The Maze Game 讓你可以直接比較兩種解法策略，因為每一次遊玩都使用相同的確定性 9 × 9 佈局，計分公式 1,000 − 10 × accepted steps 是固定的，而且被阻擋的箭頭按鍵從不計入步數總和。若要將兩種策略並列比較，請先執行第一種策略一次並記錄步數計數器上顯示的步數，接著按下 Restart，再執行第二種策略並記錄其步數總和。步數較少者在同一個迷宮中勝出，且因為計分公式會對每一個接受的移動扣十分，分數較低等同於表現較佳。迷宮最短的可能路線為 24 個有效移動，恰好產生 760 分，因此一次乾淨的記憶重玩應該會落在這些數字上，而任何探索性的遊玩結果都會高於它們。因為每次重新開始都會還原完全相同的走廊圖案，這個比較在跨時段是可重現的：你可以在不同日子重複實驗，迷宮幾何配置始終保持一致。
Why the Fixed Layout Makes Comparison Possible
The Maze Game 是一個確定性的 9 × 9 棋盤，這代表每次重新開始時都會出現相同的走廊形狀、牆壁、起點與星星終點。頁面在每一輪開始前也會從起點到終點執行一次廣度優先可達性檢查，因此終點永遠是可達的，且路線永遠是單一相連的走廊。由於幾何配置不會改變，兩種策略之間的比較便具有意義：你不是在比較不同的迷宮，而是在同一個迷宮上比較不同的決策。計分公式同樣是固定的：score = 1,000 − 10 × accepted steps，下限為 0，因此每一步接受的移動無論發生在遊玩中的哪個時刻，都恰好價值十分。
正是這種可重現性，把一個休閒謎題變成了一個小型實驗。你可以今天玩一次、什麼都不做、明天再玩一次，兩次遊玩仍然在比較同一條路線。如果佈局在每次載入時都隨機化，那麼分數或步數上的任何差異都有一部分反映的是新的牆壁，而非策略本身。正因為佈局是固定的，差異反映的是你所做的選擇。
The Two Approaches You Can Compare in Maze Game
大多數在本頁比較策略的讀者會設定兩種對比的策略。第一種是探索遊玩（discovery run）：你從零開始遊玩這個迷宮，將每次按下的方向鍵視為一次探測。你嘗試一個方向、撞牆、再試另一個，有時還會折返，讓走廊隨著一步步的進行逐漸顯現出來。最終的步數與分數反映的是你在實際路線之外額外進行的回溯次數。
第二種策略是記憶或回想遊玩（memory or recall run）：你憑藉第一次嘗試或事先規劃的心理地圖重玩這個迷宮。因為你已經知道死路的位置，所以你會避開它們；你會修正曾經走過頭的轉角，只在暢通的走廊格子上按下方向鍵。一次乾淨的這類遊玩目標是達成迷宮的最短路線，而本頁將其定義為 24 步 accepted steps。
你也可以比較更細分的變體：例如積極試牆的探索方式與緊貼一側牆壁的走廊跟隨方式，或純鍵盤操作與觸控加鍵盤混合操作。不過，對於一次公平的並列比較而言，最乾淨的對比是探索與記憶，因為這兩種策略的差異在於使用了多少資訊，而不是在於輸入是如何送出的。
Run Both Approaches on the Same Board
- Open the Maze Game and let the initial board load. The player dot sits in the upper-left corridor and the star goal sits near the lower-right corner.
- Run your first approach. Press the arrow keys to move the player through open cells, ignore the fact that walls block your input, and finish at the star. The step counter will show every accepted move and the score will update accordingly.
- Note the numbers. Write down the final step count and the final score from this run, or remember them long enough to compare against the second run.
- Select Restart to reset the player, step counter, and score back to their starting values. The board itself is unchanged because the layout is deterministic.
- Run your second approach. Use the same arrow keys, but apply the strategy you want to compare, and reach the star a second time.
- Compare the two step counts. The run with fewer steps wins on the same fixed board, and because the score formula only subtracts ten per accepted step, the run with fewer steps also has the higher score.
Reading the Score, Steps, and Best Result
The score formula is the easiest way to convert a step count into a result you can compare. For a single example, the maze's shortest route is 24 accepted moves, so the formula gives 1,000 − 10 × 24 = 1,000 − 240 = 760 points. A discovery run that takes 32 accepted steps would score 1,000 − 10 × 32 = 680 points, which is 80 points behind a clean 24-step route. Because the score cannot drop below zero, the formula holds for every reachable step total.
The page also keeps a best score in your browser's localStorage under a game-specific key, so once you finish a run that beats your previous high, that becomes the new saved value. The next session starts from that stored best, so a sequence of runs forms a personal record you can use to see whether your memory is improving over time.
Two practical numbers make the comparison concrete:
| Approach | Accepted steps | Score formula | Final score |
|---|---|---|---|
| Discovery run (first attempt) | 32 | 1,000 − 10 × 32 | 680 |
| Memory or recall run (clean) | 24 | 1,000 − 10 × 24 | 760 |
| Long, exploratory path | 40 | 1,000 − 10 × 40 | 600 |
These figures show the direction of the comparison: fewer accepted steps means a higher score, and the gap between a discovery run and a memory run on the same fixed board is exactly the points you spent on backtracking.
When Discovery Beats Memory (and Vice Versa)
Discovery is the better approach on the first play, simply because there is nothing to recall yet. A discovery run is also the only approach that tells you the corridor layout, so it has to come first in any two-approach comparison. After one or two discovery runs, the memory approach becomes the one that measures improvement, because it removes exploration time and isolates the cost of unnecessary moves.
If your goal is to learn the maze layout itself, the discovery approach is the one that produces that information. If your goal is to test how cleanly you can recall a known route, the memory approach is the better measure. Comparing the two on the same board turns the difference between those two goals into a single number: the gap in steps, and therefore the gap in score, between the two runs.
For a related score question that often comes up alongside a comparison, see Do Wall Collisions Lower the Score in Maze Game? The answer there explains why blocked inputs do not change either the step count or the final result, which is the rule that makes this comparison fair in the first place.
Comparison Limits Worth Knowing
A few rules of the maze matter when you read the comparison. Blocked arrow presses do not consume a step or subtract from the score, so the displayed step total only reflects accepted moves through corridor cells. The score also cannot drop below zero, which means a very long run that repeatedly hits walls could still register many accepted steps while the score never goes negative. After you reach the star, the board freezes with the final step count and score visible until you press Restart, so you do not lose the result by accident. Restart itself restores the player, steps, score, completion state, and the deadlock check, but it does not change the board, because the layout is deterministic. The two approaches being compared therefore always face the same walls, the same start point, and the same goal.
If you're weighing options, How to Compare Two Approaches in Math Crossword covers this in detail.