是否可以暴力破解这款 5*5 井字游戏？

Question

所以我编造了这个游戏，但我无法找到始终获胜的好策略。

它与original 3×3 Tic-Tac-Toe 非常相似；但有变化。

所以你画了一个 5×5 的棋盘。然后每个玩家轮流放一个十字架和一个圆圈。然后我们计算“分数”。

This is a completed game 我画的。得分是通过计算每 3 次连续罢工来计算的。因此，例如在第一行，跨玩家获得 1 分。

然后，您可以水平、垂直和对角两种方式进行计数；对于每一行、每一列和对角线。

对于 4-in-a-row，您将获得 2 分，因为您可以将其视为 2 个不同的 3-in-a-rows。类似地，一个 5-in-a-row 将获得 3 分。

在示例游戏中，cross 获得 9，而 circle 仅获得 7。

我经常玩这个；但总是很难说出下一步该往哪里走。我注意到，首先开始会给您带来显着的优势。为了弥补这一点，我将第一个开始的玩家的分数降低了一个。

是否有可能强制计算机学习每场比赛的最佳动作？

提前致谢！

旁注：如果有人可以将其编程为一个带有随机计算机动作的简单游戏，那就太好了。我刚刚开始编程，我很难弄清楚如何去做。

Answer 1

暴力破解

下面的 sn-p 将暴力破解玩家 X 和玩家 O 的所有结束游戏

有 33,542,145 种排列可供测试，其中约 5,000,000 种是有效的最终游戏。为了防止页面锁定，它将任务分成 250,000 个排列的组

X 的最高分是 16，O 的最高分是 14。运行 sn-p 以查看示例结束游戏布局和其他详细信息。

我没有包括任何障碍。

这只能做最终游戏，因为它使用位字段来保持高性能。然而位域没有空棋盘位置的空间。

可以通过反转每个游戏排列的位来优化同时玩两个玩家

const tag = (tag, props = {}) => Object.assign(document.createElement(tag), props);
const append = (par, ...sibs) => sibs.reduce((p, sib) => (p.appendChild(sib), p), par);
const log = (el, data, add = true) => add ? append(el, tag("div", {textContent: data.toString()})) :  el.textContent = data.toString();
   
      

const scores = {
    [0b00111] : 1, 
    [0b01110] : 1, 
    [0b11100] : 1,
    [0b11101] : 1, 
    [0b10111] : 1,
    [0b01111] : 2,
    [0b11110] : 2,
    [0b11111] : 3,
};
const rotateMat = [
    0, 5, 10, 15, 20,
    1, 6, 11, 16, 21,
    2, 7, 12, 17, 22,
    3, 8, 13, 18, 23,
    4, 9, 14, 19, 24
];
const diagonMat = [
    2,   8, 14, -1, -1,
    1,   7, 13, 19, -1, 
    0,   6, 12, 18, 24,
    5,  11, 17, 23, -1,
    10, 16, 22, -1, -1,
];
const diagonMatUp = [
    10, 6,  2, -1, -1,
    15, 11, 7,  3, -1,
    20, 16, 12, 8,  4,
    21, 17, 13, 9, -1,
    22, 18, 14,-1, -1,
];

function transform(board, matrix) {
    var i = 25, b = 0;
    while (i--) { matrix[i] > -1 && (board & (1 << matrix[i])) && (b |= 1 << i) }
    return b;
}
function scoreLines(board) {
    var i = 5, score = 0, l = 0;
    while (i--) {  score += scores[(board >> (i * 5)) & 0b11111] ?? 0 }        
    return score;
}
function score(board) {
    return scoreLines(board) + 
        scoreLines(transform(board, rotateMat)) +
        scoreLines(transform(board, diagonMat)) +
        scoreLines(transform(board, diagonMatUp));
}
function isValidGame(board, side) {
    var c = 0, i = 25, bits = side + 1;
    while (i-- && c < bits) { (board & (1 << i)) && c++ }
    return c === side;
}
function showBoard(board, score, side) {
    var i = 5;
    log(games, "------------------------");
    log(games, "End game score: " + score + " player: " + (side===13 ? "X" : "O"));
    log(games, "Example end game");
    while (i--) { 
        const line = ((board >> (i * 5)) & 0b11111).toString(2).padStart(5, "0");
        const lined = side === 13 ? 
            line.replace(/1/g,"X").replace(/0/g,"O") :
            line.replace(/1/g,"O").replace(/0/g,"X");
         log(games,  lined); 
    }    
}
function brute(side = 13) {
    function doSet(i) {
        var ii = 251357;
        while (i >= min && ii--) {
            if (isValidGame(i, side)) {
                gameCount ++;
                const s = score(i);
                if (s >= maxScore) {
                    if (s > maxScore) { 
                        bestEndGames.length = 0 
                        game = i;
                    }
                    maxScore = s;
                    bestEndGames.push(i);
                }
            }
            i--;
        }        
        if (i >= min) {
            setTimeout(doSet, 8, i);
            log(progress, status + " is: "  + maxScore + " tested: " + ((max - min) - (i - min)) + " of " + (max - min) + " permutations", false);
        } else {
            log(games, status + " is: " + maxScore + " of " + gameCount + " end games");
            log(games, "Number of end games with best score: " + bestEndGames.length);           
            showBoard(game, maxScore, side);
            if (side === 13) { setTimeout(brute, 1000, 12) }
            else { log(progress, "Done", false) } 
        }
    }
    var game, gameCount = 0;
    var maxScore = 0;
    const bestEndGames = [];
    const status = "Best score player: " + (side===13 ? "X" : "O");
    const [min, max] = side === 13 ? [0b1111111111111, 0b1111111111111000000000000] : [0b111111111111, 0b1111111111110000000000000];
    doSet(max)
}
brute(13);

<div id="progress"></div>
<div id="games"></div>

为了得分，下一个 sn-p 将这样做。有点hack，在输入字段中输入游戏并会吐出分数。

const tag = (tag, props = {}) => Object.assign(document.createElement(tag), props);
const append = (par, ...sibs) => sibs.reduce((p, sib) => (p.appendChild(sib), p), par);
const log = (el, data, add = true) => add ? append(el, tag("div", {textContent: data.toString()})) :  el.textContent = data.toString();
   
      

const scores = {
    [0b00111] : 1, 
    [0b01110] : 1, 
    [0b11100] : 1,
    [0b11101] : 1, 
    [0b10111] : 1,
    [0b01111] : 2,
    [0b11110] : 2,
    [0b11111] : 3,
};
const rotateMat = [
    0, 5, 10, 15, 20,
    1, 6, 11, 16, 21,
    2, 7, 12, 17, 22,
    3, 8, 13, 18, 23,
    4, 9, 14, 19, 24
];
const diagonMat = [
    2,   8, 14, -1, -1,
    1,   7, 13, 19, -1, 
    0,   6, 12, 18, 24,
    5,  11, 17, 23, -1,
    10, 16, 22, -1, -1,
];
const diagonMatUp = [
    10, 6,  2, -1, -1,
    15, 11, 7,  3, -1,
    20, 16, 12, 8,  4,
    21, 17, 13, 9, -1,
    22, 18, 14,-1, -1,
];

function transform(board, matrix) {
    var i = 25, b = 0;
    while (i--) { matrix[i] > -1 && (board & (1 << matrix[i])) && (b |= 1 << i) }
    return b;
}
function scoreLines(board) {
    var i = 5, score = 0, l = 0;
    while (i--) {  score += scores[(board >> (i * 5)) & 0b11111] ?? 0 }        
    return score;
}
function score(board) {
    return scoreLines(board) + 
        scoreLines(transform(board, rotateMat)) +
        scoreLines(transform(board, diagonMat)) +
        scoreLines(transform(board, diagonMatUp));
}
function isValidGame(board, side, asStr) {
    var c = 0, i = 25, bits = side + 1;
    while (i-- && c < bits) { (
        (asStr[24-i] !== "-" &&  asStr[24-i] !== " ") && board & (1 << i)) && c++ 
    }
    return [c <= side, c];
}
function showBoard(board, asStr) {
    var i = 0;
    var j = 0;
    while (i < 5) { 
        const line = ((board >> ((4-i) * 5)) & 0b11111).toString(2).padStart(5, "0");
        const lined = line.replace(/1/g,"X").replace(/0/g,"O");
        var str = "";
        j = 0;
        while (j < 5) {
            str += (asStr[i * 5 + j] !== "-" && asStr[i * 5 + j] !== " ") ? lined[j] : ".";
            j++;
        }
        log(games,  str); 
        i++;
    }    
}
gameVal1.addEventListener("input", testGame);
gameVal2.addEventListener("input", testGame);
gameVal3.addEventListener("input", testGame);
gameVal4.addEventListener("input", testGame);
gameVal5.addEventListener("input", testGame);

function testGame() {
    var board = gameVal1.value.slice(0,5).padEnd(5, "-");
    board += gameVal2.value.slice(0,5).padEnd(5, "-");
    board += gameVal3.value.slice(0,5).padEnd(5, "-");
    board += gameVal4.value.slice(0,5).padEnd(5, "-");
    board += gameVal5.value.slice(0,5).padEnd(5, "-");
    board = board.replace(/[^OX\- ]/gi,"-");
    const X = eval("0B" + board.replace(/X/gi,"1").replace(/O|-| /gi,"0"));
    const O = eval("0B" + board.replace(/X|-| /gi,"0").replace(/O/gi,"1"));
    const [vx, movesX] = isValidGame(X, 13, board);
    const [vo, movesY] = isValidGame(O, 12, board);
    vx && log(resultX, "Player X score: " + score(X) + " moves: " + movesX, false);
    vo && log(resultO, "Player O score: " + score(O) + " moves: " + movesY, false);
    games.innerHTML = "";
    showBoard(X, board);
}
testGame()

input  {
   font-family: monospace;
   font-size: large;
}
.fixFont {
   font-family: monospace;
   font-size: large;
}
#games {
   position: absolute;
   top: 28px;
   left: 80px;
   border: 1px solid black;
   padding: 0px 3px;
   letter-spacing: 3px;
}
#resultX {
   position: absolute;
   top: 40px;
   left: 160px;
}
#resultO {
   position: absolute;
   top: 60px;
   left: 160px;
}

<div class="fixFont">
Enter "x" "x" "O" or "o". Empty slots "-" or space<br>
<input type="text" id="gameVal1" value="XXXXX" size="5"><br>
<input type="text" id="gameVal2" value="XXXXO" size="5"><br>
<input type="text" id="gameVal3" value="XXXXO" size="5"><br>
<input type="text" id="gameVal4" value="OOOOO" size="5"><br>
<input type="text" id="gameVal5" value="OOOOO" size="5"><br>
<div id="resultX"></div>
<div id="resultO"></div>
<div id="games"></div>
</div>