[{"data":1,"prerenderedAt":535},["ShallowReactive",2],{"post-zh-poker-combinations-explained":3},{"item":4},{"id":5,"title":6,"body":7,"description":496,"extension":497,"meta":498,"navigation":530,"path":531,"seo":532,"stem":533,"__hash__":534},"content/zh/blog/poker-combinations-explained.md","德州组合数：把“可能有”算清楚",{"type":8,"value":9,"toc":484},"minimark",[10,14,17,23,26,29,37,42,45,48,51,56,59,74,78,83,86,92,95,101,106,113,118,121,130,136,139,143,146,151,179,182,187,193,199,205,209,212,233,239,242,260,263,268,271,275,278,309,312,317,329,332,344,348,351,358,363,366,371,374,380,387,390,397,401,406,409,414,423,428,431,437,441,444,464,470,473,479],[11,12,13],"p",{},"“他可能有 AA，也可能有 KK，还可能拿 AQ 诈唬。”",[11,15,16],{},"听起来是三个选项。于是有人顺手一除：我只赢 AQ，那不就是三分之一吗？",[11,18,19],{},[20,21,22],"strong",{},"不一定。三个牌名，不代表三份相同的概率。",[11,24,25],{},"“AA”里面可能装着六种具体底牌，“AQ”里面可能装着十几种。更关键的是，对手未必会拿每一种牌，以相同的频率走到这里、选择下注。",[11,27,28],{},"组合数，就是把这些模糊的“可能有”，拆成可以核对的具体手牌。",[30,31,32],"blockquote",{},[11,33,34],{},[20,35,36],{},"先数牌，再看他会怎么打；最后，才轮到底池给你的价格。",[38,39,41],"h2",{"id":40},"一组合不是牌名而是两张具体的牌","一、组合不是牌名，而是两张具体的牌",[11,43,44],{},"AA 是一个起手牌类别。A♠ A♥ 是一个具体组合，A♦ A♣ 则是另一个。",[11,46,47],{},"拿到的顺序不重要：A♠ A♥ 和 A♥ A♠，算同一组。",[11,49,50],{},"一副标准的 52 张牌，任选两张、不重复计顺序，一共是：",[11,52,53],{},[20,54,55],{},"52 × 51 ÷ 2 = 1326 个起手牌组合。",[11,57,58],{},"你常见的 169 格起手牌表，是把这些组合归成 169 类，而不是说每一格出现的机会都一样。",[11,60,61,62,65,66,73],{},"入门先记四个数：",[20,63,64],{},"每种口袋对子 6 组；固定两个不同点数，同花 4 组，非同花 12 组，合计 16 组。"," 这些是没有相关已知牌时的基础数量。",[67,68,72],"a",{"href":69,"rel":70},"https://pokercoaching.com/blog/wp-content/uploads/2025/10/Poker-Combinations-PDF-Guide.pdf",[71],"nofollow","PokerCoaching 组合数速查","也采用这一组基础数字。",[38,75,77],{"id":76},"二641216究竟怎么来的","二、6、4、12、16，究竟怎么来的？",[11,79,80],{},[20,81,82],{},"对子：AA 为什么是 6 组？",[11,84,85],{},"四张 A，两两配对，只有下面六种：",[87,88],"article-illustration",{"alt":89,"caption":90,"src":91},"AA 的六种组合：黑桃红桃、黑桃方块、黑桃梅花、红桃方块、红桃梅花、方块梅花","这是六种可能的底牌，不是同一副牌里同时发出的六手牌。交换两张牌的顺序，不增加新组合。","/images/poker-combinations/six-ace-pairs.webp",[11,93,94],{},"先选一张有 4 种，第二张剩 3 种，得到 4 × 3 = 12；但每一对都被前后颠倒数了两次，所以：",[11,96,97,100],{},[20,98,99],{},"4 × 3 ÷ 2 = 6。"," KK、QQ 等口袋对子同理。",[11,102,103],{},[20,104,105],{},"同花牌：AKs 为什么是 4 组？",[11,107,108,109,112],{},"只有 A♠ K♠、A♥ K♥、A♦ K♦、A♣ K♣，每种花色一组，共 4 组。这里的 ",[20,110,111],{},"s 是 suited，意思是同花色","。",[11,114,115],{},[20,116,117],{},"非同花牌：AKo 为什么是 12 组？",[11,119,120],{},"每张 A 可以搭配三张不同花色的 K。例如 A♠ 可以配 K♥、K♦、K♣。四张 A 各有三种选择：",[11,122,123,126,127,112],{},[20,124,125],{},"4 × 3 = 12。"," 这里的 ",[20,128,129],{},"o 是 offsuit，意思是不同花色",[11,131,132,133],{},"如果只写 AK，不限制花色，每张 A 都能配四张 K：",[20,134,135],{},"4 × 4 = 16，也就是 4 组 AKs 加 12 组 AKo。",[11,137,138],{},"这里不用除以 2，因为我们固定先选 A、再选 K，没有把 K 配 A 重新算一遍。",[38,140,142],{"id":141},"三看见一张牌就要重新数","三、看见一张牌，就要重新数",[11,144,145],{},"你手里的牌、公共牌，以及其他确实已知且不可能在对手手里的牌，都要从可用牌中扣掉。这就是阻断牌（Blocker）的起点。",[11,147,148],{},[20,149,150],{},"对子，看同一点数还剩几张。",[152,153,154,161,167,173],"ul",{},[155,156,157,158,112],"li",{},"剩 4 张：4 × 3 ÷ 2 = ",[20,159,160],{},"6 组",[155,162,163,164,112],{},"剩 3 张：3 × 2 ÷ 2 = ",[20,165,166],{},"3 组",[155,168,169,170,112],{},"剩 2 张：2 × 1 ÷ 2 = ",[20,171,172],{},"1 组",[155,174,175,176,112],{},"只剩 1 张或没有：",[20,177,178],{},"0 组",[11,180,181],{},"例如牌面已经有 K♠ K♥，对手的 KK 只剩 K♦ K♣ 这一组，不再是六组。",[11,183,184],{},[20,185,186],{},"不同点数、不限花色，用剩余数量相乘。",[11,188,189,190,112],{},"假设已知 A♠ 和 K♥ 不在对手手里，A、K 各剩三张，AK 就是 ",[20,191,192],{},"3 × 3 = 9 组",[11,194,195,196,112],{},"但 AKs 不能随便拿 9 除以 4。黑桃缺 A，红桃缺 K，只有 A♦ K♦、A♣ K♣ 两组同花。于是 AKo 是 ",[20,197,198],{},"9 − 2 = 7 组",[11,200,201,204],{},[20,202,203],{},"算同花，要逐个花色看两张牌是否都还可用。"," 同时别重复相加：AK 已经包括 AKs 和 AKo，不能把 16 组 AK 再加上 4 组 AKs。",[38,206,208],{"id":207},"四把aakkaq算成一个范围","四、把“AA、KK、AQ”算成一个范围",[11,210,211],{},"用一个简化的河牌教学例子，不是真人牌谱：",[152,213,214,220,226],{},[155,215,216,217,112],{},"你的手牌：",[20,218,219],{},"Q♥ J♥",[155,221,222,223,112],{},"公共牌：",[20,224,225],{},"J♣ 9♦ 6♠ 3♥ 2♣",[155,227,228,229,232],{},"暂时假设对手只会拿 ",[20,230,231],{},"AA、KK、AQ"," 下注，AQ 包括同花与非同花。",[11,234,235,236,112],{},"这是为了练计算而设定的范围，",[20,237,238],{},"不是说现实对手一定只有这三类牌",[11,240,241],{},"你的一对 J 输给 AA、KK，赢过 AQ 的 A 高牌。现在逐类数：",[152,243,244,249,254],{},[155,245,246,247,112],{},"AA：没有 A 被已知牌占用，",[20,248,160],{},[155,250,251,252,112],{},"KK：没有 K 被已知牌占用，",[20,253,160],{},[155,255,256,257,112],{},"AQ：A 有 4 张，Q♥ 在你手里，Q 只剩 3 张，",[20,258,259],{},"4 × 3 = 12 组",[11,261,262],{},"假设这些组合到达当前节点、选择这次下注的权重都相同：",[11,264,265],{},[20,266,267],{},"你赢的 12 组 ÷ 总计的（6 + 6 + 12）组 = 12 ÷ 24 = 50%。",[11,269,270],{},"不是因为三种牌里你赢一种，就只有三分之一。你要数的，是牌名背后的组合。",[38,272,274],{"id":273},"五50-能不能跟还要把价格算出来","五、50% 能不能跟？还要把价格算出来",[11,276,277],{},"继续这个例子。假设河牌是单挑，无抽水、无平局，不考虑加注，只比较跟注和弃牌。数字均为演示积分：",[279,280,281,287,294,303],"ol",{},[155,282,283,284,112],{},"对手下注前，底池有 ",[20,285,286],{},"100",[155,288,289,290,293],{},"对手下注 ",[20,291,292],{},"200","，也就是两倍底池。",[155,295,296,297,300,301,112],{},"现在底池有 ",[20,298,299],{},"100 + 200 = 300","，你需要补 ",[20,302,292],{},[155,304,305,306,112],{},"跟注后最终底池为 ",[20,307,308],{},"300 + 200 = 500",[11,310,311],{},"你投入 200，参与争夺最终的 500，最低权益门槛就是下面这个比例。本例没有平局，权益就等于获胜概率：",[11,313,314],{},[20,315,316],{},"200 ÷ 500 = 0.4 = 40%。",[11,318,319,320,323,324,328],{},"如果写成底池赔率，是 200 : 300 = 2 : 3。换成百分比必须算 ",[20,321,322],{},"2 ÷（2 + 3）","，不是 2 ÷ 3。",[67,325,327],{"href":326},"/zh/pot-odds-calculation-complete-guide","底池赔率完整推导","在这里。",[11,330,331],{},"在上述等权范围假设成立时，50% 高于 40%，跟注的筹码期望值为正。也可以从结果核验：跟赢，相对现在弃牌净增加 300；跟输，净减少 200。",[11,333,334,337,338,343],{},[20,335,336],{},"跟注 EV = 50% × 300 − 50% × 200 = +50。"," EV 是期望值，不是下一手会得到的结果。",[67,339,342],{"href":340,"rel":341},"https://blog.gtowizard.com/how-to-solve-toy-games/",[71],"GTO Wizard 的简化河牌模型","也用权益、下注范围与价格之间的关系解释这一判断。",[38,345,347],{"id":346},"六同样十二组-aq他真的都会下注吗","六、同样十二组 AQ，他真的都会下注吗？",[11,349,350],{},"现在只改一个假设：AA、KK 都会走到这个节点并下注，但 AQ 只有一半会这样做。为便于比较，其他到达条件保持相同。",[11,352,353,354,357],{},"AQ 在物理上仍有十二组，但在这个下注范围里，它的",[20,355,356],{},"加权组合数","变成：",[11,359,360],{},[20,361,362],{},"12 × 50% = 6。",[11,364,365],{},"于是你赢的权重是 6，总权重是 6 + 6 + 6 = 18：",[11,367,368],{},[20,369,370],{},"6 ÷ 18 = 1/3，约 33.3%。",[11,372,373],{},"价格仍要求 40%。在这个新假设下，跟注 EV 变为：",[11,375,376,379],{},[20,377,378],{},"1/3 × 300 − 2/3 × 200 ≈ −33.3。"," 此时弃牌优于跟注。",[11,381,382,383,386],{},"牌面没变，你的手牌没变，为什么结论反了？因为你面对的是",[20,384,385],{},"对手实际选择下注的范围","，不是所有物理上可能发给他的牌。",[11,388,389],{},"“加权组合数 = 可用组合数 × 相关行动频率”是速算表达。真实分析还要考虑前面各条街的到达频率，而且同一类牌的不同花色组合，未必采用同一种打法。出现小数权重，也不是说真的有“半手牌”。",[30,391,392],{},[11,393,394],{},[20,395,396],{},"组合数决定有多少种可能，行动频率决定这些可能占多大分量。",[38,398,400],{"id":399},"七组合数怎样改变跟注诈唬和价值下注","七、组合数怎样改变跟注、诈唬和价值下注？",[11,402,403],{},[20,404,405],{},"跟注：别只数“能赢我的牌”。",[11,407,408],{},"也要数你能赢的牌，并判断它们是否真的会下注。例子里的 Q♥ 减少了 AQ：如果 AQ 在这个模型中充当诈唬，你阻断的恰恰是自己希望看到的那部分范围。",[11,410,411],{},[20,412,413],{},"诈唬：挡住强牌，不等于自动适合下注。",[11,415,416,417,422],{},"还要看你有没有同时挡住对手本来会弃掉的牌，以及这个人到底会不会弃牌。GTO Wizard 对",[67,418,421],{"href":419,"rel":420},"https://blog.gtowizard.com/blockers-unblockers-the-secret-to-picking-great-bluffs/",[71],"阻断与不阻断的分析","强调的，正是这两个方向要一起看。",[11,424,425],{},[20,426,427],{},"价值下注：想清楚更差的牌还能有多少。",[11,429,430],{},"如果你拿走的点数，恰好大量存在于对手会跟注的更差手牌里，那么“他应该有很多牌接我”的直觉就值得重算。反过来，也别只盯着少数击败你的组合，忘了更差的跟注范围。",[11,432,433,434],{},"这些都不是自动操作指令。",[20,435,436],{},"阻断牌是修正范围的证据，不是“必须跟”或“必须诈唬”的通行证。",[38,438,440],{"id":439},"八算得准还得承认哪些是自己猜的","八、算得准，还得承认哪些是自己猜的",[11,442,443],{},"最后守住三个区别：",[152,445,446,452,458],{},[155,447,448,451],{},[20,449,450],{},"组合数不是补牌数。"," Combos 数的是可能的底牌；Outs 数的是后续能让你形成获胜牌的补牌。只让牌型变好、却仍然落后的牌，不能直接算作有效补牌。",[155,453,454,457],{},[20,455,456],{},"组合比例不总是摊牌权益。"," 上面的胜率算法适用于已到河牌、每个组合的胜负明确且无平局的简化例子。翻牌、转牌还要考虑后续发牌；单挑有平局时，还要计入平分底池的份额。",[155,459,460,463],{},[20,461,462],{},"算术准确，不等于范围准确。"," 如果对手还有其他价值牌，或者几乎从不拿 AQ 诈唬，算得再工整也不能挽救错误假设。锦标赛临近奖励、多人或边池场景，也不能直接套用这套单挑筹码 EV 判断。",[11,465,466,467],{},"可以按这个顺序做一次牌后练习：",[20,468,469],{},"列范围 → 扣已知牌 → 数组合 → 给行动权重 → 比较价格。",[11,471,472],{},"挑一手牌，分别给诈唬组合设一个保守权重和一个较高权重。若两种假设就能让跟注结论翻转，下一步最该补的，可能是对手的行为证据，而不是更多小数位。",[474,475,476],"review-principles",{},[11,477,478],{},"用组合与价格建立结构，用真实行动校准范围，再觉察自己有没有因为害怕而只数强牌，或因为不服而把每张弱牌都算成诈唬。AI 可以帮助核对，不能替缺失的证据盖章。",[11,480,481],{},[20,482,483],{},"组合数不是让你猜得更坚定，而是让每一个“他可能有”，都能被具体检查。",{"title":485,"searchDepth":486,"depth":486,"links":487},"",2,[488,489,490,491,492,493,494,495],{"id":40,"depth":486,"text":41},{"id":76,"depth":486,"text":77},{"id":141,"depth":486,"text":142},{"id":207,"depth":486,"text":208},{"id":273,"depth":486,"text":274},{"id":346,"depth":486,"text":347},{"id":399,"depth":486,"text":400},{"id":439,"depth":486,"text":440},"AA 为什么有 6 组，AK 为什么有 16 组？用一手 QJ 河牌示例，逐步算清阻断牌、范围权重、40% 跟注门槛，以及组合数怎样影响跟注、诈唬和价值下注。","md",{"subtitle":499,"keywords":500,"createdDate":501,"updatedDate":501,"coverImage":502,"ogImage":502,"alt":503,"tags":504,"categories":510,"author":514,"relates":518},"从 6、4、12、16，到阻断牌、范围权重与河牌跟注。","德州组合数,扑克组合数,Combos,阻断牌,Blocker,范围权重,河牌跟注,底池赔率,德州扑克入门","2026/10/24","/images/poker-combinations/cover.webp","原创卡通插画：成年扑克爱好者观察四张不同花色的 A，旁边用六对圆点记录可能的对子组合",[505,506,507,508,509],"组合数","范围思维","阻断牌","底池赔率","决策训练",[511,512,513],"基础概念","扑克数学","策略学习",{"name":515,"avatar":516,"description":517},"ZenPoker 教练团队","/avatars/2.png","用具体牌例和可核验的计算，帮助扑克爱好者理解决策。",[519,522,526],{"title":520,"href":326,"image":521},"底池赔率计算完全指南","/images/pot-odds-guide.png",{"title":523,"href":524,"image":525},"你在读牌，还是在害怕？","/zh/reading-the-hand-or-feeling-the-fear","/images/reading-the-hand-or-feeling-the-fear.webp",{"title":527,"href":528,"image":529},"有牌，反而不敢打？","/zh/afraid-to-value-bet","/images/afraid-to-value-bet.webp",true,"/zh/blog/poker-combinations-explained",{"title":6,"description":496},"zh/blog/poker-combinations-explained","J1nzH8BQODBYmfpVrnM1P12BZ30XkbF9YupNlRMtHs4",1793031534284]