}

/* 
 * Returns a relative evaluation of the board position from the perspective of the side about to move.
 */
int relative_evaluation(board *b) {
    int evaluation = evaluate(b);
    if (b->black_to_move) evaluation = -evaluation;
    return evaluation;
}

我正在这样调用搜索:

int result = abq(b, NEG_INFINITY, POS_INFINITY, ply);

编辑:即使我简化了搜索例程，错误仍然存​​在。引擎只是错误地去掉了碎片。通过将其加载到 XBoard(或任何其他 UCI 兼容的 GUI)并与强大的引擎进行对抗，您可以轻松地看到这一点。应 manlio 的要求，我上传了代码:

这是 GitHub 存储库(链接已删除；问题出在上面的代码片段中)。它将在 OS X 或任何 *nix 系统上使用“make”构建。

Answer 1

if (score >= best_score_yet) {

应该是:

if (score > best_score_yet) {

否则您将考虑采取糟糕的举措。第一个 best_move_yet 将是正确的(因为 best_score_yet = NEG_INFINITY)但其他 score == best_score_yet 的移动不一定更好。

改变那一行:

起始位置

Iterative Deepening Analysis Results (including cached analysis)
Searching at depth 1... d1 [+0.10]: 1.e2e4 
    (1 new nodes, 4 new qnodes, 0 qnode aborts, 0ms, 65kN/s)
    (ttable: 1/27777778 = 0.00% load, 0 hits, 0 misses, 1 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 2... d2 [+0.00]: 1.e2e4 g8f6 
    (21 new nodes, 41 new qnodes, 0 qnode aborts, 0ms, 132kN/s)
    (ttable: 26/27777778 = 0.00% load, 0 hits, 0 misses, 25 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 3... d3 [+0.30]: 1.d2d4 g8f6 2.c1f4 
    (118 new nodes, 247 new qnodes, 0 qnode aborts, 5ms, 73kN/s)
    (ttable: 187/27777778 = 0.00% load, 0 hits, 0 misses, 161 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 4... d4 [+0.00]: 1.e2e4 g8f6 2.f1d3 b8c6 
    (1519 new nodes, 3044 new qnodes, 0 qnode aborts, 38ms, 119kN/s)
    (ttable: 2622/27777778 = 0.01% load, 0 hits, 0 misses, 2435 inserts (with 0 overwrites), 1 insert failures)
Searching at depth 5... d5 [+0.10]: 1.g2g3 g8f6 2.f1g2 b8c6 3.g2f3 
    (10895 new nodes, 35137 new qnodes, 0 qnode aborts, 251ms, 184kN/s)
    (ttable: 30441/27777778 = 0.11% load, 0 hits, 0 misses, 27819 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 6... d6 [-0.08]: 1.d2d4 g8f6 2.c1g5 b8c6 3.g5f6 g7f6 
    (88027 new nodes, 249718 new qnodes, 0 qnode aborts, 1281ms, 264kN/s)
    (ttable: 252536/27777778 = 0.91% load, 0 hits, 0 misses, 222095 inserts (with 0 overwrites), 27 insert failures)
Searching at depth 7... d7 [+0.15]: 1.e2e4 g8f6 2.d2d4 b8c6 3.d4d5 c6b4 4.g1f3 
    (417896 new nodes, 1966379 new qnodes, 0 qnode aborts, 8485ms, 281kN/s)
    (ttable: 1957490/27777778 = 7.05% load, 0 hits, 0 misses, 1704954 inserts (with 0 overwrites), 817 insert failures)

在测试位置时:

Calculating...
Iterative Deepening Analysis Results (including cached analysis)
Searching at depth 1... d1 [+2.25]: 3...g8h6 4.(q)c3d5 (q)d8d5 
    (1 new nodes, 3 new qnodes, 0 qnode aborts, 0ms, 23kN/s)
    (ttable: 3/27777778 = 0.00% load, 0 hits, 0 misses, 3 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 2... d2 [-0.13]: 3...f5e4 4.c3e4 (q)d5e4 
    (32 new nodes, 443 new qnodes, 0 qnode aborts, 3ms, 144kN/s)
    (ttable: 369/27777778 = 0.00% load, 0 hits, 0 misses, 366 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 3... d3 [+0.25]: 3...g8h6 4.c3e2 h6g4 
    (230 new nodes, 2664 new qnodes, 0 qnode aborts, 24ms, 122kN/s)
    (ttable: 2526/27777778 = 0.01% load, 0 hits, 0 misses, 2157 inserts (with 0 overwrites), 0 insert failures)
Searching at depth 4... d4 [-0.10]: 3...g8f6 4.e3e4 f5e6 5.f1b5 
    (2084 new nodes, 13998 new qnodes, 0 qnode aborts, 100ms, 162kN/s)
    (ttable: 15663/27777778 = 0.06% load, 0 hits, 0 misses, 13137 inserts (with 0 overwrites), 2 insert failures)
Searching at depth 5... d5 [+0.15]: 3...g8f6 4.f1e2 h8g8 5.g2g4 f5e4 6.(q)c3e4 (q)f6e4 
   (38987 new nodes, 1004867 new qnodes, 0 qnode aborts, 2765ms, 378kN/s)
   (ttable: 855045/27777778 = 3.08% load, 0 hits, 0 misses, 839382 inserts (with 0 overwrites), 302 insert failures)