{"id":17862,"date":"2026-08-22T11:16:55","date_gmt":"2026-08-22T01:16:55","guid":{"rendered":"https:\/\/geoffreychen.com\/why-a-shuffled-deck-almost-never-repeats\/"},"modified":"2026-08-22T11:16:55","modified_gmt":"2026-08-22T01:16:55","slug":"why-a-shuffled-deck-almost-never-repeats","status":"publish","type":"post","link":"https:\/\/geoffreychen.com\/zh\/why-a-shuffled-deck-almost-never-repeats\/","title":{"rendered":"\u6d17\u724c\u540e\uff0c\u4e3a\u4ec0\u4e48\u51e0\u4e4e\u4e0d\u4f1a\u518d\u51fa\u73b0\u540c\u4e00\u526f\u987a\u5e8f\uff1f"},"content":{"rendered":"<\/p>\n<p><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/public-assets.geoffreychen.com\/wordpress\/articles\/why-a-shuffled-deck-almost-never-repeats\/c9260b2e882d5aac4919a5a2.jpg?w=1140&#038;ssl=1\" alt=\"\u6d17\u724c\u540e\uff0c\u4e3a\u4ec0\u4e48\u51e0\u4e4e\u4e0d\u4f1a\u518d\u51fa\u73b0\u540c\u4e00\u526f\u987a\u5e8f\uff1f\" loading=\"lazy\"><\/p>\n<p>\u4e00\u526f\u6807\u51c6\u7eb8\u724c\u670952\u5f20\u4e0d\u540c\u7684\u724c\u3002\u6392\u7b2c\u4e00\u5f20\u670952\u79cd\u9009\u62e9\uff0c\u7b2c\u4e8c\u5f20\u526951\u79cd\uff0c\u4f9d\u6b21\u51cf\u5c11\uff0c\u56e0\u6b64\u5168\u90e8\u53ef\u80fd\u987a\u5e8f\u662f52\u00d751\u00d7\u2026\u2026\u00d71\uff0c\u5199\u4f5c52!\u3002\u5b83\u7ea6\u7b49\u4e8e8.07\u00d710^67\uff1a\u8fd9\u4e0d\u662f\u8bf4\u6bcf\u6b21\u6d17\u724c\u90fd\u201c\u521b\u9020\u4e86\u5b87\u5b99\u4e2d\u4ece\u672a\u6709\u8fc7\u7684\u4e1c\u897f\u201d\uff0c\u800c\u662f\u8bf4\u53ef\u9009\u6392\u5217\u591a\u5f97\u8fdc\u8d85\u65e5\u5e38\u76f4\u89c9\u3002<\/p>\n<p>\u9636\u4e58\u589e\u957f\u5feb\uff0c\u662f\u56e0\u4e3a\u6bcf\u589e\u52a0\u4e00\u5f20\u724c\uff0c\u65e7\u6709\u7684\u6bcf\u4e00\u79cd\u6392\u5217\u90fd\u591a\u51fa\u8bb8\u591a\u63d2\u5165\u4f4d\u7f6e\u30025\u5f20\u724c\u53ea\u6709120\u79cd\u987a\u5e8f\uff0c10\u5f20\u5df2\u662f3628800\u79cd\uff1b\u523052\u5f20\u65f6\uff0c\u6570\u91cf\u5c31\u5de8\u5927\u5230\u96be\u4ee5\u9760\u53cd\u590d\u5c1d\u8bd5\u8986\u76d6\u3002\u82e5\u6bcf\u79d2\u68c0\u67e5\u5341\u4ebf\u79cd\u987a\u5e8f\uff0c\u4ece\u5b87\u5b99\u5f62\u6210\u81f3\u4eca\u4e5f\u53ea\u80fd\u68c0\u67e5\u5176\u4e2d\u6781\u5c0f\u7684\u4e00\u90e8\u5206\u3002<\/p>\n<p>\u4e0d\u8fc7\uff0c\u201c\u670952!\u79cd\u53ef\u80fd\u201d\u4e0d\u7b49\u4e8e\u73b0\u5b9e\u6d17\u724c\u4f1a\u7b49\u6982\u7387\u5730\u4ea7\u751f\u6bcf\u4e00\u79cd\u3002\u6d17\u724c\u624b\u6cd5\u3001\u6b21\u6570\u548c\u4eba\u7684\u52a8\u4f5c\u90fd\u4f1a\u9020\u6210\u504f\u5dee\uff1b\u6570\u5b66\u4e0a\u5747\u5300\u968f\u673a\u7684\u6a21\u578b\u662f\u4e00\u79cd\u5047\u8bbe\u3002\u4e2d\u5fc3\u7ed3\u8bba\u5e94\u5f53\u514b\u5236\uff1a\u5728\u8db3\u591f\u63a5\u8fd1\u968f\u673a\u7684\u6d17\u724c\u4e2d\uff0c\u7cbe\u786e\u91cd\u590d\u67d0\u4e2a\u65e2\u5b9a\u987a\u5e8f\u7684\u6982\u7387\u6781\u4f4e\uff1b\u6392\u5217\u6570\u8bf4\u660e\u7684\u662f\u53ef\u80fd\u7a7a\u95f4\uff0c\u800c\u4e0d\u662f\u4fdd\u8bc1\u73b0\u5b9e\u8fc7\u7a0b\u5b8c\u7f8e\u968f\u673a\u3002<\/p>\n<p><a href=\"https:\/\/mathworld.wolfram.com\/Factorial.html\" rel=\"nofollow\">https:\/\/mathworld.wolfram.com\/Factorial.html<\/a><br \/><a href=\"https:\/\/www.ams.org\/books\/mbk\/146\/\" rel=\"nofollow\">https:\/\/www.ams.org\/books\/mbk\/146\/<\/a><\/p>\n<p>","protected":false},"excerpt":{"rendered":"","protected":false},"author":17897162,"featured_media":0,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_geoff_meta_description_en":"Using 52! possible permutations, the article argues that repeating one exact shuffled order is extraordinarily unlikely, since real shuffles may be biased and not uniformly random.","_geoff_meta_description_zh":"\u6587\u7ae0\u752852!\u79cd\u53ef\u80fd\u7684\u6392\u5217\u8bf4\u660e\uff1a\u5728\u8db3\u591f\u63a5\u8fd1\u968f\u673a\u7684\u6d17\u724c\u4e2d\uff0c\u7cbe\u786e\u91cd\u590d\u67d0\u4e2a\u65e2\u5b9a\u987a\u5e8f\u7684\u6982\u7387\u6781\u4f4e\uff0c\u4f46\u73b0\u5b9e\u6d17\u724c\u4e0d\u4e00\u5b9a\u7b49\u6982\u7387\u5730\u4ea7\u751f\u5404\u6392\u5217\u3002","_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[787297218],"tags":[787297288,787297289,787297710,787297709],"class_list":["post-17862","post","type-post","status-publish","format-standard","hentry","category-daily-maths-physics-chemistry","tag-combinatorics","tag-combinatorics-zh","tag-permutations","tag-permutations-zh",""],"translatepress_titles":{"en_AU":"Why Does a Shuffled Deck Almost Never Repeat an Order?","zh_CN":"\u6d17\u724c\u540e\uff0c\u4e3a\u4ec0\u4e48\u51e0\u4e4e\u4e0d\u4f1a\u518d\u51fa\u73b0\u540c\u4e00\u526f\u987a\u5e8f\uff1f"},"jetpack_publicize_connections":[],"jetpack_likes_enabled":false,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1ar9H-4E6","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts\/17862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/users\/17897162"}],"replies":[{"embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/comments?post=17862"}],"version-history":[{"count":0,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts\/17862\/revisions"}],"wp:attachment":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/media?parent=17862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/categories?post=17862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/tags?post=17862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}