# 為什麼是 37%

Hannah Fry 的《愛情數學》第七章寫到如何應用「最優停止理論（Optimal Stopping）」，決定什麼該「定下來」，確定結婚的對象。如果你一生中打算談 n 次戀愛，或者你打算從25歲到35歲之間盡可能認識更多的人，到了35歲再決定你的他（她），怎麼做可以讓你找到最佳拍檔的機率最高。

If you want the best odds of getting the best apartment, spend 37% of your apartment hunt (eleven days, if you’ve given yourself a month for the search) noncommittally exploring options. Leave the checkbook at home; you’re just calibrating. But after that point, be prepared to immediately commit — deposit and all — to the very first place you see that beats whatever you’ve already seen. This is not merely an intuitively satisfying compromise between looking and leaping. It is the provably optimal solution.

37 這個數字，怎麼算出來的？Hannah Fry 在書裡講的很簡略，告訴我們最優停止理論給了我們一個極為簡潔的公式，用這個公式算出來的數字就是 37%。書末的參考文獻指向一篇1997年出版的論文《Searching for the Next Best Mate》，這篇論文的摘要（abstract）也只是直接說出 37 這個數字，沒有解釋來由。這篇論文的訂價是 24.95 歐元（Oops），直接放棄購買或下載的打算。

…In this paper, we analyze the third approach of mate choice as applicant screening and show through simulation analyses that a traditional optimal solution to this problem-the 37% rude-can be beaten along several dimensions by a class of simple “satisficing” algorithms we call the Take the Next Best mate choice rules. Thus, human mate search behavior should not necessarily be compared to the lofty optimal ideal, but instead may be more usefully studied through the development and analysis of possible “fast and frugal” mental mechanisms.

P 的最佳值在 x=1/e 的時候出現，大約等於 0.3679，四捨五入，就是 37%

Originally published at imrchen.wordpress.com on October 16, 2017.

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