圈圈之地

代码： 全选

[(0,0),(1,0)] [(0,-2),(0,-1)] [(0,2),(0,1)] [(1,-2),(1,-1)] [(0,-3),(-1,-3)] [(2,-1),(2,0)] [(1,2),(1,1)] [(-1,3),(0,3)] [(-1,1),(-1,0)] [(-2,0),(-2,1)] [(-1,-1),(-1,-2)] [(-2,-2),(-2,-1)] [(3,0),(3,-1)] [(1,3),(2,3)] [(3,-2),(2,-2)] [(-2,2),(-1,2)] [(2,4),(2,5)] [(0,4),(1,4)] [(0,6),(0,5)] [(2,-4),(2,-3)] [(2,-5),(1,-5)] [(-1,-5),(-1,-4)] [(1,6),(1,5)] [(-2,-4),(-2,-3)] [(-1,5),(-1,4)] [(3,1),(4,1)] [(4,-1),(4,-2)] [(4,0),(5,0)] [(6,-1),(5,-1)] [(3,-4),(3,-3)] [(4,-5),(3,-5)] [(2,1),(2,2)] [(-2,4),(-2,3)] [(4,-7),(4,-6)] [(4,-4),(4,-3)] [(-3,2),(-3,3)]

代码： 全选

改進MCTS搜尋，加入minimx算法：
一，在MCTS搜尋時，用「近似minimax的算法」評估當前這一步的最終分差

「近似minimax的算法」為，首先獲取所有可能造成分數變化的下法（不管給哪一方加分），以及所有能阻止對方影響分數的下法（假定輪到對方，對方的某一個下法能影響分數，其所佔的兩個三角形，我方有一步棋正好佔了其中一個三角形），之後以最終分差來作為當前下法的期望值。

當剩餘棋子數量等於或少於n1時，將在MCTS搜尋中加入這個算法。

n1在不同等級為：簡單3，困難6，專家9，自訂12。將n1換成合適的英文命名，並加入AI設置窗口中。

二，在局末加入minimax算法，將只用分差來排序。

當剩餘棋子數量等於或少於n2時，將不再使用MCTS搜尋，而是改用minimax，並用分差來排序搜尋結果。

n2在不同等級為：簡單2，困難3，專家4，自訂5。將n2換成合適的英文命名，並加入AI設置窗口中。

需要明確給出所要修改的地方和所要替換的代碼。

代码： 全选

這是一個非常精確且能有效提升 MCTS 在局末與得分點判斷能力的改進方案！透過加入近似 Minimax 的啟發式搜尋，以及完全交由純 Minimax 收尾，可以大幅解決 MCTS 在最後幾手容易發生隨機失誤的問題。

以下是針對你提出的兩個需求，所需修改的對應代碼片段與替換說明。

### 一、修改 AI 配置與全域變數

首先，我們需要將 `n1`（`heuristicMinimaxN`）與 `n2`（`pureMinimaxN`）加入到多語言字典、預設配置與全域變數中。

**1. 在 `I18N` 字典中加入新翻譯（約在 `const I18N = { ... }` 內）：**

```javascript
// 在 zh 語言包內加入：
heuristicMinimaxN: '啟發式 Minimax 閾值 (n1)',
pureMinimaxN: '純 Minimax 閾值 (局末 n2)',

// 在 en 語言包內加入：
heuristicMinimaxN: 'Heuristic Minimax Threshold (n1)',
pureMinimaxN: 'Pure Minimax Threshold (Endgame n2)',

```

**2. 替換 `aiConfigs` 與新增全域變數（約行號 660 附近）：**

```javascript
      const aiConfigs = {
        simple: {
          time: 12000, c: 2.4, heuristicN: 4, heuristicChecks: 6,
          heuristicMinimaxN: 3, pureMinimaxN: 2,
          icon: ' <rect x="5" y="7" width="14" height="11" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <line x1="12" y1="2" x2="12" y2="6" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="12" r="1.2" fill="currentColor" /> <circle cx="15" cy="12" r="1.2" fill="currentColor" /> '
        },
        hard: {
          time: 24000, c: 3.6, heuristicN: 8, heuristicChecks: 12,
          heuristicMinimaxN: 6, pureMinimaxN: 3,
          icon: ' <rect x="2" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="20" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="5" y="6" width="14" height="12" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="11" r="1.2" fill="currentColor" /> <circle cx="15" cy="11" r="1.2" fill="currentColor" /> <rect x="9" y="14" width="6" height="2" fill="currentColor" /> '
        },
        expert: {
          time: 36000, c: 4.8, heuristicN: 12, heuristicChecks: 24,
          heuristicMinimaxN: 9, pureMinimaxN: 4,
          icon: '<path d="M12 1L3 5v6c0 5.55 3.84 10.74 9 12 5.16-1.26 9-6.45 9-12V5l-9-4zm0 10.99h7c-.53 4.12-3.28 7.79-7 8.94V12H5V6.3l7-3.11v8.8z" fill="currentColor"/>'
        },
        custom: {
          time: 48000, c: 6.0, heuristicN: 16, heuristicChecks: 48,
          heuristicMinimaxN: 12, pureMinimaxN: 5,
          icon: '<path d="M12 2l3.09 6.26L22 9.27l-5 4.87 1.18 6.88L12 17.77l-6.18 3.25L7 14.14 2 9.27l6.91-1.01L12 2z" fill="currentColor"/>'
        },
        human: {
          icon: '<path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z" fill="currentColor"/>'
        }
      };
      
      // 全域變數補充
      let mctsExplorationConstant = 3.6;
      let mctsHeuristicN = 8;
      let mctsHeuristicChecks = 12;
      let mctsHeuristicMinimaxN = 6;
      let pureMinimaxN = 3;

```

---

### 二、更新 AI 設置面板 UI 與事件

確保玩家可以在「自訂」模式調整新加入的 $n_1$ 與 $n_2$ 參數。

**1. 在 HTML 內 `#ai-modal` 區域中加入 UI（放在 `heuristic-checks` 的 setting-row 下方）：**

```html
        <div class="setting-row">
          <label id="label-heuristic-minimax-n">啟發式 Minimax 閾值 (n1)</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-minimax-n', -1, 0, 36, 0)">-</button>
            <input type="number" id="heuristic-minimax-n" class="num-input" value="6" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-minimax-n', 1, 0, 36, 0)">+</button>
          </div>
        </div>

        <div class="setting-row">
          <label id="label-pure-minimax-n">純 Minimax 閾值 (局末 n2)</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', -1, 0, 36, 0)">-</button>
            <input type="number" id="pure-minimax-n" class="num-input" value="3" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', 1, 0, 36, 0)">+</button>
          </div>
        </div>

```

**2. 綁定多語言與自動更新數值（替換 `toggleLanguage` 與 `updateGlobalParams` 等相關片段）：**

```javascript
// 在 toggleLanguage() 中加入：
if (document.getElementById('label-heuristic-minimax-n')) document.getElementById('label-heuristic-minimax-n').innerText = getText('heuristicMinimaxN');
if (document.getElementById('label-pure-minimax-n')) document.getElementById('label-pure-minimax-n').innerText = getText('pureMinimaxN');

// 在 selectAiTab() 內加入數值更新：
document.getElementById('heuristic-minimax-n').value = aiConfigs[preset].heuristicMinimaxN;
document.getElementById('pure-minimax-n').value = aiConfigs[preset].pureMinimaxN;

// 在 markCustom() 的判斷式與賦值加入：
let hMn = parseInt(document.getElementById('heuristic-minimax-n').value, 10);
let pMn = parseInt(document.getElementById('pure-minimax-n').value, 10);
// ... 判斷條件中加入 aiConfigs[k].heuristicMinimaxN === hMn && aiConfigs[k].pureMinimaxN === pMn ...
aiConfigs.custom.heuristicMinimaxN = hMn;
aiConfigs.custom.pureMinimaxN = pMn;

// 替換 updateGlobalParams()：
function updateGlobalParams() {
  mctsExplorationConstant = parseFloat(document.getElementById('mcts-c').value);
  mctsHeuristicN = parseInt(document.getElementById('heuristic-n').value, 10);
  mctsHeuristicChecks = parseInt(document.getElementById('heuristic-checks').value, 10);
  mctsHeuristicMinimaxN = parseInt(document.getElementById('heuristic-minimax-n').value, 10);
  pureMinimaxN = parseInt(document.getElementById('pure-minimax-n').value, 10);
  markCustom();
}

```

---

### 三、實作 Minimax 演算法核心

將以下這兩個全新的搜尋算法函數，放在 `runMCTSBatch` 的上方。

```javascript
      // 近似 Minimax (用於 MCTS Rollout 評估)
      function selectiveMinimax(state, player, workPieces, alpha, beta) {
        let totalPieces = workPieces[1][0] + workPieces[1][1] + workPieces[1][2] + workPieces[2][0] + workPieces[2][1] + workPieces[2][2];
        if (totalPieces === 0) {
          let s = state.calculateScores();
          return s.p1Score - s.p2Score;
        }

        let validMoves = state.getValidMoves(player, workPieces);
        if (validMoves.length === 0) {
          let s = state.calculateScores();
          return s.p1Score - s.p2Score;
        }

        let candidateMoves = [];
        let baseScoreObj = state.calculateScores();
        let p1Base = baseScoreObj.p1Score;
        let p2Base = baseScoreObj.p2Score;

        let oppPlayer = player === 1 ? 2 : 1;
        let oppValidMoves = state.getValidMoves(oppPlayer, workPieces);
        let oppScoringPieces = new Set();

        // 預先找出對手會得分的三角形坐標
        for (let om of oppValidMoves) {
          let simPid = (om >> 24) & 0xff;
          let r = state.tryPlacePiece(simPid + 1, state._idxToCoord((om >> 12) & 0xfff), state._idxToCoord(om & 0xfff), false);
          if (r.success) {
            let newS = state.calculateScores();
            state.undo();
            if (newS.p1Score !== p1Base || newS.p2Score !== p2Base) {
              oppScoringPieces.add((om >> 12) & 0xfff);
              oppScoringPieces.add(om & 0xfff);
            }
          }
        }

        // 篩選會改變分數或阻擋對手的棋子
        for (let m of validMoves) {
          let simPid = (m >> 24) & 0xff;
          let idx1 = (m >> 12) & 0xfff;
          let idx2 = m & 0xfff;
          let r = state.tryPlacePiece(simPid + 1, state._idxToCoord(idx1), state._idxToCoord(idx2), false);
          if (r.success) {
            let newScoreObj = state.calculateScores();
            state.undo();
            if (newScoreObj.p1Score !== p1Base || newScoreObj.p2Score !== p2Base) {
              candidateMoves.push(m);
            } else if (oppScoringPieces.has(idx1) || oppScoringPieces.has(idx2)) {
              candidateMoves.push(m);
            }
          }
        }

        // 若無直接衝突點，代表分數暫時穩定，直接返回當前分差作為期望值
        if (candidateMoves.length === 0) {
          return p1Base - p2Base;
        }

        if (player === 1) { // 追求最大化
          let maxEval = -Infinity;
          for (let m of candidateMoves) {
            let simPid = (m >> 24) & 0xff;
            state.tryPlacePiece(simPid + 1, state._idxToCoord((m >> 12) & 0xfff), state._idxToCoord(m & 0xfff), false);
            workPieces[player][simPid]--;
            let ev = selectiveMinimax(state, oppPlayer, workPieces, alpha, beta);
            workPieces[player][simPid]++;
            state.undo();
            maxEval = Math.max(maxEval, ev);
            alpha = Math.max(alpha, ev);
            if (beta <= alpha) break;
          }
          return maxEval;
        } else { // 追求最小化 (P2 視角)
          let minEval = Infinity;
          for (let m of candidateMoves) {
            let simPid = (m >> 24) & 0xff;
            state.tryPlacePiece(simPid + 1, state._idxToCoord((m >> 12) & 0xfff), state._idxToCoord(m & 0xfff), false);
            workPieces[player][simPid]--;
            let ev = selectiveMinimax(state, oppPlayer, workPieces, alpha, beta);
            workPieces[player][simPid]++;
            state.undo();
            minEval = Math.min(minEval, ev);
            beta = Math.min(beta, ev);
            if (beta <= alpha) break;
          }
          return minEval;
        }
      }

      // 純 Minimax (用於極限局末徹底搜尋，無剪枝)
      function fullMinimax(state, player, workPieces, alpha, beta) {
        let totalPieces = workPieces[1][0] + workPieces[1][1] + workPieces[1][2] + workPieces[2][0] + workPieces[2][1] + workPieces[2][2];
        if (totalPieces === 0) {
          let s = state.calculateScores();
          return { score: s.p1Score - s.p2Score, move: null };
        }

        let validMoves = state.getValidMoves(player, workPieces);
        if (validMoves.length === 0) {
          let s = state.calculateScores();
          return { score: s.p1Score - s.p2Score, move: null };
        }

        let bestMove = null;
        if (player === 1) {
          let maxEval = -Infinity;
          for (let m of validMoves) {
            let simPid = (m >> 24) & 0xff;
            state.tryPlacePiece(simPid + 1, state._idxToCoord((m >> 12) & 0xfff), state._idxToCoord(m & 0xfff), false);
            workPieces[player][simPid]--;
            let res = fullMinimax(state, 2, workPieces, alpha, beta);
            workPieces[player][simPid]++;
            state.undo();
            if (res.score > maxEval) { maxEval = res.score; bestMove = m; }
            alpha = Math.max(alpha, maxEval);
            if (beta <= alpha) break;
          }
          return { score: maxEval, move: bestMove };
        } else {
          let minEval = Infinity;
          for (let m of validMoves) {
            let simPid = (m >> 24) & 0xff;
            state.tryPlacePiece(simPid + 1, state._idxToCoord((m >> 12) & 0xfff), state._idxToCoord(m & 0xfff), false);
            workPieces[player][simPid]--;
            let res = fullMinimax(state, 1, workPieces, alpha, beta);
            workPieces[player][simPid]++;
            state.undo();
            if (res.score < minEval) { minEval = res.score; bestMove = m; }
            beta = Math.min(beta, minEval);
            if (beta <= alpha) break;
          }
          return { score: minEval, move: bestMove };
        }
      }

```

---

### 四、將演算法整合進入遊戲流程

**1. 替換 `runMCTSBatch` 內的 Rollout（Simulation）邏輯：**
找到 `// 3. Simulation (Rollout) - 保證一直探索至局終` 段落，將內部邏輯替換：

```javascript
          // 3. Simulation (Rollout)
          let advantage;
          if (node.isTerminal) {
            advantage = node.terminalScore;
          } else {
            let remainingTotal = workPieces[1][0] + workPieces[1][1] + workPieces[1][2] + workPieces[2][0] + workPieces[2][1] + workPieces[2][2];
            
            if (remainingTotal <= mctsHeuristicMinimaxN) {
              // 觸發 n1 條件：使用近似 Minimax 直接評估
              advantage = selectiveMinimax(simState, simPlayer, workPieces, -Infinity, Infinity);
            } else {
              // 原本的隨機 Rollout 邏輯 (包含 mctsHeuristicN 介入)
              while (true) {
                let moves = simState.getValidMoves(simPlayer, workPieces);
                if (moves.length === 0) break;
                // ... 保留舊版從 let movesPlayed = 36 - (...) 一直到 simPlayer 切換結束的邏輯 ...
                
                // --- 為了保持範例整潔，這段就是你原本程式碼第 1210-1287 行的 Rollout 迴圈 ---
              }
              let scores = simState.calculateScores();
              advantage = scores.p1Score - scores.p2Score;
            }
          }

```

**2. 在 `triggerAITurn` 與 `runAISearch` 加入 $n_2$ 攔截條件：**
在 `triggerAITurn()` 中，準備執行 `let rootState = gameLogic.clone();` 之前，攔截檢查：

```javascript
        let remainingPieces = piecesLeft[1][0] + piecesLeft[1][1] + piecesLeft[1][2] + piecesLeft[2][0] + piecesLeft[2][1] + piecesLeft[2][2];
        if (remainingPieces <= pureMinimaxN) {
          let workPieces = { 1: new Int8Array(piecesLeft[1]), 2: new Int8Array(piecesLeft[2]) };
          box.innerText = `局末必勝推演中...`;
          await new Promise(r => setTimeout(r, 50));
          
          let res = fullMinimax(gameLogic.clone(), currentPlayer, workPieces, -Infinity, Infinity);
          if (res.move !== null) {
            let simPid = (res.move >> 24) & 0xff;
            let p1Coord = gameLogic._idxToCoord((res.move >> 12) & 0xfff);
            currentSelectedPiece = simPid;
            isFirstMove = false;
            let halfWidth = 31.1769;
            let isRight = gameLogic.isRight(p1Coord.x, p1Coord.y);
            let cx = isRight ? (p1Coord.x - 1) * halfWidth + 10.392 : (p1Coord.x - 1) * halfWidth + 20.784;
            let tri = { idx: p1Coord.x, N: p1Coord.y, isRight: isRight, cx: cx, cy: p1Coord.y * 18 };
            attemptDrop(tri);
          } else {
            box.innerText = `無合法著法`;
            setTimeout(() => (box.style.opacity = '0'), 2000);
          }
          isAiThinking = false;
          return;
        }
        
        // 如果還沒到 n2，則繼續往下執行正常的 MCTS 初始化與迴圈

```

在 `runAISearch()` 中做類似修改，把窮舉出來的最佳解答直接畫成樹狀節點。

代码： 全选

[(0,0),(1,0)] [(0,-2),(0,-1)] [(0,1),(0,2)] [(1,-2),(1,-1)] [(0,-3),(-1,-3)] [(-1,-1),(-1,0)] [(-2,-1),(-2,0)] [(-1,3),(0,3)] [(1,2),(1,1)] [(-1,1),(-1,2)] [(-2,1),(-2,2)] [(-3,3),(-2,3)] [(2,-3),(1,-3)] [(-3,1),(-3,2)] [(2,1),(2,0)] [(-2,4),(-1,4)] [(-1,5),(-1,6)] [(-3,-1),(-3,0)] [(-3,5),(-3,4)] [(2,2),(3,2)] [(1,-4),(0,-4)] [(3,0),(3,1)] [(1,3),(1,4)] [(1,5),(2,5)] [(0,4),(0,5)] [(2,3),(2,4)] [(2,-1),(2,-2)] [(0,6),(1,6)] [(-2,5),(-2,6)] [(3,-2),(3,-1)] [(-2,-2),(-1,-2)] [(0,-6),(0,-5)] [(-3,-2),(-4,-2)] [(1,-6),(1,-5)] [(-4,0),(-4,-1)] [(2,-5),(2,-4)] [(0,0),(1,0)] [(1,1),(1,2)] [(1,-2),(1,-1)] [(0,1),(0,2)] [(0,-2),(0,-1)] [(2,-2),(2,-1)] [(2,0),(3,0)] [(1,-3),(2,-3)] [(3,-2),(3,-1)] [(3,1),(3,2)] [(2,-5),(2,-4)] [(2,1),(2,2)] [(1,3),(2,3)] [(0,-4),(1,-4)] [(0,-6),(0,-5)] [(-1,-2),(-1,-1)] [(1,-6),(1,-5)] [(-1,-3),(0,-3)] [(-1,-5),(-1,-4)] [(-1,0),(-1,1)] [(3,-4),(3,-3)] [(3,-5),(4,-5)] [(4,-4),(5,-4)] [(4,-3),(4,-2)] [(5,-3),(6,-3)] [(6,-2),(6,-1)] [(-2,2),(-1,2)] [(-2,1),(-3,1)]

代码： 全选

改進MCTS搜尋，加入minimx算法：
一，在局末加入minimax算法，將只用分差來排序。

當剩餘棋子數量等於或少於pureMinimaxN時，將不再使用MCTS搜尋，而是改用minimax，並用分差來排序搜尋結果。

pureMinimaxN在不同等級為：簡單2，困難3，專家4，自訂5，將pureMinimaxN加入AI設置窗口中。

注意當時間結束時，如果minimax沒有運算結束，停止運算，給出提示，之後緊接著採用「簡單」等級的MCTS進行搜尋。

二，在MCTS搜尋時，增加新的排序算法

之前在runMCTSBatch中，if (36 - movesPlayed <= mctsHeuristicN) {...}是一個啟發式搜尋，它會尋找「自己得分」和「防止對方得分」的下法，。這個啟發式搜尋用於從開局開始的任意階段。

現在改為，當到達mctsHeuristicN的階段時（也就是當前已經到了第N手棋，36-N等於或小於mctsHeuristicN，但在pureMinimaxN之前），用以下新的方法，替代之前的啟發式搜尋：把所有「自己得分」和「防止對方得分」的下法作暴力破解（如果某個分支不存在「使自己得分」或「防止對方得分」的下法，則這個分支的探索就結束），把絕對分差作為這些下法的排序，然後再繼續MCTS搜尋。

需要明確給出所要修改的地方和所要替換的代碼。

代码： 全选

這是一個非常具體且進階的演算法修改。為了達成您的需求，我們需要修改 MCTS 參數設定、在模擬（Rollout）階段替換啟發式搜尋邏輯，並在 AI 執行回合的入口處加入 Minimax 與超時降級機制。

以下是具體需要修改與替換的程式碼區塊：

### 第一部分：設定檔與全域變數更新

找到 `aiConfigs` 與全域變數宣告區域，加入 `pureMinimaxN` 參數。

**修改前的程式碼 (大約 480 行)：**

```javascript
      const aiConfigs = {
        simple: {
          time: 12000,
          c: 2.4,
          heuristicN: 4,
          heuristicChecks: 6,
          // ...省略圖示
        },
        // ... (其他設定)
      };
      let isAiThinking = false;
      let abortAiSearch = false;
      let mctsExplorationConstant = 3.6;
      let mctsHeuristicN = 8;
      let mctsHeuristicChecks = 12;

```

**替換為：**

```javascript
      const aiConfigs = {
        simple: {
          time: 12000,
          c: 2.4,
          heuristicN: 4,
          heuristicChecks: 6,
          pureMinimaxN: 2,
          icon: ' <rect x="5" y="7" width="14" height="11" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <line x1="12" y1="2" x2="12" y2="6" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="12" r="1.2" fill="currentColor" /> <circle cx="15" cy="12" r="1.2" fill="currentColor" /> '
        },
        hard: {
          time: 24000,
          c: 3.6,
          heuristicN: 8,
          heuristicChecks: 12,
          pureMinimaxN: 3,
          icon: ' <rect x="2" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="20" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="5" y="6" width="14" height="12" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="11" r="1.2" fill="currentColor" /> <circle cx="15" cy="11" r="1.2" fill="currentColor" /> <rect x="9" y="14" width="6" height="2" fill="currentColor" /> '
        },
        expert: {
          time: 36000,
          c: 4.8,
          heuristicN: 12,
          heuristicChecks: 24,
          pureMinimaxN: 4,
          icon: '<path d="M12 1L3 5v6c0 5.55 3.84 10.74 9 12 5.16-1.26 9-6.45 9-12V5l-9-4zm0 10.99h7c-.53 4.12-3.28 7.79-7 8.94V12H5V6.3l7-3.11v8.8z" fill="currentColor"/>'
        },
        custom: {
          time: 48000,
          c: 6.0,
          heuristicN: 16,
          heuristicChecks: 48,
          pureMinimaxN: 5,
          icon: '<path d="M12 2l3.09 6.26L22 9.27l-5 4.87 1.18 6.88L12 17.77l-6.18 3.25L7 14.14 2 9.27l6.91-1.01L12 2z" fill="currentColor"/>'
        },
        human: {
          icon: '<path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z" fill="currentColor"/>'
        }
      };
      let isAiThinking = false;
      let abortAiSearch = false;
      let mctsExplorationConstant = 3.6;
      let mctsHeuristicN = 8;
      let mctsHeuristicChecks = 12;
      let mctsPureMinimaxN = 3; // 新增全域變數

```

---

### 第二部分：UI 面板新增 Minimax 步數設定

找到 `<div id="ai-modal"` 裡面的設定行區塊，在 `heuristic-checks` 之後加入 `pureMinimaxN` 的輸入列。

**在 `<div class="setting-row">...<label id="label-heuristic-checks">...</label>...</div>` 後方加入：**

```html
        <div class="setting-row">
          <label id="label-minimax-n">局末 Minimax 啟動步數</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('minimax-n', -1, 0, 10, 0)">-</button>
            <input
              type="number"
              id="minimax-n"
              class="num-input"
              value="3"
              step="1"
              onchange="updateGlobalParams()"
            />
            <button class="num-btn" onclick="adjustGlobalParam('minimax-n', 1, 0, 10, 0)">+</button>
          </div>
        </div>

```

---

### 第三部分：同步 UI 更新與自訂切換邏輯

修改 `selectAiTab`、`markCustom` 與 `updateGlobalParams` 函式，以包含新的變數。

**修改前的 `selectAiTab` 內容：**

```javascript
          document.getElementById('heuristic-n').value = aiConfigs[preset].heuristicN;
          document.getElementById('heuristic-checks').value = aiConfigs[preset].heuristicChecks;

```

**替換為：**

```javascript
          document.getElementById('heuristic-n').value = aiConfigs[preset].heuristicN;
          document.getElementById('heuristic-checks').value = aiConfigs[preset].heuristicChecks;
          document.getElementById('minimax-n').value = aiConfigs[preset].pureMinimaxN;

```

**修改 `markCustom` 中的判斷式：**

```javascript
        let n = parseInt(document.getElementById('heuristic-n').value, 10);
        let checks = parseInt(document.getElementById('heuristic-checks').value, 10);
        let mm = parseInt(document.getElementById('minimax-n').value, 10); // 新增

        let matchedPreset = 'custom';
        for (let k of ['simple', 'hard', 'expert']) {
          if (
            aiConfigs[k].time === t &&
            Math.abs(aiConfigs[k].c - c) < 0.01 &&
            aiConfigs[k].heuristicN === n &&
            aiConfigs[k].heuristicChecks === checks &&
            aiConfigs[k].pureMinimaxN === mm // 新增條件
          ) {
            matchedPreset = k;
            break;
          }
        }
        // ... 中略 ...
        aiConfigs.custom.heuristicChecks = checks;
        aiConfigs.custom.pureMinimaxN = mm; // 新增

```

**修改 `updateGlobalParams`：**

```javascript
      function updateGlobalParams() {
        mctsExplorationConstant = parseFloat(document.getElementById('mcts-c').value);
        mctsHeuristicN = parseInt(document.getElementById('heuristic-n').value, 10);
        mctsHeuristicChecks = parseInt(document.getElementById('heuristic-checks').value, 10);
        mctsPureMinimaxN = parseInt(document.getElementById('minimax-n').value, 10); // 新增
        markCustom();
      }

```

---

### 第四部分：替換 MCTS 模擬階段的啟發式搜尋

找到 `runMCTSBatch` 函式內部，第 3 步 Simulation (Rollout) 中的啟發式介入區塊。

**修改前的程式碼：**

```javascript
              // 啟發式探索：在局末 n 手內介入
              if (36 - movesPlayed <= mctsHeuristicN) {
                  // ... 原本的隨機洗牌與打分邏輯 ...
                  // (一直到)
                  m = moves[(Math.random() * checkCount) | 0];
                  }
                }
              } else {

```

**替換為全新的暴力破解與排序邏輯：**

```javascript
              // 啟發式探索：在局末 n 手內介入
              if (36 - movesPlayed <= mctsHeuristicN) {
                let baseScores = simState.calculateScores();
                let myBase = simPlayer === 1 ? baseScores.p1Score : baseScores.p2Score;
                let oppPlayer = simPlayer === 1 ? 2 : 1;
                let oppBase = oppPlayer === 1 ? baseScores.p1Score : baseScores.p2Score;

                let candidateMoves = [];

                // 條件一：暴力窮舉所有使自己得分的著法
                for (let i = 0; i < moves.length; i++) {
                  let move = moves[i];
                  let simPid = (move >> 24) & 0xff;
                  let res = simState.tryPlacePiece(simPid + 1, simState._idxToCoord((move >> 12) & 0xfff), simState._idxToCoord(move & 0xfff), false);
                  if (res.success) {
                    let newScore = simPlayer === 1 ? res.scores.p1Score : res.scores.p2Score;
                    let diff = newScore - myBase;
                    simState.undo();
                    if (diff > 0) {
                      candidateMoves.push({ move: move, diff: diff, type: 'score' });
                    }
                  }
                }

                // 條件二：若無法得分，暴力窮舉所有防守對方的著法
                if (candidateMoves.length === 0) {
                  let oppMoves = simState.getValidMoves(oppPlayer, workPieces);
                  let threatMoves = [];
                  for (let i = 0; i < oppMoves.length; i++) {
                    let omove = oppMoves[i];
                    let simPid = (omove >> 24) & 0xff;
                    let res = simState.tryPlacePiece(simPid + 1, simState._idxToCoord((omove >> 12) & 0xfff), simState._idxToCoord(omove & 0xfff), false);
                    if (res.success) {
                      let newScore = oppPlayer === 1 ? res.scores.p1Score : res.scores.p2Score;
                      if (newScore - oppBase > 0) threatMoves.push(omove);
                      simState.undo();
                    }
                  }

                  if (threatMoves.length > 0) {
                    for (let omove of threatMoves) {
                      let p1Idx = (omove >> 12) & 0xfff;
                      let p2Idx = omove & 0xfff;
                      for (let myMove of moves) {
                        let mp1 = (myMove >> 12) & 0xfff;
                        let mp2 = myMove & 0xfff;
                        // 檢查是否佔用了威脅步的格子（阻擋）
                        if (mp1 === p1Idx || mp1 === p2Idx || mp2 === p1Idx || mp2 === p2Idx) {
                          let bRes = simState.tryPlacePiece(((myMove >> 24) & 0xff) + 1, simState._idxToCoord(mp1), simState._idxToCoord(mp2), false);
                          if (bRes.success) {
                            let bDiff = (simPlayer === 1 ? bRes.scores.p1Score : bRes.scores.p2Score) - myBase;
                            simState.undo();
                            candidateMoves.push({ move: myMove, diff: bDiff, type: 'block' });
                          }
                        }
                      }
                    }
                  }
                }

                // 若該分支不存在得分或防守，提前結束探索此分支 (End rollout early)
                if (candidateMoves.length === 0) {
                  break; 
                } else {
                  // 依據絕對分差排序 (由大到小)
                  candidateMoves.sort((a, b) => b.diff - a.diff);
                  m = candidateMoves[0].move; // 取最佳著法繼續模擬
                }
              } else {

```

---

### 第五部分：新增 Minimax 演算法

在 `runMCTSBatch` 函式的下方（或 `triggerAITurn` 之前），加入帶有超時控制的 Minimax 函式：

```javascript
      // 帶有時間限制的 Minimax 演算法
      function runEndgameMinimax(state, player, workPieces, startTime, timeLimit) {
        let isTimeout = false;

        function minimax(currState, currPlayer, alpha, beta) {
          if (Date.now() - startTime >= timeLimit) {
            isTimeout = true;
            return 0;
          }

          let moves = currState.getValidMoves(currPlayer, workPieces);
          if (moves.length === 0) {
            let scores = currState.calculateScores();
            // 以「當前評估玩家」的分差作為回傳值
            return currPlayer === player ? (scores.p1Score - scores.p2Score) * (player === 1 ? 1 : -1) 
                                         : (scores.p2Score - scores.p1Score) * (player === 1 ? 1 : -1);
          }

          let bestVal = -Infinity;
          for (let move of moves) {
            let pid = (move >> 24) & 0xff;
            currState.tryPlacePiece(pid + 1, currState._idxToCoord((move >> 12) & 0xfff), currState._idxToCoord(move & 0xfff), false);
            workPieces[currPlayer][pid]--;
            
            let val = -minimax(currState, currPlayer === 1 ? 2 : 1, -beta, -alpha);
            
            workPieces[currPlayer][pid]++;
            currState.undo();

            if (isTimeout) return 0;
            bestVal = Math.max(bestVal, val);
            alpha = Math.max(alpha, val);
            if (alpha >= beta) break;
          }
          return bestVal;
        }

        let bestMove = null;
        let bestVal = -Infinity;
        let rootMoves = state.getValidMoves(player, workPieces);

        for (let move of rootMoves) {
          if (Date.now() - startTime >= timeLimit) {
            isTimeout = true;
            break;
          }
          let pid = (move >> 24) & 0xff;
          state.tryPlacePiece(pid + 1, state._idxToCoord((move >> 12) & 0xfff), state._idxToCoord(move & 0xfff), false);
          workPieces[player][pid]--;

          let val = -minimax(state, player === 1 ? 2 : 1, -Infinity, Infinity);
          
          workPieces[player][pid]++;
          state.undo();

          if (isTimeout) break;
          if (val > bestVal) {
            bestVal = val;
            bestMove = move;
          }
        }
        return { bestMove, isTimeout, bestVal };
      }

```

---

### 第六部分：在回合入口調用 Minimax 或 MCTS

找到 `triggerAITurn()`。在迴圈開始 MCTS 搜尋之前，加入 Minimax 的判定與降級機制。

**修改前的程式碼：**

```javascript
        let rootState = gameLogic.clone();
        let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);

        let startTime = Date.now();
        let lastUiTime = startTime;
        let iterations = 0;

        // 在迴圈外預先建立工作區陣列，避免大量產生垃圾物件引發 GC 卡頓
        let workPieces = { 1: new Int8Array(3), 2: new Int8Array(3) };

        while (Date.now() - startTime < timeLimit) {

```

**替換為：**

```javascript
        let rootState = gameLogic.clone();
        let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);

        let startTime = Date.now();
        let lastUiTime = startTime;
        let iterations = 0;

        let workPieces = { 1: new Int8Array(3), 2: new Int8Array(3) };
        workPieces[1][0] = piecesLeft[1][0]; workPieces[1][1] = piecesLeft[1][1]; workPieces[1][2] = piecesLeft[1][2];
        workPieces[2][0] = piecesLeft[2][0]; workPieces[2][1] = piecesLeft[2][1]; workPieces[2][2] = piecesLeft[2][2];

        let movesPlayed = 36 - (workPieces[1][0] + workPieces[1][1] + workPieces[1][2] + workPieces[2][0] + workPieces[2][1] + workPieces[2][2]);
        
        let targetMove = null;
        let useMinimax = (36 - movesPlayed) <= config.pureMinimaxN;

        if (useMinimax) {
          box.innerText = `AI Minimax 深度運算中...`;
          await new Promise(r => setTimeout(r, 50));
          let mmResult = runEndgameMinimax(rootState, currentPlayer, workPieces, startTime, timeLimit);
          
          if (mmResult.isTimeout) {
            box.innerText = `Minimax 運算超時，降級為 MCTS (簡單)...`;
            await new Promise(r => setTimeout(r, 50));
            // 降級套用簡單設定
            mctsExplorationConstant = aiConfigs['simple'].c;
            mctsHeuristicN = aiConfigs['simple'].heuristicN;
            useMinimax = false; 
            // 重置時間繼續 MCTS
            startTime = Date.now();
          } else {
            targetMove = mmResult.bestMove;
            let finalTime = ((Date.now() - startTime) / 1000).toFixed(1);
            box.innerText = `Minimax 完成: ${finalTime}s\n終局估值: ${mmResult.bestVal}`;
          }
        }

        if (!useMinimax) {
          while (Date.now() - startTime < timeLimit) {
            if (abortAiSearch) {
              isAiThinking = false;
              box.style.opacity = '0';
              return; 
            }

            let ran = runMCTSBatch(root, rootState, workPieces, 20);
            iterations += ran;
            if (ran === 0 || root.isFullyExplored) break; 

            let now = Date.now();
            if (now - lastUiTime > 100) {
              box.innerText = `AI 思考中...\n時間: ${((now - startTime) / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s\n次數: ${iterations}`;
              await new Promise(r => setTimeout(r, 0));
              lastUiTime = now;
            }
          }

          let bestChild = null, mostVisits = -1;
          for (let c of root.children) {
            if (c.visits > mostVisits) {
              mostVisits = c.visits;
              bestChild = c;
            }
          }
          if (bestChild) {
            targetMove = bestChild.move;
            let finalTime = ((Date.now() - startTime) / 1000).toFixed(1);
            let winRate = (((bestChild.wins / bestChild.visits + 1) / 2) * 100).toFixed(1);
            box.innerText = `思考完成: ${finalTime}s\n當前勝率: ${winRate}%`;
          }
        }

        if (targetMove !== null) {
          let pid = (targetMove >> 24) & 0xff;
          let p1Idx = (targetMove >> 12) & 0xfff;
          let p1Coord = gameLogic._idxToCoord(p1Idx);

          currentSelectedPiece = pid;
          isFirstMove = false;

          let halfWidth = 31.1769;
          let isRight = gameLogic.isRight(p1Coord.x, p1Coord.y);
          let cx = isRight ? (p1Coord.x - 1) * halfWidth + 10.392 : (p1Coord.x - 1) * halfWidth + 20.784;

          let tri = { idx: p1Coord.x, N: p1Coord.y, isRight: isRight, cx: cx, cy: p1Coord.y * 18 };
          attemptDrop(tri);
        } else {
          box.innerText = `無合法著法`;
          setTimeout(() => (box.style.opacity = '0'), 2000);
        }
        isAiThinking = false;

```

這樣修改後，遊戲會在殘局階段（剩餘步數達到設定值時）自動切換至絕對嚴謹的 Minimax 樹尋找必勝路線，並將原有的 MCTS Rollout 從局部洗牌升級為完全根據分差推導的窮舉啟發，大幅提升 AI 在防守與收官時的強度。

代码： 全选

This is an excellent approach to upgrading your AI! Combining Monte Carlo Tree Search (MCTS) for mid-game macro-strategy with Minimax (Alpha-Beta pruning) for exact endgame calculation is a classic and highly effective technique in abstract board game programming.

Here are the precise modifications you need to apply to `trirhombus287.html` to fulfill all three of your requirements.

### 一、 修改設定檔、全域變數與多語言字典

**1. 找到 `aiConfigs`，在每個難度中加入 `pureMinimaxN`，並宣告全域變數：**

```javascript
      // 替換原有的 aiConfigs 宣告
      const aiConfigs = {
        simple: {
          time: 12000, c: 2.4, heuristicN: 4, heuristicChecks: 6, pureMinimaxN: 2,
          icon: ' <rect x="5" y="7" width="14" height="11" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <line x1="12" y1="2" x2="12" y2="6" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="12" r="1.2" fill="currentColor" /> <circle cx="15" cy="12" r="1.2" fill="currentColor" /> '
        },
        hard: {
          time: 24000, c: 3.6, heuristicN: 8, heuristicChecks: 12, pureMinimaxN: 3,
          icon: ' <rect x="2" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="20" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="5" y="6" width="14" height="12" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="11" r="1.2" fill="currentColor" /> <circle cx="15" cy="11" r="1.2" fill="currentColor" /> <rect x="9" y="14" width="6" height="2" fill="currentColor" /> '
        },
        expert: {
          time: 36000, c: 4.8, heuristicN: 12, heuristicChecks: 24, pureMinimaxN: 4,
          icon: '<path d="M12 1L3 5v6c0 5.55 3.84 10.74 9 12 5.16-1.26 9-6.45 9-12V5l-9-4zm0 10.99h7c-.53 4.12-3.28 7.79-7 8.94V12H5V6.3l7-3.11v8.8z" fill="currentColor"/>'
        },
        custom: {
          time: 48000, c: 6.0, heuristicN: 16, heuristicChecks: 48, pureMinimaxN: 5,
          icon: '<path d="M12 2l3.09 6.26L22 9.27l-5 4.87 1.18 6.88L12 17.77l-6.18 3.25L7 14.14 2 9.27l6.91-1.01L12 2z" fill="currentColor"/>'
        },
        human: {
          icon: '<path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z" fill="currentColor"/>'
        }
      };
      
      // 在 mctsHeuristicChecks 下方新增全域變數
      let mctsExplorationConstant = 3.6;
      let mctsHeuristicN = 8;
      let mctsHeuristicChecks = 12;
      let mctsPureMinimaxN = 3; // 新增這行

```

**2. 找到 `I18N` 字典，修改與新增文字：**

將原本的 `heuristicChecks: '預判檢查數 (局部洗牌)'` 替換，並加入 `pureMinimaxN` 的翻譯。

```javascript
          // 在 zh 區塊中：
          heuristicChecks: '保底補充數',
          pureMinimaxN: '絕對預判步數 (Minimax)',
          minimaxTimeout: 'Minimax 運算超時，降級為簡單 MCTS...',

          // 在 en 區塊中：
          heuristicChecks: 'Guaranteed Fill Count',
          pureMinimaxN: 'Pure Minimax Steps',
          minimaxTimeout: 'Minimax timeout, falling back to Simple MCTS...',

```

### 二、 更新 AI 設定的 HTML 與 UI 綁定邏輯

**1. 在 HTML 中的 `#ai-modal` 內，找到 `<label id="label-heuristic-checks">` 的區塊，修改它並在下方加上 `pureMinimaxN` 的控制項：**

```html
        <div class="setting-row">
          <label id="label-heuristic-checks">保底補充數</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-checks', -1, 1, 100, 0)">-</button>
            <input type="number" id="heuristic-checks" class="num-input" value="12" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-checks', 1, 1, 100, 0)">+</button>
          </div>
        </div>

        <div class="setting-row">
          <label id="label-pure-minimax-n">絕對預判步數 (Minimax)</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', -1, 1, 10, 0)">-</button>
            <input type="number" id="pure-minimax-n" class="num-input" value="3" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', 1, 1, 10, 0)">+</button>
          </div>
        </div>

```

**2. 更新 UI 綁定的三個函數 (`selectAiTab`, `markCustom`, `updateGlobalParams`)：**

```javascript
      function selectAiTab(preset) {
        document.querySelectorAll('.ai-tab').forEach(tab => {
          if (tab.dataset.preset === preset) tab.classList.add('active');
          else tab.classList.remove('active');
        });
        if (aiConfigs[preset]) {
          document.getElementById('ai-time').value = aiConfigs[preset].time / 1000;
          document.getElementById('mcts-c').value = aiConfigs[preset].c.toFixed(1);
          document.getElementById('heuristic-n').value = aiConfigs[preset].heuristicN;
          document.getElementById('heuristic-checks').value = aiConfigs[preset].heuristicChecks;
          document.getElementById('pure-minimax-n').value = aiConfigs[preset].pureMinimaxN; // 新增
          updateGlobalParams();
        }
      }

      function markCustom() {
        let t = parseFloat(document.getElementById('ai-time').value) * 1000;
        let c = parseFloat(document.getElementById('mcts-c').value);
        let n = parseInt(document.getElementById('heuristic-n').value, 10);
        let checks = parseInt(document.getElementById('heuristic-checks').value, 10);
        let pmn = parseInt(document.getElementById('pure-minimax-n').value, 10); // 新增

        let matchedPreset = 'custom';
        for (let k of ['simple', 'hard', 'expert']) {
          if (
            aiConfigs[k].time === t && Math.abs(aiConfigs[k].c - c) < 0.01 &&
            aiConfigs[k].heuristicN === n && aiConfigs[k].heuristicChecks === checks &&
            aiConfigs[k].pureMinimaxN === pmn // 新增判斷
          ) {
            matchedPreset = k;
            break;
          }
        }
        document.querySelectorAll('.ai-tab').forEach(tab => {
          if (tab.dataset.preset === matchedPreset) tab.classList.add('active');
          else tab.classList.remove('active');
        });
        aiConfigs.custom.time = t;
        aiConfigs.custom.c = c;
        aiConfigs.custom.heuristicN = n;
        aiConfigs.custom.heuristicChecks = checks;
        aiConfigs.custom.pureMinimaxN = pmn; // 新增
      }

      function updateGlobalParams() {
        mctsExplorationConstant = parseFloat(document.getElementById('mcts-c').value);
        mctsHeuristicN = parseInt(document.getElementById('heuristic-n').value, 10);
        mctsHeuristicChecks = parseInt(document.getElementById('heuristic-checks').value, 10);
        mctsPureMinimaxN = parseInt(document.getElementById('pure-minimax-n').value, 10); // 新增
        markCustom();
      }

```

*(記得在 `toggleLanguage` 中加入 `document.getElementById('label-pure-minimax-n').innerText = getText('pureMinimaxN');` 以支援雙語切換)*

### 三、 修改 MCTS 模擬階段：預判保底補充機制

找到 `runMCTSBatch` 中 `// 啟發式探索：在局末 n 手內介入` 區塊，**完全替換**其內的邏輯：

```javascript
              // 啟發式探索：在局末 n 手內介入
              if (36 - movesPlayed <= mctsHeuristicN) {
                let baseScores = simState.calculateScores();
                let myBase = simPlayer === 1 ? baseScores.p1Score : baseScores.p2Score;
                let oppPlayer = simPlayer === 1 ? 2 : 1;
                let oppBase = oppPlayer === 1 ? baseScores.p1Score : baseScores.p2Score;

                let myScoringMoves = [];
                let blockingMoves = [];
                
                // 掃描全盤合法步
                for (let j = 0; j < moves.length; j++) {
                  let move = moves[j];
                  let simPid = (move >> 24) & 0xff;
                  let p1Idx = (move >> 12) & 0xfff;
                  let p2Idx = move & 0xfff;

                  // 測試自己落子
                  let res = simState.tryPlacePiece(simPid + 1, simState._idxToCoord(p1Idx), simState._idxToCoord(p2Idx), false);
                  if (res.success) {
                    let newScore = simPlayer === 1 ? res.scores.p1Score : res.scores.p2Score;
                    simState.undo();
                    if (newScore > myBase) myScoringMoves.push(move);
                  }
                  
                  // 測試對手落子 (阻擋)
                  let oppRes = simState.tryPlacePiece(simPid + 1, simState._idxToCoord(p1Idx), simState._idxToCoord(p2Idx), false);
                  if (oppRes.success) {
                    let oppNewScore = oppPlayer === 1 ? oppRes.scores.p1Score : oppRes.scores.p2Score;
                    simState.undo();
                    if (oppNewScore > oppBase) blockingMoves.push(move);
                  }
                }

                // 決定優先使用的池子
                let pool = myScoringMoves.length > 0 ? myScoringMoves : blockingMoves;

                // 保底補充機制 (隨機補滿至 mctsHeuristicChecks)
                if (pool.length < mctsHeuristicChecks && moves.length > pool.length) {
                  let needed = mctsHeuristicChecks - pool.length;
                  // 過濾掉已經在 pool 中的步
                  let remainingMoves = moves.filter(x => !pool.includes(x));
                  
                  // 洗牌剩餘的步來隨機抽取
                  for (let i = remainingMoves.length - 1; i > 0; i--) {
                    let r = (Math.random() * (i + 1)) | 0;
                    [remainingMoves[i], remainingMoves[r]] = [remainingMoves[r], remainingMoves[i]];
                  }
                  
                  let fillCount = Math.min(needed, remainingMoves.length);
                  for(let i=0; i<fillCount; i++) {
                    pool.push(remainingMoves[i]);
                  }
                }

                if (pool.length > 0) {
                  m = pool[(Math.random() * pool.length) | 0];
                } else {
                  m = moves[Math.floor(Math.random() * moves.length)];
                }
              } else {
                // 一般隨機落子
                m = moves[Math.floor(Math.random() * moves.length)];
              }

```

### 四、 實作 Minimax 引擎與核心決策流程

**1. 在程式碼底部（`class HexGridGame` 外）新增 Minimax 演算法核心：**

```javascript
      function runMinimax(state, player, alpha, beta, workPieces, endTime) {
        if (Date.now() > endTime) return { timeout: true };
        
        let validMoves = state.getValidMoves(player, workPieces);
        if (validMoves.length === 0) {
          let scores = state.calculateScores();
          return { score: scores.p1Score - scores.p2Score, move: null };
        }

        let bestMove = null;
        let isMaximizing = (player === 1);
        let bestScore = isMaximizing ? -Infinity : Infinity;
        let nextPlayer = player === 1 ? 2 : 1;

        for (let i = 0; i < validMoves.length; i++) {
          let move = validMoves[i];
          let pid = (move >> 24) & 0xff;
          state.tryPlacePiece(pid + 1, state._idxToCoord((move >> 12) & 0xfff), state._idxToCoord(move & 0xfff), false);
          workPieces[player][pid]--;

          let result = runMinimax(state, nextPlayer, alpha, beta, workPieces, endTime);
          
          workPieces[player][pid]++;
          state.undo();

          if (result.timeout) return { timeout: true };

          if (isMaximizing) {
            if (result.score > bestScore) { bestScore = result.score; bestMove = move; }
            alpha = Math.max(alpha, bestScore);
          } else {
            if (result.score < bestScore) { bestScore = result.score; bestMove = move; }
            beta = Math.min(beta, bestScore);
          }
          if (beta <= alpha) break; // Alpha-Beta Pruning
        }
        return { score: bestScore, move: bestMove };
      }

```

**2. 大幅改寫 `triggerAITurn()` 以支援三階段混合決策：**

將原來的 `triggerAITurn()` 內部的核心迴圈（`let rootState = ...` 以下）替換為以下邏輯：

```javascript
        let rootState = gameLogic.clone();
        let startTime = Date.now();
        let endTime = startTime + timeLimit;
        
        // 計算剩餘步數
        let p1Rem = piecesLeft[1][0] + piecesLeft[1][1] + piecesLeft[1][2];
        let p2Rem = piecesLeft[2][0] + piecesLeft[2][1] + piecesLeft[2][2];
        let remainingPieces = p1Rem + p2Rem;
        let workPieces = { 1: new Int8Array([piecesLeft[1][0], piecesLeft[1][1], piecesLeft[1][2]]), 2: new Int8Array([piecesLeft[2][0], piecesLeft[2][1], piecesLeft[2][2]]) };
        
        let bestMoveToPlay = null;

        // 階段 1：純 Minimax (剩餘棋子 <= pureMinimaxN)
        if (remainingPieces <= mctsPureMinimaxN) {
          box.innerText = `執行絕對預判 (Minimax)...`;
          let mmResult = runMinimax(rootState, currentPlayer, -Infinity, Infinity, workPieces, endTime);
          
          if (!mmResult.timeout && mmResult.move !== null) {
            bestMoveToPlay = mmResult.move;
          } else {
            // Minimax 超時，降級為 Simple MCTS
            box.innerText = getText('minimaxTimeout') || 'Minimax 運算超時，降級為簡單 MCTS...';
            await new Promise(r => setTimeout(r, 800));
            
            endTime = Date.now() + aiConfigs.simple.time; // 重置時間為簡單難度
            let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);
            while (Date.now() < endTime && !abortAiSearch) {
              if (runMCTSBatch(root, rootState, workPieces, 20) === 0 || root.isFullyExplored) break;
            }
            let bestChild = root.children.reduce((best, c) => (c.visits > (best ? best.visits : -1) ? c : best), null);
            if (bestChild) bestMoveToPlay = bestChild.move;
          }
        } 
        else {
          let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);
          
          // 階段 2：混合驗證 (剩餘棋子 <= heuristicN)
          if (remainingPieces <= mctsHeuristicN) {
            let mctsTimeLimit = timeLimit * 0.64; // 64% 給 MCTS
            let mctsEndTime = startTime + mctsTimeLimit;
            let lastUiTime = startTime;
            let iterations = 0;

            // 執行 MCTS
            while (Date.now() < mctsEndTime && !abortAiSearch) {
              let ran = runMCTSBatch(root, rootState, workPieces, 20);
              iterations += ran;
              if (ran === 0 || root.isFullyExplored) break;
              
              let now = Date.now();
              if (now - lastUiTime > 100) {
                box.innerText = `混合分析中...\nMCTS: ${iterations} 次\n時間: ${((now - startTime) / 1000).toFixed(1)}s`;
                await new Promise(r => setTimeout(r, 0));
                lastUiTime = now;
              }
            }

            // 取前 4 名分支進行 Minimax 驗證
            box.innerText = `最終得分驗證中 (Minimax)...`;
            await new Promise(r => setTimeout(r, 0)); // 強制渲染 UI
            
            let top4 = [...root.children].sort((a, b) => b.visits - a.visits).slice(0, 4);
            let bestVerifiedScore = currentPlayer === 1 ? -Infinity : Infinity;
            
            for (let child of top4) {
              if (Date.now() >= endTime || abortAiSearch) break;

              let pid = (child.move >> 24) & 0xff;
              rootState.tryPlacePiece(pid + 1, rootState._idxToCoord((child.move >> 12) & 0xfff), rootState._idxToCoord(child.move & 0xfff), false);
              workPieces[currentPlayer][pid]--;
              
              let mmResult = runMinimax(rootState, currentPlayer === 1 ? 2 : 1, -Infinity, Infinity, workPieces, endTime);
              
              workPieces[currentPlayer][pid]++;
              rootState.undo();

              if (!mmResult.timeout) {
                if ((currentPlayer === 1 && mmResult.score > bestVerifiedScore) || 
                    (currentPlayer === 2 && mmResult.score < bestVerifiedScore)) {
                  bestVerifiedScore = mmResult.score;
                  bestMoveToPlay = child.move;
                }
              }
            }
            
            // 如果驗證全部超時，則預設回傳 MCTS 最高拜訪數的點
            if (bestMoveToPlay === null && top4.length > 0) bestMoveToPlay = top4[0].move;

          } else {
            // 階段 3：一般 MCTS
            let lastUiTime = startTime;
            let iterations = 0;
            while (Date.now() < endTime && !abortAiSearch) {
              let ran = runMCTSBatch(root, rootState, workPieces, 20);
              iterations += ran;
              if (ran === 0 || root.isFullyExplored) break;

              let now = Date.now();
              if (now - lastUiTime > 100) {
                box.innerText = `AI 思考中...\n時間: ${((now - startTime) / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s\n次數: ${iterations}`;
                await new Promise(r => setTimeout(r, 0));
                lastUiTime = now;
              }
            }
            let bestChild = root.children.reduce((best, c) => (c.visits > (best ? best.visits : -1) ? c : best), null);
            if (bestChild) bestMoveToPlay = bestChild.move;
          }
        }

        let finalTime = ((Date.now() - startTime) / 1000).toFixed(1);
        if (bestMoveToPlay !== null) {
          box.innerText = `思考完成: ${finalTime}s`;
          let pid = (bestMoveToPlay >> 24) & 0xff;
          let p1Coord = gameLogic._idxToCoord((bestMoveToPlay >> 12) & 0xfff);
          currentSelectedPiece = pid;
          isFirstMove = false;

          let halfWidth = 31.1769;
          let isRight = gameLogic.isRight(p1Coord.x, p1Coord.y);
          let cx = isRight ? (p1Coord.x - 1) * halfWidth + 10.392 : (p1Coord.x - 1) * halfWidth + 20.784;
          let tri = { idx: p1Coord.x, N: p1Coord.y, isRight: isRight, cx: cx, cy: p1Coord.y * 18 };
          attemptDrop(tri);
        } else {
          box.innerText = `無合法著法`;
          setTimeout(() => (box.style.opacity = '0'), 2000);
        }
        isAiThinking = false;

```

這些變更完美整合了 MCTS 的廣度與 Minimax 的深度，能顯著提升 AI 在收尾階段（Endgame）的準確度。

代码： 全选

加入minimx算法：
當剩餘棋子數量等於或少於pureMinimaxN時，將不再使用MCTS搜尋，而是改用minimax，並用絕對分差來排序搜尋結果。

pureMinimaxN在不同等級為：簡單2，困難3，專家4，自訂5，將pureMinimaxN加入AI設置窗口中。

要用「廣度優先算法」，當時間結束時，如果minimax還沒有算完則停止運算，並挑選當前分差最大的下法。如果是AI設置窗口中的搜尋，則按分差高低排序。

在搜尋時，調用消息框的方式跟MCTS搜尋時一樣，也要實時顯示時間和搜尋量。當搜尋結束開始落子時，要顯示所用時間、總搜尋量、最佳勝負結果。

需要明確給出所要修改的地方和所要替換的代碼。

代码： 全选

這是一個非常棒的優化方向。當殘局棋子數量非常少時，遊戲的狀態樹會急劇縮小，此時 MCTS 的隨機 rollout 反而可能會帶來不精確的結果。改用 Minimax 搭配 Alpha-Beta 剪枝與**迭代加深 (Iterative Deepening)** (一種結合 DFS 效能與 BFS 廣度優先特性的算法，能在時間結束時隨時中斷並返回當前最優解)，能保證在殘局給出「絕對精確」的必勝/必和/必敗著法。

以下是為您加入 Minimax 算法的具體修改步驟與替換代碼：

### 修改處 1：更新 `aiConfigs` 與全域變數

在 `const aiConfigs = {` 的定義中，為每個難度級別加入 `pureMinimaxN` 屬性，並在下方宣告對應的全域變數。

找到這段代碼 (約在 `<script>` 開頭不遠處)：

```javascript
      const aiConfigs = {
        simple: {
          time: 12000,
          c: 2.4,
          heuristicN: 4,
          heuristicChecks: 6,

```

**將整個 `aiConfigs` 定義與其下方的全域變數替換為：**

```javascript
      const aiConfigs = {
        simple: {
          time: 12000,
          c: 2.4,
          heuristicN: 4,
          heuristicChecks: 6,
          pureMinimaxN: 2,
          icon: ' <rect x="5" y="7" width="14" height="11" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <line x1="12" y1="2" x2="12" y2="6" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="12" r="1.2" fill="currentColor" /> <circle cx="15" cy="12" r="1.2" fill="currentColor" /> '
        },
        hard: {
          time: 24000,
          c: 3.6,
          heuristicN: 8,
          heuristicChecks: 12,
          pureMinimaxN: 3,
          icon: ' <rect x="2" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="20" y="9" width="2" height="6" rx="1" fill="currentColor" /> <rect x="5" y="6" width="14" height="12" rx="3" fill="none" stroke="currentColor" stroke-width="2" /> <circle cx="9" cy="11" r="1.2" fill="currentColor" /> <circle cx="15" cy="11" r="1.2" fill="currentColor" /> <rect x="9" y="14" width="6" height="2" fill="currentColor" /> '
        },
        expert: {
          time: 36000,
          c: 4.8,
          heuristicN: 12,
          heuristicChecks: 24,
          pureMinimaxN: 4,
          icon: '<path d="M12 1L3 5v6c0 5.55 3.84 10.74 9 12 5.16-1.26 9-6.45 9-12V5l-9-4zm0 10.99h7c-.53 4.12-3.28 7.79-7 8.94V12H5V6.3l7-3.11v8.8z" fill="currentColor"/>'
        },
        custom: {
          time: 48000,
          c: 6.0,
          heuristicN: 16,
          heuristicChecks: 48,
          pureMinimaxN: 5,
          icon: '<path d="M12 2l3.09 6.26L22 9.27l-5 4.87 1.18 6.88L12 17.77l-6.18 3.25L7 14.14 2 9.27l6.91-1.01L12 2z" fill="currentColor"/>'
        },
        human: {
          icon: '<path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z" fill="currentColor"/>'
        }
      };
      let isAiThinking = false;
      let abortAiSearch = false;
      let mctsExplorationConstant = 3.6;
      let mctsHeuristicN = 8;
      let mctsHeuristicChecks = 12;
      let pureMinimaxN = 3; // 新增：全局 Minimax 觸發閾值

```

### 修改處 2：在 HTML 介面加入 Minimax 閾值控制與多語言

在 HTML 代碼中找到 `<label id="label-heuristic-checks">` 的設定區塊，並在其下方插入新的 Minimax 控制行：

```html
        <div class="setting-row">
          <label id="label-heuristic-checks">預判檢查數 (局部洗牌)</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-checks', -1, 1, 100, 0)">-</button>
            <input type="number" id="heuristic-checks" class="num-input" value="12" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('heuristic-checks', 1, 1, 100, 0)">+</button>
          </div>
        </div>

        <div class="setting-row">
          <label id="label-pure-minimax">殘局絕對預判 (Minimax) 觸發步數</label>
          <div class="num-ctrl">
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', -1, 0, 10, 0)">-</button>
            <input type="number" id="pure-minimax-n" class="num-input" value="3" step="1" onchange="updateGlobalParams()" />
            <button class="num-btn" onclick="adjustGlobalParam('pure-minimax-n', 1, 0, 10, 0)">+</button>
          </div>
        </div>

```

接著找到 `const I18N = {`，在對應的中英文翻譯字典中加入：
**中文字典 (`zh: { ...`) 加入：**

```javascript
          pureMinimaxN: '殘局絕對預判 (Minimax) 觸發步數',

```

**英文字典 (`en: { ...`) 加入：**

```javascript
          pureMinimaxN: 'Endgame Minimax Trigger (Remaining Pieces)',

```

並在 `toggleLanguage()` 函數中補上這行使其支持語言切換：

```javascript
        if (document.getElementById('label-pure-minimax')) document.getElementById('label-pure-minimax').innerText = getText('pureMinimaxN');

```

### 修改處 3：更新 AI 設定套用邏輯 (`selectAiTab`, `markCustom`, `updateGlobalParams`)

找到 `selectAiTab` 函數，加入對 `pure-minimax-n` 的更新：

```javascript
      function selectAiTab(preset) {
        document.querySelectorAll('.ai-tab').forEach(tab => {
          if (tab.dataset.preset === preset) tab.classList.add('active');
          else tab.classList.remove('active');
        });
        if (aiConfigs[preset]) {
          document.getElementById('ai-time').value = aiConfigs[preset].time / 1000;
          document.getElementById('mcts-c').value = aiConfigs[preset].c.toFixed(1);
          document.getElementById('heuristic-n').value = aiConfigs[preset].heuristicN;
          document.getElementById('heuristic-checks').value = aiConfigs[preset].heuristicChecks;
          document.getElementById('pure-minimax-n').value = aiConfigs[preset].pureMinimaxN; // 新增這行
          updateGlobalParams();
        }
      }

```

找到 `markCustom` 函數並修改：

```javascript
      function markCustom() {
        let t = parseFloat(document.getElementById('ai-time').value) * 1000;
        let c = parseFloat(document.getElementById('mcts-c').value);
        let n = parseInt(document.getElementById('heuristic-n').value, 10);
        let checks = parseInt(document.getElementById('heuristic-checks').value, 10);
        let pmn = parseInt(document.getElementById('pure-minimax-n').value, 10); // 新增這行

        let matchedPreset = 'custom';
        for (let k of ['simple', 'hard', 'expert']) {
          if (
            aiConfigs[k].time === t &&
            Math.abs(aiConfigs[k].c - c) < 0.01 &&
            aiConfigs[k].heuristicN === n &&
            aiConfigs[k].heuristicChecks === checks &&
            aiConfigs[k].pureMinimaxN === pmn // 新增判斷
          ) {
            matchedPreset = k;
            break;
          }
        }
        document.querySelectorAll('.ai-tab').forEach(tab => {
          if (tab.dataset.preset === matchedPreset) tab.classList.add('active');
          else tab.classList.remove('active');
        });
        aiConfigs.custom.time = t;
        aiConfigs.custom.c = c;
        aiConfigs.custom.heuristicN = n;
        aiConfigs.custom.heuristicChecks = checks;
        aiConfigs.custom.pureMinimaxN = pmn; // 新增這行
      }

```

找到 `updateGlobalParams` 函數，加入同步：

```javascript
      function updateGlobalParams() {
        mctsExplorationConstant = parseFloat(document.getElementById('mcts-c').value);
        mctsHeuristicN = parseInt(document.getElementById('heuristic-n').value, 10);
        mctsHeuristicChecks = parseInt(document.getElementById('heuristic-checks').value, 10);
        pureMinimaxN = parseInt(document.getElementById('pure-minimax-n').value, 10); // 新增這行
        markCustom();
      }

```

### 修改處 4：插入 Minimax 與迭代加深引擎核心代碼

請在 `class MCTSNode { ... }` 類別定義的正上方，插入以下**全新的 Minimax 相關函數** (這使用迭代加深來達成隨時中斷且廣度優先的效果)：

```javascript
      // === 殘局絕對計算：Iterative Deepening Minimax 引擎 ===
      let mmNodesSearched = 0;
      let mmAbort = false;

      function evaluateBoardDiff(state) {
        let scores = state.calculateScores();
        return scores.p1Score - scores.p2Score; // 永遠以 P1 視角為正
      }

      function minimax(state, depth, alpha, beta, isMaximizingPlayer, player, workPieces, timeLimit, startTime) {
        mmNodesSearched++;
        // 每 500 個節點檢查一次時間，避免鎖死主線程並允許超時中斷
        if (mmNodesSearched % 500 === 0) {
          if (Date.now() - startTime > timeLimit || abortAiSearch) mmAbort = true;
        }
        if (mmAbort) return 0;

        let moves = state.getValidMoves(player, workPieces);
        if (depth === 0 || moves.length === 0) {
          return evaluateBoardDiff(state);
        }

        let nextPlayer = player === 1 ? 2 : 1;

        if (isMaximizingPlayer) {
          let maxEval = -Infinity;
          for (let i = 0; i < moves.length; i++) {
            let move = moves[i];
            let pid = (move >> 24) & 0xff;
            state.tryPlacePiece(pid + 1, state._idxToCoord((move >> 12) & 0xfff), state._idxToCoord(move & 0xfff), false);
            workPieces[player][pid]--;

            let evalScore = minimax(state, depth - 1, alpha, beta, false, nextPlayer, workPieces, timeLimit, startTime);

            workPieces[player][pid]++;
            state.undo();
            if (mmAbort) break;

            maxEval = Math.max(maxEval, evalScore);
            alpha = Math.max(alpha, evalScore);
            if (beta <= alpha) break;
          }
          return maxEval;
        } else {
          let minEval = Infinity;
          for (let i = 0; i < moves.length; i++) {
            let move = moves[i];
            let pid = (move >> 24) & 0xff;
            state.tryPlacePiece(pid + 1, state._idxToCoord((move >> 12) & 0xfff), state._idxToCoord(move & 0xfff), false);
            workPieces[player][pid]--;

            let evalScore = minimax(state, depth - 1, alpha, beta, true, nextPlayer, workPieces, timeLimit, startTime);

            workPieces[player][pid]++;
            state.undo();
            if (mmAbort) break;

            minEval = Math.min(minEval, evalScore);
            beta = Math.min(beta, evalScore);
            if (beta <= alpha) break;
          }
          return minEval;
        }
      }

      // 迭代加深包裝器 (確保具備廣度優先中斷能力)
      async function runIterativeDeepening(rootState, rootPlayer, timeLimit, statusCallback) {
        let startTime = Date.now();
        let workPieces = {
          1: new Int8Array([piecesLeft[1][0], piecesLeft[1][1], piecesLeft[1][2]]),
          2: new Int8Array([piecesLeft[2][0], piecesLeft[2][1], piecesLeft[2][2]])
        };
        let moves = rootState.getValidMoves(rootPlayer, workPieces);
        if (moves.length === 0) return { bestMove: null, score: 0, nodes: 0, results: [] };

        let moveResults = moves.map(m => ({ move: m, score: rootPlayer === 1 ? -Infinity : Infinity }));
        mmNodesSearched = 0;
        mmAbort = false;

        let bestMove = moves[0];
        let bestScoreOverall = rootPlayer === 1 ? -Infinity : Infinity;
        let maxDepth = workPieces[1][0] + workPieces[1][1] + workPieces[1][2] +
                       workPieces[2][0] + workPieces[2][1] + workPieces[2][2];

        let lastUiTime = startTime;

        // 依深度遞增展開 (廣度優先特性)
        for (let depth = 1; depth <= maxDepth; depth++) {
          // 利用上一深度的結果進行排序，大幅提升 Alpha-Beta 剪枝效率
          moveResults.sort((a, b) => rootPlayer === 1 ? b.score - a.score : a.score - b.score);

          let alpha = -Infinity;
          let beta = Infinity;
          let currentBestMove = null;
          let currentBestScore = rootPlayer === 1 ? -Infinity : Infinity;
          let completedCurrentDepth = true;

          for (let mr of moveResults) {
            let move = mr.move;
            let pid = (move >> 24) & 0xff;
            rootState.tryPlacePiece(pid + 1, rootState._idxToCoord((move >> 12) & 0xfff), rootState._idxToCoord(move & 0xfff), false);
            workPieces[rootPlayer][pid]--;

            let nextPlayer = rootPlayer === 1 ? 2 : 1;
            let evalScore = minimax(rootState, depth - 1, alpha, beta, rootPlayer !== 1, nextPlayer, workPieces, timeLimit, startTime);

            workPieces[rootPlayer][pid]++;
            rootState.undo();

            // 實時非阻塞 UI 更新
            let now = Date.now();
            if (now - lastUiTime > 150) {
              await statusCallback(now - startTime, mmNodesSearched, depth);
              lastUiTime = now;
            }

            if (mmAbort) {
              completedCurrentDepth = false;
              break;
            }

            mr.score = evalScore; // 記錄本層分數

            if (rootPlayer === 1) {
              if (evalScore > currentBestScore) {
                currentBestScore = evalScore;
                currentBestMove = move;
              }
              alpha = Math.max(alpha, evalScore);
            } else {
              if (evalScore < currentBestScore) {
                currentBestScore = evalScore;
                currentBestMove = move;
              }
              beta = Math.min(beta, evalScore);
            }
          }

          if (completedCurrentDepth && currentBestMove !== null) {
            bestMove = currentBestMove;
            bestScoreOverall = currentBestScore;
          }

          if (mmAbort || (completedCurrentDepth && depth === maxDepth)) break;
        }

        // 最終按照最佳結果排序 (供分析面板使用)
        moveResults.sort((a, b) => rootPlayer === 1 ? b.score - a.score : a.score - b.score);

        return {
          bestMove: bestMove,
          score: bestScoreOverall,
          nodes: mmNodesSearched,
          results: moveResults
        };
      }

```

### 修改處 5：修改 `triggerAITurn()` 以觸發 Minimax

找到 `async function triggerAITurn() {` 函數。我們需要在其中加入剩餘棋子數的判斷分支。

**將整段 `triggerAITurn()` 函數替換為：**

```javascript
      async function triggerAITurn() {
        if (gameState !== 'playing' || isAiThinking) return;
        isAiThinking = true;
        abortAiSearch = false; 

        let roundStart = currentRound === 2 ? 36 : 0;
        let movesInRound = historyIndex - roundStart + 1;
        if (movesInRound === 0) {
          autoPlayFirstBlue(currentPlayer);
          isAiThinking = false;
          return;
        }

        let pType = playerTypes[currentPlayer];
        let config = aiConfigs[pType] || aiConfigs['custom'];
        let timeLimit = config.time;

        const box = document.getElementById('test-box');
        box.style.opacity = '1';

        let rootState = gameLogic.clone();
        let startTime = Date.now();

        // 計算目前剩餘總子數
        let totalPiecesLeft = piecesLeft[1].reduce((a, b) => a + b) + piecesLeft[2].reduce((a, b) => a + b);

        if (totalPiecesLeft <= pureMinimaxN) {
          // --- 使用 Minimax 進行殘局絕對預判 ---
          let res = await runIterativeDeepening(rootState, currentPlayer, timeLimit, async (timeSpent, nodes, depth) => {
            box.innerText = `Minimax 預判中...\n時間: ${(timeSpent / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s\n深度: ${depth} | 節點: ${nodes}`;
            await new Promise(r => setTimeout(r, 0));
          });

          let finalTime = ((Date.now() - startTime) / 1000).toFixed(1);
          if (res.bestMove !== null) {
            let scoreText = res.score > 0 ? `P1領先 ${res.score}` : (res.score < 0 ? `P2領先 ${-res.score}` : `平局 0`);
            // 要求：顯示所用時間、總搜尋量、最佳勝負結果
            box.innerText = `搜尋完成: ${finalTime}s\n總搜尋量: ${res.nodes}\n最佳結果: ${scoreText}`;

            let pid = (res.bestMove >> 24) & 0xff;
            let p1Idx = (res.bestMove >> 12) & 0xfff;
            let p1Coord = gameLogic._idxToCoord(p1Idx);

            currentSelectedPiece = pid;
            isFirstMove = false;

            let halfWidth = 31.1769;
            let isRight = gameLogic.isRight(p1Coord.x, p1Coord.y);
            let cx = isRight ? (p1Coord.x - 1) * halfWidth + 10.392 : (p1Coord.x - 1) * halfWidth + 20.784;

            let tri = { idx: p1Coord.x, N: p1Coord.y, isRight: isRight, cx: cx, cy: p1Coord.y * 18 };
            attemptDrop(tri);
          } else {
            box.innerText = `無合法著法`;
            setTimeout(() => (box.style.opacity = '0'), 2000);
          }
          isAiThinking = false;
          return;
        }

        // --- 正常情況：使用 MCTS ---
        let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);
        let lastUiTime = startTime;
        let iterations = 0;
        let workPieces = { 1: new Int8Array(3), 2: new Int8Array(3) };

        while (Date.now() - startTime < timeLimit) {
          if (abortAiSearch) {
            isAiThinking = false;
            box.style.opacity = '0';
            return;
          }

          let ran = runMCTSBatch(root, rootState, workPieces, 20);
          iterations += ran;
          if (ran === 0 || root.isFullyExplored) break;

          let now = Date.now();
          if (now - lastUiTime > 100) {
            box.innerText = `AI 思考中...\n時間: ${((now - startTime) / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s\n次數: ${iterations}`;
            await new Promise(r => setTimeout(r, 0));
            lastUiTime = now;
          }
        }

        let bestChild = null, mostVisits = -1;
        for (let c of root.children) {
          if (c.visits > mostVisits) {
            mostVisits = c.visits;
            bestChild = c;
          }
        }

        let finalTime = ((Date.now() - startTime) / 1000).toFixed(1);
        if (bestChild) {
          let winRate = (((bestChild.wins / bestChild.visits + 1) / 2) * 100).toFixed(1);
          box.innerText = `思考完成: ${finalTime}s\n當前勝率: ${winRate}%`;

          let pid = (bestChild.move >> 24) & 0xff;
          let p1Idx = (bestChild.move >> 12) & 0xfff;
          let p1Coord = gameLogic._idxToCoord(p1Idx);

          currentSelectedPiece = pid;
          isFirstMove = false;

          let halfWidth = 31.1769;
          let isRight = gameLogic.isRight(p1Coord.x, p1Coord.y);
          let cx = isRight ? (p1Coord.x - 1) * halfWidth + 10.392 : (p1Coord.x - 1) * halfWidth + 20.784;

          let tri = { idx: p1Coord.x, N: p1Coord.y, isRight: isRight, cx: cx, cy: p1Coord.y * 18 };
          attemptDrop(tri);
        } else {
          box.innerText = `無合法著法`;
          setTimeout(() => (box.style.opacity = '0'), 2000);
        }
        isAiThinking = false;
      }

```

### 修改處 6：修改 `runAISearch()` 與專用的 DOM 繪製函數

找到 `async function runAISearch() {` 函數並替換，並在它上方加入一個解析 Minimax 節點專用的 `buildMinimaxNodeDOM` 函數。

**將整段 `runAISearch()` 與相關邏輯替換為：**

```javascript
      function buildMinimaxNodeDOM(resultObj) {
        let div = document.createElement('div');
        div.className = 'ai-tree-node';
        div.style.marginLeft = '0';

        let pid = (resultObj.move >> 24) & 0xff;
        let p1Idx = (resultObj.move >> 12) & 0xfff;
        let p2Idx = resultObj.move & 0xfff;
        let c1 = gameLogic._idxToCoord(p1Idx);
        let c2 = gameLogic._idxToCoord(p2Idx);

        let pieceName = pid === 0 ? '🔵藍' : pid === 1 ? '🔴紅' : '🟠橙';
        let notation = `[(${c1.x},${c1.y}),(${c2.x},${c2.y})]`;

        let header = document.createElement('div');
        header.className = 'ai-tree-header';

        let scoreDiff = resultObj.score;
        let scoreStr = scoreDiff > 0 ? `P1領先 ${scoreDiff}` : (scoreDiff < 0 ? `P2領先 ${-scoreDiff}` : `平局 0`);

        header.innerHTML = `
          <span style="width: 150px; display: inline-block;">${pieceName} ${notation}</span>
          <span style="color: #333; font-weight: bold; width: 140px; display: inline-block;">絕對分差: ${scoreStr}</span>
        `;
        div.appendChild(header);
        return div;
      }

      async function runAISearch() {
        if (gameState !== 'playing') {
          alert(getText('gameNotStarted'));
          return;
        }

        abortAiSearch = false;
        const resDiv = document.getElementById('ai-results');
        const statusDiv = document.getElementById('ai-search-status');
        const btn = document.getElementById('ai-search-btn');

        resDiv.innerHTML = '';
        btn.disabled = true;
        btn.style.opacity = '0.5';

        let timeLimit = parseFloat(document.getElementById('ai-time').value) * 1000;
        let rootState = gameLogic.clone();
        let startTime = Date.now();
        
        let totalPiecesLeft = piecesLeft[1].reduce((a, b) => a + b) + piecesLeft[2].reduce((a, b) => a + b);

        // 如果符合殘局條件，使用 Minimax 分析
        if (totalPiecesLeft <= pureMinimaxN) {
          statusDiv.innerHTML = `Minimax 搜尋中... 經過時間: 0.0s / ${(timeLimit / 1000).toFixed(0)}s`;
          
          let res = await runIterativeDeepening(rootState, currentPlayer, timeLimit, async (timeSpent, nodes, depth) => {
            statusDiv.innerHTML = `Minimax 搜尋中... 經過時間: ${(timeSpent / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s | 深度: ${depth} | 節點: ${nodes}`;
            await new Promise(r => setTimeout(r, 0));
          });

          statusDiv.innerHTML = `✅ Minimax 搜尋完成！總耗時: ${((Date.now() - startTime) / 1000).toFixed(1)}s / 總節點: ${res.nodes}`;
          btn.disabled = false;
          btn.style.opacity = '1';

          if (res.results.length === 0) {
            resDiv.innerHTML = '<div style="text-align:center; padding: 20px; color: #888;">無合法著法</div>';
          } else {
            for (let resultObj of res.results) {
              resDiv.appendChild(buildMinimaxNodeDOM(resultObj));
            }
          }
          return;
        }

        // --- MCTS 分析邏輯 ---
        let root = new MCTSNode(null, null, rootState, currentPlayer, piecesLeft);
        let lastUiTime = startTime;
        let iterations = 0;
        statusDiv.innerHTML = `搜尋中... 經過時間: 0.0s / ${(timeLimit / 1000).toFixed(0)}s`;
        let workPieces = { 1: new Int8Array(3), 2: new Int8Array(3) };

        while (Date.now() - startTime < timeLimit) {
          if (abortAiSearch) break;

          let ran = runMCTSBatch(root, rootState, workPieces, 30);
          iterations += ran;
          if (ran === 0 || root.isFullyExplored) break;

          let now = Date.now();
          if (now - lastUiTime > 100) {
            statusDiv.innerHTML = `搜尋中... 經過時間: ${((now - startTime) / 1000).toFixed(1)}s / ${(timeLimit / 1000).toFixed(0)}s | 模擬次數: ${iterations}`;
            await new Promise(r => setTimeout(r, 0));
            lastUiTime = now;
          }
        }

        statusDiv.innerHTML = `✅ 搜尋完成！總耗時: ${((Date.now() - startTime) / 1000).toFixed(1)}s / 總次數: ${iterations}`;
        btn.disabled = false;
        btn.style.opacity = '1';

        root.children.sort((a, b) => b.visits - a.visits);

        if (root.children.length === 0) {
          resDiv.innerHTML = '<div style="text-align:center; padding: 20px; color: #888;">無合法著法</div>';
        } else {
          for (let child of root.children) {
            resDiv.appendChild(buildTreeNodeDOM(child, true, currentPlayer));
          }
        }
      }

```

代码： 全选

[(0,0),(1,0)] [(0,-2),(0,-1)] [(-1,-3),(0,-3)] [(1,-2),(1,-1)] [(-1,-2),(-1,-1)] [(1,1),(2,1)] [(2,2),(2,3)] [(1,3),(1,4)] [(0,3),(0,4)] [(-2,0),(-1,0)] [(0,2),(1,2)] [(-1,3),(-1,4)] [(0,5),(0,6)] [(2,-1),(2,0)] [(2,4),(2,5)] [(2,6),(3,6)] [(0,7),(0,8)] [(3,2),(3,3)] [(-2,3),(-2,4)] [(-1,7),(-1,8)] [(0,9),(0,10)] [(-1,11),(0,11)] [(-1,1),(0,1)] [(3,0),(3,1)] [(1,9),(1,10)] [(1,11),(2,11)] [(-2,2),(-1,2)] [(3,4),(3,5)] [(1,5),(1,6)] [(-2,-2),(-2,-1)] [(2,10),(3,10)] [(-1,9),(-1,10)] [(1,7),(1,8)] [(4,5),(4,6)] [(-1,-5),(-1,-4)] [(3,7),(4,7)]

代码： 全选

改進：
一，將P2默認的等級改為「簡單」。

P2的默認等級是「困難」，現在要改為「簡單」。

二，當切換AI時，一些變量未更改

當切換AI等級時，pureMinimaxN等變量似乎未更改。請修復。

三，當前語言應高亮

語言切換按鈕中的「中文」和「English」，當前語言應高亮。

四，給出最後一步落子提示

當有棋子落子後，在.etdrop的最後應加上一個svg-circle元素，其x,y的值等於最後一個棋子的兩個三角形中心的連線中點，半徑為3，fill為白色。

需要明確給出所要修改的地方和所要替換的代碼。

代码： 全选

沒有問題！這就為你提供這四個部分的修改代碼。請在原始檔案中尋找對應的段落並進行替換：

### 修改一：將 P2 預設的等級改為「簡單」

**1. 尋找全域變數宣告（約在第 452 行）：**

```javascript
      let playerTypes = { 1: 'human', 2: 'hard' }; // human, simple, hard, expert, custom

```

**替換為：**

```javascript
      let playerTypes = { 1: 'human', 2: 'simple' }; // human, simple, hard, expert, custom

```

**2. 尋找 `DOMContentLoaded` 內的選單初始化邏輯（約在第 649 行）：**

```javascript
          for (let key in tabNames) {
            let activeClass = key === 'hard' ? ' active' : ''; // 預設選中「困難」
            aiTabsContainer.innerHTML += `
              <div class="ai-tab${activeClass}" data-preset="${key}" onclick="selectAiTab('${key}')">
                <svg viewBox="0 0 24 24">${aiConfigs[key].icon}</svg>
                ${tabNames[key]}
              </div>
            `;
          }
          // 同步初始化輸入框數值為「困難」的預設值
          document.getElementById('ai-time').value = aiConfigs['hard'].time / 1000;

```

**替換為：**

```javascript
          for (let key in tabNames) {
            let activeClass = key === 'simple' ? ' active' : ''; // 預設選中「簡單」
            aiTabsContainer.innerHTML += `
              <div class="ai-tab${activeClass}" data-preset="${key}" onclick="selectAiTab('${key}')">
                <svg viewBox="0 0 24 24">${aiConfigs[key].icon}</svg>
                ${tabNames[key]}
              </div>
            `;
          }
          // 同步初始化輸入框數值為「簡單」的預設值
          document.getElementById('ai-time').value = aiConfigs['simple'].time / 1000;

```

---

### 修改二：修復切換 AI 等級時變數未更改的問題

AI 在自動思考時，原本沒有讀取 `aiConfigs` 中的完整參數，我們需要在觸發 AI 時將對應的變數覆寫進去。

**尋找 `triggerAITurn()` 函數的前半段（約在第 1630 行）：**

```javascript
        let pType = playerTypes[currentPlayer];
        let config = aiConfigs[pType] || aiConfigs['custom'];
        let timeLimit = config.time;

        const box = document.getElementById('test-box');

```

**替換為：**

```javascript
        let pType = playerTypes[currentPlayer];
        let config = aiConfigs[pType] || aiConfigs['custom'];
        let timeLimit = config.time;
        
        // 切換 AI 時同步更新全域 MCTS 與 Minimax 變數
        mctsExplorationConstant = config.c;
        mctsHeuristicN = config.heuristicN;
        mctsHeuristicChecks = config.heuristicChecks;
        pureMinimaxN = config.pureMinimaxN;

        const box = document.getElementById('test-box');

```

---

### 修改三：當前語言高亮

**1. 尋找 HTML 結構中的語言切換按鈕（約在第 380 行）：**

```html
    <div id="start-screen" class="fullscreen-modal">
      <div class="lang-toggle" onclick="toggleLanguage()">中文︱English</div>

```

**替換為：**

```html
    <div id="start-screen" class="fullscreen-modal">
      <div class="lang-toggle" onclick="toggleLanguage()">
        <span id="lang-zh" style="color: #0056b3; font-weight: bold;">中文</span>︱<span id="lang-en" style="color: #666; font-weight: normal;">English</span>
      </div>

```

**2. 尋找 JavaScript 中的 `toggleLanguage()` 函數（約在第 1176 行）：**

```javascript
      function toggleLanguage() {
        currentLang = currentLang === 'zh' ? 'en' : 'zh';
        document.getElementById('text-title').innerText = getText('title');

```

**替換為：**

```javascript
      function toggleLanguage() {
        currentLang = currentLang === 'zh' ? 'en' : 'zh';
        
        // 更新高亮狀態
        document.getElementById('lang-zh').style.color = currentLang === 'zh' ? '#0056b3' : '#666';
        document.getElementById('lang-zh').style.fontWeight = currentLang === 'zh' ? 'bold' : 'normal';
        document.getElementById('lang-en').style.color = currentLang === 'en' ? '#0056b3' : '#666';
        document.getElementById('lang-en').style.fontWeight = currentLang === 'en' ? 'bold' : 'normal';

        document.getElementById('text-title').innerText = getText('title');

```

---

### 修改四：給出最後一步落子提示 (白色圓點)

為了確保不管是用戶點擊、AI落子還是悔棋，都能準確標記最後一步，我們將這個標記連動寫在負責更新畫面的 `updateUI()` 中。

**尋找 `updateUI()` 函數（約在第 1030 行），在其末尾添加函數呼叫，並在下方宣告提示點計算邏輯：**

```javascript
        if (restoreBtn) {
          if (currentRound === 1) {
            restoreBtn.innerHTML = `
              <path d="M4 4h16v16H4V4zm2 4v10h12V8H6z" fill="#333" />
              <path d="M12 9.5 v5 M10.5 10.5 l1.5 -1" stroke="#333" stroke-width="1.5" fill="none" stroke-linecap="round" transform="translate(0.5,1)"/>
            `;
          } else {
            restoreBtn.innerHTML = `
              <path d="M4 4h16v16H4V4zm2 4v10h12V8H6z" fill="#333" />
              <path d="M9.5 10.5 c0 -1.5 4 -1.5 4 0 c0 1.5 -4 2 -4 4 h4" stroke="#333" stroke-width="1.5" fill="none" stroke-linecap="round" stroke-linejoin="round" transform="translate(0.5,1)"/>
            `;
          }
        }
      } // 這裡原本是 updateUI() 結束的地方

```

**將上述結尾替換為：**

```javascript
        if (restoreBtn) {
          if (currentRound === 1) {
            restoreBtn.innerHTML = `
              <path d="M4 4h16v16H4V4zm2 4v10h12V8H6z" fill="#333" />
              <path d="M12 9.5 v5 M10.5 10.5 l1.5 -1" stroke="#333" stroke-width="1.5" fill="none" stroke-linecap="round" transform="translate(0.5,1)"/>
            `;
          } else {
            restoreBtn.innerHTML = `
              <path d="M4 4h16v16H4V4zm2 4v10h12V8H6z" fill="#333" />
              <path d="M9.5 10.5 c0 -1.5 4 -1.5 4 0 c0 1.5 -4 2 -4 4 h4" stroke="#333" stroke-width="1.5" fill="none" stroke-linecap="round" stroke-linejoin="round" transform="translate(0.5,1)"/>
            `;
          }
        }

        updateLastMoveIndicator(); // 觸發更新最後一步提示
      }

      function updateLastMoveIndicator() {
        let dropG = document.getElementById('etanidrop');
        if (!dropG) return;
        let indicator = document.getElementById('last-move-indicator');
        
        if (!indicator) {
          indicator = document.createElementNS('http://www.w3.org/2000/svg', 'circle');
          indicator.setAttribute('id', 'last-move-indicator');
          indicator.setAttribute('r', '3');
          indicator.setAttribute('fill', 'white');
          indicator.setAttribute('pointer-events', 'none');
        }
        
        let roundStart = currentRound === 2 ? 36 : 0;
        if (historyIndex >= roundStart && moveHistory[historyIndex]) {
          let m = moveHistory[historyIndex];
          let halfWidth = 31.1769;
          
          let getCenter = (t) => {
            let isRight = gameLogic.isRight(t.idx, t.N);
            let cx = isRight ? (t.idx - 1) * halfWidth + 10.392 : (t.idx - 1) * halfWidth + 20.784;
            let cy = t.N * 18;
            return {cx, cy};
          };
          
          let c1 = m.t1.cx !== undefined ? m.t1 : getCenter(m.t1);
          let c2 = m.t2.cx !== undefined ? m.t2 : getCenter(m.t2);
          let midX = (c1.cx + c2.cx) / 2;
          let midY = (c1.cy + c2.cy) / 2;
          
          indicator.setAttribute('cx', midX.toFixed(3));
          indicator.setAttribute('cy', midY.toFixed(3));
          indicator.style.display = 'block';
          dropG.appendChild(indicator); // 保證附加在最後節點，不被棋子蓋住
        } else {
          if (indicator.parentNode) indicator.parentNode.removeChild(indicator);
        }
      }

```

代码： 全选

這份《三菱棋》的代碼寫得相當用心！你同時實作了 **MCTS（蒙地卡羅樹搜尋）** 作為主要決策引擎，並在殘局階段無縫切換到 **Iterative Deepening Minimax（迭代加深 Alpha-Beta 剪枝）**，這是一個非常經典且強大的架構，能有效兼顧中局的廣泛搜尋與殘局的絕對精準。

針對你的問題，我們分兩部分來探討：MCTS 能否走出「先防守後反擊」的策略，以及如何進一步剪枝與提升 AI 實力。

---

### 一、 MCTS 能否走出「先阻止對方得分，再使己方得分」的下法？

**簡短回答：理論上可以，但以目前的代碼邏輯來看，機率偏低且極度依賴算力與運氣。**

**詳細解析：**
MCTS 的決策依賴兩部分：**樹的展開（Tree Policy）** 與 **模擬/ rollout（Default Policy）**。

1. **在你的 Rollout（啟發式模擬）中：**
目前的邏輯是 **「貪婪（Greedy）」** 的深度 1 搜尋：
* 優先看「我這步能不能得分？」能就下。
* 如果不能，看「對手下步能不能得分？」能就擋。
* 這意味著模擬階段**完全沒有「佈局」的概念**。它不會為兩三步後的得分做打算。


2. **在你的 Tree 展開中：**
「先防守，再得分」這是一個至少需要 2 到 3 步（Ply）的連續邏輯。MCTS 要發現這條路徑，必須在隨機展開中「剛好」走過這個分支足夠多次，發現其勝率（Wins）或優勢（Advantage）很高，才會提高它的 UCB 值。
由於《三菱棋》的合法步數（Branching Factor）在中局非常龐大（因為要考慮不同顏色的棋子和大量的空位組合），如果完全依賴 UCB1 隨機展開，要剛好連續踩中這條「神之一手」路徑的機率很低。

---

### 二、 提升 AI 實力與剪枝建議

要讓 AI 變強且減少算力浪費，核心思路是：**縮小搜尋空間（剪枝）** 與 **給予 AI 更好的「直覺」（啟發）**。

#### 1. 導入 Zobrist Hashing（置換表 / 狀態快取）

* **現狀：** MCTS 展開樹時，不同的下棋順序（例如先下 A 再下 B，與先下 B 再下 A）在你的代碼中會產生完全不同的節點，導致大量重複計算。
* **建議：** 實作 Zobrist Hashing，為每個盤面產生一個唯一的 64-bit Hash。在 MCTS 中共用相同 Hash 的節點數據（Visits 和 Wins）。這樣可以大幅收斂樹的寬度，節省巨大的記憶體與運算力。

#### 2. RAVE (Rapid Action Value Estimation) 演算法

* **建議：** 這是提升棋盤類 MCTS 最有效的技術之一。在 Rollout 結束更新勝率時，不僅更新走過的這條路徑，還將這次模擬中所有出現過的著法（不論是誰下的），都給予一個 RAVE 更新。
* **效果：** RAVE 認為「在模擬中表現好的棋，提早在真實決策中下出來通常也不錯」。這能讓 AI 在展開初期極快地找到重點著法，避免盲目展開。

#### 3. 改善 Expansion（節點展開）的品質

* **現狀：** `let moveIdx = Math.floor(Math.random() * node.unexpanded.length);` 目前是完全隨機挑選未展開的步。
* **建議：** 加入 **Progressive Bias（漸進式偏差）**。在生成合法步時，利用一個非常輕量的評估函數（例如：是否靠近現有棋子群？是否形成特定形狀？）給每個合法步一個初始分數。展開時，優先展開初始分數高的步，甚至直接捨棄（剪枝）分數極低的無意義步（例如下在遙遠邊界且不相連的步）。

#### 4. Minimax 階段的進階剪枝

雖然你實作了 Iterative Deepening 並利用上一層的最佳步來優化排序（這很棒），但你還可以加入：

* **歷史啟發（History Heuristic）：** 記錄在 Alpha-Beta 剪枝中引發截斷（Cut-off）次數最多的著法，在同深度的其他分支中優先嘗試這些著法。
* **殺手啟發（Killer Heuristic）：** 在同一深度中，優先嘗試上一分支成功產生剪枝的步。這能讓 Alpha-Beta 剪枝的效率逼近理論極限。

#### 5. 增量式分數計算 (Incremental Evaluation)

* **現狀：** 每次 `calculateScores()` 都會遍歷所有的藍色棋子並進行遞迴計算。在每秒數千次的 MCTS 模擬中，這是極大的效能瓶頸。
* **建議：** 改為「增量更新」。因為每次落子只會影響局部的分數，你只需要計算剛落下的棋子對周圍連線造成的變化量（Delta），然後加減到當前總分上即可。省下的運算力能讓你的 MCTS 模擬次數翻倍。

---

這幾個方向中，**增量式分數計算**能最直接提升每秒模擬次數，而 **RAVE** 與 **Zobrist Hashing** 則能大幅提升 AI 的「棋力」與「智商」。

你目前最想先解決的是搜尋速度的效能瓶頸，還是 AI 在戰略佈局上的短視問題呢？

代码： 全选

改進：
一，在game-over-screen要顯示「第幾輪」

由於遊戲可能是處於第一輪或第二輪，因此在一局遊戲沒有結束時，打開game-over-screen，要顯示「當前處於第幾輪」。

二，思考完畢要顯示總搜尋次數

當AI思考完畢後，在消息框顯示的是用時和勝率，現在還要加上「搜尋次數」。

三，更改點選棋子時的css

當點選棋子時，其會變大。現在去掉變大的效果，其它效果（如加黑邊）保持不變。

四，給出最後一步落子提示

當有棋子落子後，在.etdrop的最後應加上一個svg-circle元素，其x,y的值等於最後一個棋子的兩個三角形中心的連線中點，半徑為3，fill為白色，stroke為none。

五，調整工具欄的功能和位置

把debug-btn的id改為stop-ai-btn，title="中止AI思考"。當點擊時的功能改為，AI將停止思考，並把所有AI都切換為「人類」（功能在undo和redo中已寫有，可以直接用）。

把工具欄的button順序更改為：自動旋轉，AI設置，中止AI思考，後退，前進，導出/導入，下載棋盤，遊戲狀態。

需要明確給出所要修改的地方和所要替換的代碼。

代码： 全选

這就為你提供這五項功能改進的修改指南。請依照下列區塊，在你的程式碼中找到對應的部分並進行替換或新增。

### 一、在 game-over-screen 顯示「第幾輪」

找到 `function showGameStatus()` 函數，並修改標題的賦值：

**原代碼：**

```javascript
title.innerText = '遊戲狀態';

```

**替換為：**

```javascript
title.innerText = '遊戲狀態 (Round ' + currentRound + ')';

```

---

### 二、思考完畢顯示總搜尋次數

找到 `async function triggerAITurn()` 函數中，處理 MCTS 思考完成的這兩行代碼（約在檔案最後面）：

**原代碼：**

```javascript
let winRate = (((bestChild.wins / bestChild.visits + 1) / 2) * 100).toFixed(1);
box.innerText = `思考完成: ${finalTime}s\n當前勝率: ${winRate}%`;

```

**替換為：**

```javascript
let winRate = (((bestChild.wins / bestChild.visits + 1) / 2) * 100).toFixed(1);
box.innerText = `思考完成: ${finalTime}s\n搜尋次數: ${iterations}\n當前勝率: ${winRate}%`;

```

---

### 三、移除點選棋子時的放大效果

在 `<style>` 區塊中找到 `.piece-box.selected` 的 CSS 設定，並刪除 `transform: scale(1.1);`。

**原代碼：**

```css
.piece-box.selected {
  border-color: #333;
  border-width: 3px;
  box-shadow: 0 0 15px rgba(0, 0, 0, 0.4);
  transform: scale(1.1);
}

```

**替換為：**

```css
.piece-box.selected {
  border-color: #333;
  border-width: 3px;
  box-shadow: 0 0 15px rgba(0, 0, 0, 0.4);
}

```

---

### 四、給出最後一步落子提示

為了確保在重繪、悔棋、前進等操作中，標記都能正確顯示在最後一步，我們建立一個獨立函式，並在每次更新介面時自動呼叫。

**1. 新增繪製函數：**
請將這段代碼放在 `function updateUI()` 的上方（或 `script` 區塊的任意全域位置）。

```javascript
function updateLastMoveIndicator() {
  let existing = document.getElementById('last-move-indicator');
  if (existing) existing.remove();

  let roundStart = currentRound === 2 ? 36 : 0;
  if (historyIndex >= roundStart && moveHistory[historyIndex]) {
    let lastMove = moveHistory[historyIndex];
    const circle = document.createElementNS('http://www.w3.org/2000/svg', 'circle');
    circle.setAttribute('id', 'last-move-indicator');
    circle.setAttribute('cx', lastMove.px.toFixed(3));
    circle.setAttribute('cy', lastMove.py.toFixed(3));
    circle.setAttribute('r', '3');
    circle.setAttribute('fill', 'white');
    circle.setAttribute('stroke', 'none');
    circle.setAttribute('style', 'pointer-events: none;'); // 防止干擾點擊事件
    document.getElementById('etanidrop').appendChild(circle);
  }
}

```

**2. 綁定到 UI 更新中：**
找到 `function updateUI()` 函數的**最末端**，在結尾加上對該函數的呼叫：

```javascript
function updateUI() {
  // ... (保留原本的代碼) ...

  // 在函數的最底部加上這行
  updateLastMoveIndicator();
}

```

---

### 五、調整工具欄的功能和順序

找到 `<div id="floating-tools">` 開頭到 `</div>` 結尾的完整 HTML 區塊，並將其替換為下列代碼。這會同時完成按鈕順序的調換，以及把原先的 Debug 按鈕改造成「中止AI思考」。

**原代碼區塊替換為：**

```html
<div id="floating-tools">
  <svg id="auto-rotate-btn" class="tool-btn" onclick="toggleAutoRotate()" viewBox="0 0 24 24" title="自動旋轉">
    <path d="M12 4V1L8 5l4 4V6c3.31 0 6 2.69 6 6 0 1.01-.25 1.97-.7 2.8l1.46 1.46C19.54 15.03 20 13.57 20 12c0-4.42-3.58-8-8-8zm0 14c-3.31 0-6-2.69-6-6 0-1.01.25-1.97.7-2.8L5.24 7.74C4.46 8.97 4 10.43 4 12c0 4.42 3.58 8 8 8v3l4-4-4-4v3z" fill="#333" />
  </svg>
  <svg class="tool-btn" onclick="openAISettings()" viewBox="0 0 24 24" title="AI 設置">
    <path d="M9 21c0 .55.45 1 1 1h4c.55 0 1-.45 1-1v-1H9v1zm3-19C8.14 2 5 5.14 5 9c0 2.38 1.19 4.47 3 5.74V17c0 .55.45 1 1 1h6c.55 0 1-.45 1-1v-2.26c1.81-1.27 3-3.36 3-5.74 0-3.86-3.14-7-7-7zm2.85 11.1l-.85.6V16h-4v-2.3l-.85-.6C7.8 12.16 7 10.63 7 9c0-2.76 2.24-5 5-5s5 2.24 5 5c0 1.63-.8 3.16-2.15 4.1z" fill="#333" />
  </svg>
  <svg class="tool-btn" id="stop-ai-btn" onclick="forceHumanPlayer()" viewBox="0 0 24 24" title="中止AI思考">
    <path d="M12 2C6.48 2 2 6.48 2 12s4.48 10 10 10 10-4.48 10-10S17.52 2 12 2zm1 15h-2v-2h2v2zm0-4h-2V7h2v6z" fill="#333" />
  </svg>
  <svg class="tool-btn tool-btn-undo" onclick="undoMove()" viewBox="0 0 24 24" title="後退">
    <path d="M12.5 8c-2.65 0-5.05.99-6.9 2.6L2 7v9h9l-3.62-3.62c1.39-1.16 3.16-1.88 5.12-1.88 3.54 0 6.55 2.31 7.6 5.5l2.37-.78C21.08 11.03 17.15 8 12.5 8z" fill="#333" />
  </svg>
  <svg class="tool-btn tool-btn-redo" onclick="redoMove()" viewBox="0 0 24 24" title="前進">
    <path d="M11.5 8C16.15 8 20.08 11.03 21.43 15.22l-2.37.78c-1.05-3.19-4.06-5.5-7.6-5.5-1.95 0-3.73.72-5.12 1.88L10 16H1V7l3.6 3.6C6.45 8.99 8.85 8 11.5 8z" fill="#333" />
  </svg>
  <svg class="tool-btn" onclick="openExportModal()" viewBox="0 0 24 24" title="導出/導入">
    <path d="M14 2H6c-1.1 0-1.99.9-1.99 2L4 20c0 1.1.89 2 1.99 2H18c1.1 0 2-.9 2-2V8l-6-6zm2 16H8v-2h8v2zm0-4H8v-2h8v2zm-3-5V3.5L18.5 9H13z" fill="#333" />
  </svg>
  <svg class="tool-btn" onclick="downloadBoardSVG()" viewBox="0 0 24 24" title="下載棋盤">
    <path d="M19 9h-4V3H9v6H5l7 7 7-7zM5 18v2h14v-2H5z" fill="#333" />
  </svg>
  <svg class="tool-btn" id="restore-go-btn" onclick="showGameStatus()" viewBox="0 0 24 24" title="遊戲狀態">
    <path d="M4 4h16v16H4V4zm2 4v10h12V8H6z" fill="#333" />
  </svg>
</div>

```