斗地主，出现王炸的概率是多少？
按时间排序
想知道为什么地主多拿牌会减少王炸出现的概率
为方便理解，首先将一副牌按1~54编号，假设地主先拿（其实谁先都一样）拿牌情况如下：地主 农民 农民
54地主20张牌，出现王炸概率是：P1=（20/54）*（19/53）两个农民各17张，出现王炸概率是：P2=（17/54）*（16/53）*2所以王炸概率P=P1+P2=924/85
你们都弱爆了。大一时候数学分析上Matlab的大作业，那时候英语渣渣，但是本答案考虑了场上的每个人持牌情况，可以根据情况算出别人手上有炸弹的概率。算自己手上有炸弹毛用啊：The Probability About If There Is A BombEvery time when the Spring Festival comes,we Chinese persons would stop busy working to enjoy eating,drinking,relaxing,and playing holiday.As for me,like every teenager,I always sit before my computer during the dull-dry and stay-at-home time.Due to my parents wouldn’t be happy to see me playing games,I had to do other things but staring at any screens.So I focused on the way of entertainment which belongs to my elder generation.It’s very simple--Fight the Landlord,a kind of Chinese Poker.As we know,the key of this game is figuring out what kind of cards they left,either u r a Farmer or the Landlord.Maybe we can remember how many jokers,twos,or Aces hasn’t be shown.But anther point--the most important thing is inferring whether the others have the bomb.When my father was facing this problem,I think maybe a can give him some professionally suggestions.Ok,stop joking.Let’s do this.In the beginning,the Farmers has 17 cards while the Landlord has 21.If one of the F Find there’s a number he lack,maybe there’s a bomb in others’ hand.I make P(FF1) =/ instant of the probability of anther F has the bomb when the F know there is a lost number.(It seems very easy to get the expression,while they nearly takes my whole afternoon for i forgot what i had learnt on the probability lessons.)And P(LF1) =/
instant of the probability of the L has the bomb in the same case.We can easily get the answer if we type the following sentences into MATLAB:P = nchoosek(33,13)/nchoosek(37,17)
(Enter)P = 0.0360P(FF1) = 0.0360P = nchoosek(33,16)/nchoosek(37,20)
(Enter)P = 0.0734P(LF1) = 0.0734It seems the L maybe really strong but it is just the beginning.As the game gose by,everthing is changing.So let’s continue:function [l,m,p] = ff1(l,m) %l is the amount of the other F’s cords
%m is the amount of the others’ cordsfor l=5:17
for m=5:37
p=((factorial(m-4)).*(factorial(l)))./((factorial(l-4)).*(factorial(m)))
endendThan,type :ff1(5,5)
(Enter)When l&5 or m&5,we can get the answer from the nchoosekFrom this solution，we can know how big the probability of our friend has a bomb is.And we can guess what cords left in the L’s hands.Similarly,if I am a L,I can use the same way:function [l,m,p] = ff1(l,m) %l is the amount of one of the F’s cords
%m is the amount of the Fs’ cordsfor l=5:17
for m=5:34
p=((factorial(m-4)).*(factorial(l)))./((factorial(l-4)).*(factorial(m)))
endendThan,type :ff1(5,5)
(Enter)Actually,if the probability is larger than 0.05 that means the person has a big chance to get a bomb.Particularly as the cards he has becoming fewer and fewer,but the lose card is till absent.Because of the rules of the game,players may get the pairs,straights,Three of Kind,etc. Together and the Three of Kind’s probability approaches to the bomb’s,though it seems the bomb has more chance to be left at the ending of the game.That’s why the probability doesn’t need to be very big.Is really important to remember the cards that has been used.Not only because it is helpful for us to get the probability,but also give us many other information.Example:a single K always means he has no more K,and there is no bomb of K,and if u also have a K,that always means the other one has a pair,etc.In this game,math is not everything,but the most important thing.I’d like to discussing the other situation of this game.But I still has too much to learn.This homework is still a few part of them.To be honest,it’s more a talk than a homework.I don’t know this style is okay.But it really make me feel more relax to figure out the real questions during the homework writing.---XXXXXXXXXClass2 of Mathematics
我们都知道一副牌有54张，三人斗地主时，没人17张，3张做底牌。此题不考虑有人摸到大小王但不出王炸的情况。并三个玩家每个人当地主的概率相等。大小王都在底牌的概率是 。大小王只有一张在底牌的概率是 。大小王都不在底牌的概率是 。出现王炸有三种情况：第一种，大小王都在底牌，谁当地主谁手上就会有王炸。这时王炸出现的概率 。第二种，大小王都不在底牌，也就是看三个人谁运气好，谁能同时摸到大小王。每个人摸到大小王的概率均等。这时王炸出现的概率 。第三种，大小王只有一张在底牌，看谁能摸到，并且摸到的人必须是地主。这时王炸出现的概率 。所以，出现王炸的概率为 。
Z = {小明抓到王炸}；A1 = {扣牌底下3张牌没有王， 且一手牌中有2张王}；A2 = {扣牌底下3张牌有1张王，且一手牌中有1张王}；A3 = {扣牌底下3张牌有2张王，且任意一手牌}；P(A1) = (C52 3/C54 3)
* ((C49 15*C2 2)/C51 17)
= 272/2862P(A2) = (C52 2*C2 1)/C54 3= 306/2862P(A3) = (C52 1*C2 2)/C54 3= 6/2862B = {在未翻扣牌前，小明抓到有可能抓到王炸的牌}P(A1B) = p(B|A1)*p(A1)
= 1/3 * 272/2862P(A2B) = p(B|A2)*p(A2)
= 1/3 * 306/2862P(A3B) = p(B|A3)*p(A3)
= 1 * 6/2862假设叫地主的时候3个人的机会均等都是1/3。C = {小明叫到了地主}P(Z|A1B(CUC非)) = p(A1B)P(Z|A2BC) = p(C|A2B)*p(A2B)P(Z|A3BC) = p(C|A3B)*
p(A3B)P(Z) = p(A1B) + p(C|A2B)*p(A2B)
+ p(C|A3B)* p(A3B) = 1/3 * 272/2862 + 1/3
* 306/2862 * 1/3 + 1/3 * 1 * 6/2862 = 380/8586 = 0.0443所以特定的一个人抓到王炸的概率为0.0443.就是我们自己大概25把能抓到一把王炸（由于知乎排版显示不出来word上的小上小下，在求组合的时候就用空格了）
根据我长期欢乐斗地主的经验，百分之九十是有地
脑洞大开的答案：把大王小王考虑成一份，一共53，地主有20次机会，实际操作来讲需要用19次完成20次的抽牌（大小王一整体）19/53 = 0.。。。。。折叠我吧。。。。
很多知友都算出了32.29%, 但我们实际玩起来感觉概率比这个大, 几乎玩两三把就能出现一次, 这是为什么呢? 让我们根据斗地主玩法的实际情况增加一些复杂度:1. 假设前面51张牌是随机分.2. 在叫地主阶段, 假设没有王的人叫地主的概率是p. (在低端局中p比较接近0, 相比之下中端局和高手局中p值会更大, 不过无所谓我们最后结果会带着p).OK, 计算开始:1. 计算前面51张牌中两个王已经被分配出去的概率(即王不在底牌): 概率=C(2,51) / C(2,54)=0.8912. 计算前面51张牌中只有一个王被分配出去的概率: 概率=(51*3)*2/(54*53)=0.1073. 计算两个王都在底牌的概率: 概率=C(2,3) / C(2, 54)=0.0021'. 在两个王在前51张的情况下, 计算两王在同一人手中的概率: 概率=16/50=0.322'. 如果有一个王在底牌, 那么按照前面的假设2, 出现王炸的概率为: (1-p)3'. 假设两个王都在底牌, 那么如果不考虑全放弃重新发牌, 那么出现王炸的可能性为1.那么根据条件概率, 出现王炸的可能性为: 0.891*0.32 + 0.107*(1-p) + 0.002 = 0.394 - 0.107p结论就是: 当叫不叫地主是随机选择跟手牌无关时，即p=2/3时，出现王炸的概率就是32.3%，符合32.29%的答案。即低端局中, 如果玩家没有王就不敢叫地主, p=0, 出现王炸为39.4%.符合经验直觉。
我什么我觉得是3*3/3*3*3=1/3呢
这个题，真正的口算应该忽略地主比农民多3张牌这一差异，直接转化为将大小两个王分配给ABC三个人的情形，大王可能在3个人的任一个人手里，小王也可能在3个人的任一个人手里，总共有3x3=9种情况，其中大小王同时在A手里、同时在B手里、同时在C手里各1种，共3种情况，于是出现王炸的概率约为1/3。打桥牌、玩德州扑克，顶级高手们肯定是把概率表背到烂熟的。但是对于普通的数学爱好者而言，采用忽略微小差异的方法，迅速心算出概率，并永远按照获胜概率高的方法出牌，久赌必胜。
个人玩家表示抓到炸弹的几率都不到30%，，，打十把有2把炸弹最多了。2张王，3个玩家，，不是1/3几率拿到第一张王，1/3几率拿到第二张王，，两个相乘应该是1/9几率才对啊每看清题主的题目，如果是3个人的几率的话，就是1/3。 单独我的几率应该是1/9
楼主没有描述地主是如何确定的，大家的回答大多是是按照随机选取地主得到的结果，如果考虑到joker在底牌的情况，抢地主导致王炸出现的概率可能比随机发牌选地主略高一些。这会受到玩家整体行为的影响。
我觉得一定会有朋友和我一样对斗地主不把补的三张牌分开计算不舒服，我试着也算了一下，作为其他答案的补充。一副牌54张，每人17张，地主多补3张。1：王炸出现在多补的三张中，概率为52/（54*53*52）。2：一张王在地主的17张牌中，一张王在多补三张中，概率为（52*51*6）/（54*53*52）*1/3。3：王炸出现在其中一人的17张牌中，概率为（52*51*50）/（54*53*52）*（16/50）。总的概率：（1+51*6/3+51*16）/（54*53）=924/2862约为0.32285
1/3这个问题可以变化成这样来思考：王出现在当前拿着另一个王的人手里的概率，就是1/3。第一张王出现在三个人手里的概率是100%就是1，只算第二张牌出现在那个人手里就行了，一张牌出现在某个人手里的概率不就是1/3吗谢谢大家讨论让我知道这个答案不对 没考虑到地主多三张牌，平时不玩斗地主，考虑问题不全面。
0.3229.别问我为什么，我参考上面的答案
简单口算一下，17张牌、20张牌和两张牌相差很多，可以近似17和20相等。所以问题简化为2张牌分3个人，2张牌同时在1个人手中的概率。2张牌同时在1个人手中有3种情况。2张牌分别在不同人手中有6种情况。3/(3+6)=1/3
54张的牌堆&&3张（地主和农民的牌差）；且54张的牌堆&&1张（大王的占位）；所以牌桌上直接估算为1/3就好了......同理，升级（80分、拖拉机）里有人有一对黑桃2的概率约等于四分之一.....
谢邀。做数学题时，我们不仅仅要追求正确的答案，更要追求巧妙的方法，这才是数学的趣味所在。王希的答案是正确的，但是计算过程过于复杂，不是太好。这其实是一道可以口算的概率题。简单的解法：一共 54 张牌，其中地主 20 张，两个农民各 17 张。将牌重新组合，将 54 张牌一次排成一列，分成三堆，前 20 张给地主，中间 17 张给第一个农民，最后 17 张给第二个农民。问题关键：仅考虑大小王的位置，而不考虑其它所有牌。所有情况：王炸在地主手里：王炸在农民手里：所求概率：
感谢邀请。@stanley 的答案是正确的，但模型有误。一副牌54张，斗地主时并不是每个人拿18张，而是两个人拿17张一个人拿20张，每种分配方式的概率是相同的，一共有种。如果王炸在地主（拿20张牌者）手上，共有种情况，即先把王炸给地主，再给地主补足牌，最后分配农民的牌；如果王炸在农民（拿17张牌者）手上，共有种情况，即先把王炸给农民，再给他补足手牌，然后给地主分牌，最后给第二个农民分牌。由于两个农民是对称的，因此乘2.按照这个模型，所求概率即为两种符合条件概率相加除以总方法数，结果约为154/477，约等于32.28%。
三个玩家（不妨设为张三、李四、小明）拿到两张王的概率, 满足：
已有帐号？
无法登录？
社交帐号登录斗地主大家都会的吧，一副扑克三个人玩，四个相同的或两张王都算炸弹。那么斗地主一局中至少有一人有至少一个炸弹的概率是多少？qq游戏出现炸弹的概率是不是故意调大了？
0.096，和王炸0.095概率差不多——————————————好吧，解释下怎么算的————————————农民摸牌数为C(17, 54)，摸到王炸组合数为C(15, 52)，概率为0.095。摸到普通炸弹的概率为1 - 没有摸到普通炸弹的概率，定义13个属于{0, 1, 2, 3}的数和为N的组合数为D(N)，没有摸到普通炸弹的总数为D(15) + 2 * D(16) + D(17)。D(N)可以用动态规划算法来计算。计算得到的至少有普通炸弹的概率为0.096。
斗地主一局中炸弹出现的概率(≈0.5445)确实挺大，下面是我的推导思路(动态规划)：&br&&br&“至少一人有炸弹”与“每个人都没炸弹”互为对立命题，方便起见我们先求“每个人都没炸弹”的概率。&br&&br&假设当三个玩家(A、B、C)的座次选定，一副牌随机打乱发完时，A得到1-17号、B得到18-34号、C(地主)得到35-54号。现在不妨把这个发牌方式转化为另一种等效的方式：先发4张1，从A、B、C的54个牌位中随机挑选4个位置，再发4张2，从剩下的50个排位中随机挑选4个位置……因此整个发牌过程就划分成了14个阶段(13*4普通牌+1*2Joker)。&br&&br&现在我们需要每次发的4张普通牌(或者2张Joker)不能落到同一段(1-17、18-34、35-54)，因为同一段的牌位属于同一个人，这样就构成炸弹了。&br&&br&定义&img src=&///equation?tex=d_%7Bijk%7D%5E%7B%28m%29%7D& alt=&d_{ijk}^{(m)}& eeimg=&1&&表示在第&img src=&///equation?tex=m& alt=&m& eeimg=&1&&阶段、A获得&img src=&///equation?tex=i& alt=&i& eeimg=&1&&张牌、B获得&img src=&///equation?tex=j& alt=&j& eeimg=&1&&张牌、C获得&img src=&///equation?tex=k& alt=&k& eeimg=&1&&张牌时没有出现炸弹的概率，那么在阶段与阶段之间应该有如下递推公式：&br&&img src=&///equation?tex=d_%7Bijk%7D%5E%7B%28m%29%7D+%3D+%5Csum+p_%7B%28i%27j%27k%27+%5Crightarrow+ijk%29%7D+%5Ccdot+d_%7Bi%27j%27k%27%7D%5E%7B%28m-1%29%7D& alt=&d_{ijk}^{(m)} = \sum p_{(i'j'k' \rightarrow ijk)} \cdot d_{i'j'k'}^{(m-1)}& eeimg=&1&&&br&这里的&img src=&///equation?tex=%28i%27%2Cj%27%2Ck%27%29& alt=&(i',j',k')& eeimg=&1&&是&img src=&///equation?tex=m-1& alt=&m-1& eeimg=&1&&阶段可以转移到&img src=&///equation?tex=m& alt=&m& eeimg=&1&&阶段&img src=&///equation?tex=%28i%2Cj%2Ck%29& alt=&(i,j,k)& eeimg=&1&&的合法状态，&img src=&///equation?tex=p_%7B%28i%27j%27k%27+%5Crightarrow+ijk%29%7D& alt=&p_{(i'j'k' \rightarrow ijk)}& eeimg=&1&&是其对应的转移概率，再注意考虑好边界条件应该就可以做了。&br&&br&其实你仔细观察会发现，表示阶段这个上标实际上是多余的，在我们重新确定的发牌过程中&img src=&///equation?tex=%28i%2Cj%2Ck%29& alt=&(i,j,k)& eeimg=&1&&本身就足以定义好状态了，所以上面的公式可以重新改写成下面这个最终版：&br&&img src=&///equation?tex=d_%7Bijk%7D+%3D+%5Csum+p_%7B%28i%27j%27k%27+%5Crightarrow+ijk%29%7D+%5Ccdot+d_%7Bi%27j%27k%27%7D& alt=&d_{ijk} = \sum p_{(i'j'k' \rightarrow ijk)} \cdot d_{i'j'k'}& eeimg=&1&&&br&&br&简单写了段C/C++的求解代码：&br&&div class=&highlight&&&pre&&code class=&language-cpp&&&span class=&cp&&#include &iostream&&/span&
&span class=&k&&using&/span& &span class=&k&&namespace&/span& &span class=&n&&std&/span&&span class=&p&&;&/span&
&span class=&k&&const&/span& &span class=&kt&&double&/span& &span class=&n&&eps&/span& &span class=&o&&=&/span& &span class=&mf&&1e-8&/span&&span class=&p&&;&/span&
&span class=&kt&&double&/span& &span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&mi&&18&/span&&span class=&p&&][&/span&&span class=&mi&&18&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&p&&{&/span&&span class=&mf&&1.0&/span&&span class=&p&&};&/span&
&span class=&kt&&int&/span& &span class=&n&&dx&/span&&span class=&p&&[&/span&&span class=&mi&&15&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&p&&{&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&};&/span&
&span class=&kt&&int&/span& &span class=&n&&dy&/span&&span class=&p&&[&/span&&span class=&mi&&15&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&p&&{&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&};&/span&
&span class=&kt&&double&/span& &span class=&nf&&solve&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&k&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&&span class=&p&&;&/span& &span class=&n&&k&/span& &span class=&o&&&&/span& &span class=&mi&&15&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&k&/span&&span class=&p&&)&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&17&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&o&&--&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&o&&=&/span& &span class=&mi&&17&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&o&&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&o&&--&/span&&span class=&n&&j&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&][&/span&&span class=&n&&j&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&kt&&int&/span& &span class=&n&&t1&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&,&/span& &span class=&n&&t2&/span& &span class=&o&&=&/span& &span class=&mi&&12&/span&&span class=&p&&,&/span& &span class=&n&&s&/span& &span class=&o&&=&/span& &span class=&mi&&4&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&k&/span& &span class=&o&&&&/span& &span class=&mi&&13&/span&&span class=&p&&)&/span& &span class=&n&&t1&/span&&span class=&o&&=&/span&&span class=&mi&&12&/span&&span class=&p&&,&/span&&span class=&n&&t2&/span&&span class=&o&&=&/span&&span class=&mi&&15&/span&&span class=&p&&,&/span&&span class=&n&&s&/span&&span class=&o&&=&/span&&span class=&mi&&2&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&t&/span& &span class=&o&&=&/span& &span class=&n&&t1&/span&&span class=&p&&;&/span& &span class=&n&&t&/span& &span class=&o&&&&/span& &span class=&n&&t2&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&t&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&a&/span&&span class=&o&&=&/span&&span class=&n&&dx&/span&&span class=&p&&[&/span&&span class=&n&&t&/span&&span class=&p&&],&/span& &span class=&n&&b&/span&&span class=&o&&=&/span&&span class=&n&&dy&/span&&span class=&p&&[&/span&&span class=&n&&t&/span&&span class=&p&&],&/span& &span class=&n&&c&/span&&span class=&o&&=&/span&&span class=&n&&s&/span&&span class=&o&&-&/span&&span class=&n&&a&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&;&/span&
&span class=&kt&&int&/span& &span class=&n&&sa&/span&&span class=&o&&=&/span&&span class=&mi&&17&/span&&span class=&o&&-&/span&&span class=&n&&i&/span&&span class=&o&&+&/span&&span class=&n&&a&/span&&span class=&p&&,&/span& &span class=&n&&sb&/span&&span class=&o&&=&/span&&span class=&mi&&17&/span&&span class=&o&&-&/span&&span class=&n&&j&/span&&span class=&o&&+&/span&&span class=&n&&b&/span&&span class=&p&&,&/span& &span class=&n&&sc&/span&&span class=&o&&=&/span&&span class=&mi&&54&/span&&span class=&o&&-&/span&&span class=&p&&(&/span&&span class=&n&&k&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&mi&&4&/span&&span class=&o&&-&/span&&span class=&n&&sa&/span&&span class=&o&&-&/span&&span class=&n&&sb&/span&&span class=&p&&;&/span&
&span class=&kt&&double&/span& &span class=&n&&prob&/span&&span class=&p&&(&/span&&span class=&kt&&int&/span&&span class=&p&&,&/span&&span class=&kt&&int&/span&&span class=&p&&,&/span&&span class=&kt&&int&/span&&span class=&p&&,&/span&&span class=&kt&&int&/span&&span class=&p&&,&/span&&span class=&kt&&int&/span&&span class=&p&&,&/span&&span class=&kt&&int&/span&&span class=&p&&);&/span&
&span class=&kt&&double&/span& &span class=&n&&p&/span& &span class=&o&&=&/span& &span class=&n&&prob&/span&&span class=&p&&(&/span&&span class=&n&&sa&/span&&span class=&p&&,&/span&&span class=&n&&sb&/span&&span class=&p&&,&/span&&span class=&n&&sc&/span&&span class=&p&&,&/span&&span class=&n&&a&/span&&span class=&p&&,&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&c&/span&&span class=&p&&);&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&p&/span& &span class=&o&&&&/span& &span class=&n&&eps&/span&&span class=&p&&)&/span& &span class=&k&&continue&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&o&&-&/span&&span class=&n&&a&/span&&span class=&p&&][&/span&&span class=&n&&j&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&eps&/span&&span class=&p&&)&/span& &span class=&k&&continue&/span&&span class=&p&&;&/span&
&span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&][&/span&&span class=&n&&j&/span&&span class=&p&&]&/span& &span class=&o&&+=&/span& &span class=&n&&p&/span&&span class=&o&&*&/span&&span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&o&&-&/span&&span class=&n&&a&/span&&span class=&p&&][&/span&&span class=&n&&j&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&];&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&k&&return&/span& &span class=&p&&(&/span&&span class=&mf&&1.0&/span&&span class=&o&&-&/span&&span class=&n&&dp&/span&&span class=&p&&[&/span&&span class=&mi&&17&/span&&span class=&p&&][&/span&&span class=&mi&&17&/span&&span class=&p&&]);&/span&
&span class=&p&&}&/span&
&span class=&kt&&int&/span& &span class=&nf&&main&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&n&&cout&/span& &span class=&o&&&&&/span& &span class=&n&&solve&/span&&span class=&p&&()&/span& &span class=&o&&&&&/span& &span class=&n&&endl&/span&&span class=&p&&;&/span&
&span class=&k&&return&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&span class=&kt&&double&/span& &span class=&nf&&prob&/span&&span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&sa&/span&&span class=&p&&,&/span& &span class=&kt&&int&/span& &span class=&n&&sb&/span&&span class=&p&&,&/span& &span class=&kt&&int&/span& &span class=&n&&sc&/span&
&span class=&p&&,&/span&&span class=&kt&&int&/span& &span class=&n&&a&/span&&span class=&p&&,&/span&
&span class=&kt&&int&/span& &span class=&n&&b&/span&&span class=&p&&,&/span&
&span class=&kt&&int&/span& &span class=&n&&c&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&
&span class=&n&&a&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span& &span class=&o&&||&/span&
&span class=&n&&b&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span& &span class=&o&&||&/span& &span class=&n&&c&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span&
&span class=&o&&||&/span&
&span class=&n&&sa&/span&&span class=&o&&&&/span&&span class=&n&&a&/span& &span class=&o&&||&/span&
&span class=&n&&sb&/span&&span class=&o&&&&/span&&span class=&n&&b&/span& &span class=&o&&||&/span& &span class=&n&&sc&/span&&span class=&o&&&&/span&&span class=&n&&c&/span&
&span class=&o&&||&/span& &span class=&n&&sa&/span&&span class=&o&&&&/span&&span class=&mi&&17&/span& &span class=&o&&||&/span& &span class=&n&&sb&/span&&span class=&o&&&&/span&&span class=&mi&&17&/span& &span class=&o&&||&/span& &span class=&n&&sc&/span&&span class=&o&&&&/span&&span class=&mi&&20&/span&&span class=&p&&)&/span&
&span class=&k&&return&/span& &span class=&mf&&0.0&/span&&span class=&p&&;&/span&
&span class=&kt&&double&/span& &span class=&n&&ra&/span&&span class=&o&&=&/span&&span class=&mf&&1.0&/span&&span class=&p&&,&/span& &span class=&n&&rb&/span&&span class=&o&&=&/span&&span class=&mf&&1.0&/span&&span class=&p&&,&/span& &span class=&n&&rc&/span&&span class=&o&&=&/span&&span class=&mf&&1.0&/span&&span class=&p&&,&/span& &span class=&n&&bs&/span&&span class=&o&&=&/span&&span class=&mf&&1.0&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&n&&a&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&n&&ra&/span& &span class=&o&&=&/span& &span class=&n&&ra&/span& &span class=&o&&*&/span& &span class=&p&&(&/span&&span class=&n&&sa&/span& &span class=&o&&-&/span& &span class=&n&&i&/span&&span class=&p&&)&/span& &span class=&o&&/&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&o&&+&/span& &span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&n&&b&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&n&&rb&/span& &span class=&o&&=&/span& &span class=&n&&rb&/span& &span class=&o&&*&/span& &span class=&p&&(&/span&&span class=&n&&sb&/span& &span class=&o&&-&/span& &span class=&n&&i&/span&&span class=&p&&)&/span& &span class=&o&&/&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&o&&+&/span& &span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&n&&c&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&n&&rc&/span& &span class=&o&&=&/span& &span class=&n&&rc&/span& &span class=&o&&*&/span& &span class=&p&&(&/span&&span class=&n&&sc&/span& &span class=&o&&-&/span& &span class=&n&&i&/span&&span class=&p&&)&/span& &span class=&o&&/&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&o&&+&/span& &span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&kt&&double&/span& &span class=&n&&sabc&/span&&span class=&o&&=&/span&&span class=&n&&sa&/span&&span class=&o&&+&/span&&span class=&n&&sb&/span&&span class=&o&&+&/span&&span class=&n&&sc&/span&&span class=&p&&,&/span& &span class=&n&&abc&/span&&span class=&o&&=&/span&&span class=&n&&a&/span&&span class=&o&&+&/span&&span class=&n&&b&/span&&span class=&o&&+&/span&&span class=&n&&c&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&n&&abc&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&n&&bs&/span& &span class=&o&&=&/span& &span class=&n&&bs&/span& &span class=&o&&*&/span& &span class=&p&&(&/span&&span class=&n&&sabc&/span& &span class=&o&&-&/span& &span class=&n&&i&/span&&span class=&p&&)&/span& &span class=&o&&/&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&o&&+&/span& &span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&k&&return&/span& &span class=&p&&(&/span&&span class=&n&&ra&/span&&span class=&o&&*&/span&&span class=&n&&rb&/span&&span class=&o&&*&/span&&span class=&n&&rc&/span&&span class=&o&&/&/span&&span class=&n&&bs&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&&br&为了保险起见做了个随机模拟，结果也印证了之前的结论：&br&&div class=&highlight&&&pre&&code class=&language-cpp&&&span class=&cp&&#include &iostream&&/span&
&span class=&cp&&#include &cstdlib&&/span&
&span class=&cp&&#include &ctime&&/span&
&span class=&cp&&#include &cstring&&/span&
&span class=&cp&&#include &algorithm&&/span&
&span class=&k&&using&/span& &span class=&k&&namespace&/span& &span class=&n&&std&/span&&span class=&p&&;&/span&
&span class=&kt&&void&/span& &span class=&nf&&random_cards&/span&&span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&card&/span&&span class=&p&&[],&/span& &span class=&kt&&int&/span& &span class=&n&&st&/span&&span class=&p&&,&/span& &span class=&kt&&int&/span& &span class=&n&&ed&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span&&span class=&o&&=&/span&&span class=&n&&ed&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&n&&st&/span&&span class=&p&&;&/span& &span class=&o&&--&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&o&&=&/span& &span class=&n&&st&/span& &span class=&o&&+&/span& &span class=&n&&rand&/span&&span class=&p&&()&/span&&span class=&o&&%&/span&&span class=&p&&(&/span&&span class=&n&&i&/span&&span class=&o&&-&/span&&span class=&n&&st&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&j&/span& &span class=&o&&!=&/span& &span class=&n&&i&/span&&span class=&p&&)&/span& &span class=&n&&swap&/span&&span class=&p&&(&/span&&span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&n&&j&/span&&span class=&p&&],&/span& &span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]);&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&kt&&int&/span& &span class=&nf&&main&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&n&&srand&/span&&span class=&p&&((&/span&&span class=&kt&&unsigned&/span&&span class=&p&&)&/span&&span class=&n&&time&/span&&span class=&p&&(&/span&&span class=&nb&&NULL&/span&&span class=&p&&));&/span&
&span class=&kt&&int&/span& &span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&mi&&54&/span&&span class=&p&&];&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&mi&&54&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&i&/span& &span class=&o&&/&/span& &span class=&mi&&4&/span&&span class=&p&&;&/span&
&span class=&kt&&int&/span& &span class=&n&&num&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&,&/span& &span class=&n&&sum&/span& &span class=&o&&=&/span& &span class=&mi&&1000000&/span&&span class=&p&&;&/span&
&span class=&kt&&int&/span& &span class=&n&&cnt&/span&&span class=&p&&[&/span&&span class=&mi&&3&/span&&span class=&p&&][&/span&&span class=&mi&&14&/span&&span class=&p&&];&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&t&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&t&/span& &span class=&o&&&&/span& &span class=&n&&sum&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&t&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&memset&/span&&span class=&p&&(&/span&&span class=&n&&cnt&/span&&span class=&p&&,&/span& &span class=&mh&&0x00&/span&&span class=&p&&,&/span& &span class=&mi&&3&/span&&span class=&o&&*&/span&&span class=&mi&&14&/span&&span class=&o&&*&/span&&span class=&k&&sizeof&/span&&span class=&p&&(&/span&&span class=&kt&&int&/span&&span class=&p&&));&/span&
&span class=&n&&random_cards&/span&&span class=&p&&(&/span&&span class=&n&&card&/span&&span class=&p&&,&/span& &span class=&mi&&0&/span&&span class=&p&&,&/span& &span class=&mi&&54&/span&&span class=&p&&);&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&mi&&54&/span&&span class=&p&&;&/span& &span class=&o&&++&/span&&span class=&n&&i&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&tmp&/span& &span class=&o&&=&/span& &span class=&o&&++&/span&&span class=&n&&cnt&/span&&span class=&p&&[&/span&&span class=&n&&min&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span& &span class=&n&&i&/span&&span class=&o&&/&/span&&span class=&mi&&17&/span&&span class=&p&&)][&/span&&span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]];&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&tmp&/span& &span class=&o&&&=&/span& &span class=&mi&&4&/span&
&span class=&o&&||&/span& &span class=&n&&tmp&/span& &span class=&o&&&=&/span& &span class=&mi&&2&/span&
&span class=&o&&&&&/span& &span class=&n&&card&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&==&/span& &span class=&mi&&13&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&o&&++&/span&&span class=&n&&num&/span&&span class=&p&&;&/span&
&span class=&k&&break&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&n&&cout&/span& &span class=&o&&&&&/span& &span class=&kt&&double&/span&&span class=&p&&(&/span&&span class=&n&&num&/span&&span class=&p&&)&/span& &span class=&o&&/&/span& &span class=&n&&sum&/span& &span class=&o&&&&&/span& &span class=&n&&endl&/span&&span class=&p&&;&/span&
&span class=&k&&return&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&
斗地主一局中炸弹出现的概率(≈0.5445)确实挺大，下面是我的推导思路(动态规划)：“至少一人有炸弹”与“每个人都没炸弹”互为对立命题，方便起见我们先求“每个人都没炸弹”的概率。假设当三个玩家(A、B、C)的座次选定，一副牌随机打乱发完时，A得到1-17号…
和评论一样，王炸 都 大概1/3了，丁先森算的总概率怎么可能才不到10%&br&。。。。。。。。。。分行。。。。。。。。。。。。。。&br&1，先算王炸&br&地主C(18,52)/C(20,54)+农民2*C(15,52)/C(17,54)=0.32285&br&&img src=&///equation?tex=%5Cfrac%7BC_%7B52%7D%5E%7B18%7D+%7D%7BC_%7B54%7D%5E%7B20%7D%7D+%2B2%2A%5Cfrac%7BC_%7B52%7D%5E%7B15%7D%7D%7BC_%7B54%7D%5E%7B17%7D+%7D+& alt=&\frac{C_{52}^{18} }{C_{54}^{20}} +2*\frac{C_{52}^{15}}{C_{54}^{17} } & eeimg=&1&&&br&2，算 4 个 的&br&C(1,13)[C(16,50)/C(20,54)+2*C(13,50)/C(17,54)]=0.39483&br&&img src=&///equation?tex=C_%7B13%7D%5E%7B1%7D+%2A%5Cleft%5B%5Cfrac%7BC_%7B50%7D%5E%7B16%7D+%7D%7BC_%7B54%7D%5E%7B20%7D+%7D%2B2%2A%5Cfrac%7BC_%7B50%7D%5E%7B13%7D+%7D%7BC_%7B54%7D%5E%7B17%7D+%7D++%5Cright%5D+& alt=&C_{13}^{1} *\left[\frac{C_{50}^{16} }{C_{54}^{20} }+2*\frac{C_{50}^{13} }{C_{54}^{17} }
\right] & eeimg=&1&&&br&3，算 王炸+4个 的都有的&br&[1]*[2]=0.12747
(这里有点小误差，因为是直接用第一项和第二项的数字相乘的，影响不大)&br&1+2-3就是&br&0.59021=59%&br&这是标准54张牌的算法&br&&br&分析：我想上知乎的人差不多都应该能看懂吧，高中的一点统计知识&br&&br&算了才知道，原来四个一样的炸弹要比王炸概率要高？&br&是这样么？&br&我们应该都打过斗地主吧，我们一直都是觉得王炸比四个一样的炸弹要容易得些，是吧？&br&事实上也是这样的&br&&b&化简&/b&&br&假设每个人牌都是一样多的18张&br&有王炸的概率是1/3，知道怎么来的么？&br&一个人得到 大王的 概率是1/3，小王的概率也是1/3&br&那么有人（一起3人打牌）得到王炸的概率就是 &img src=&///equation?tex=3%2A%5Cfrac%7B1%7D%7B3%7D+%2A%5Cfrac%7B1%7D%7B3%7D+%3D%5Cfrac%7B1%7D%7B3%7D+%3D%5Cfrac%7B9%7D%7B27%7D+& alt=&3*\frac{1}{3} *\frac{1}{3} =\frac{1}{3} =\frac{9}{27} & eeimg=&1&&&br&&br&那么四个一样的牌这样的炸弹的概率是多大呢？&br&&img src=&///equation?tex=13%2A3%2A%5Cfrac%7B1%7D%7B3%7D+%2A%5Cfrac%7B1%7D%7B3%7D+%2A%5Cfrac%7B1%7D%7B3%7D+%2A%5Cfrac%7B1%7D%7B3%7D+%3D%5Cfrac%7B13%7D%7B27%7D+& alt=&13*3*\frac{1}{3} *\frac{1}{3} *\frac{1}{3} *\frac{1}{3} =\frac{13}{27} & eeimg=&1&&&br&数字的意义要说么？&br&A-K
3个人打呀&br&4个1/3相乘
我得 黑桃?A*梅花A*红?A*?A的概率呀&br&。。。。。。。。。。。。分行。。。。。。。。。。。。。。。。&br&有空的时候算带一张花牌的&br&1,&br&&br&2,&br&&br&3,&br&&br&要下班了，有空再说。
和评论一样，王炸 都 大概1/3了，丁先森算的总概率怎么可能才不到10%。。。。。。。。。。分行。。。。。。。。。。。。。。1，先算王炸地主C(18,52)/C(20,54)+农民2*C(15,52)/C(17,54)=0.32285\frac{C_{52}^{18} }{C_{54}^{20}} +2*\frac{C_{52}^{15}}{C_{…
已有帐号？
无法登录？
社交帐号登录
摄影技巧达人，懂竞技游戏，对食品工业很有兴趣。