专门回答各类扑克概率问题

7Sasuke 发表于 2013-8-4 23:36
谢谢霍版，
补充问题：flop 三张牌 三杂花且任何两张都无连张概率

应该是25.3%

select count((  boardInRange('xyz') AND   (NOT     boardInRange('*[23+]'))))  as COUNT1
from game='holdem', syntax='Generic'

哦，A2忽略了，谢谢指正。23+已经包括了AK。

修改后概率为24.2%

select count(   rainbowBoard(flop) AND   
                    (NOT     boardInRange('*[23+]')) AND
                    (NOT     boardInRange('A2*'))   ) as FlopRainbowNo2Connector
from game='holdem', syntax='Generic'

7Sasuke 发表于 2013-8-11 20:44
霍版我又来麻烦您了，还是这个问题，我根据我的一些对手range，发现他们的起手牌range跟霍氏200BB指数相 ...

这个怎么听起来挺复杂的。今天要是还有时间就帮你弄一下，对不起，这么久了我都没回复。

谢谢提问

1、拿任意两同花进，flop翻出天花的概率

答：0.84%
select count(exactFlopHandCategory(PLAYER_1,FLOPFLUSH)) /* How often PLAYER_1 flop hand category is flush */ as COUNT1
from game='holdem', syntax='Generic',
     PLAYER_1='xx'

2、flop翻出3同花，假设我们手上无该花色，对手持有天花的概率

答：4.13% (假设对方是any2)
select count(exactFlopHandCategory(PLAYER_2,FLOPFLUSH)) /* How often PLAYER_2 flop hand category is flush */ as COUNT1
from game='holdem', syntax='Generic',
     board='hhh',
     PLAYER_1='ss',
     PLAYER_2='*'


3、flop翻出3同花，我们持有一张该花色，对手持有天花的概率

答：3.30% （假设对方Any2）
select count(exactFlopHandCategory(PLAYER_2,FLOPFLUSH)) /* How often PLAYER_2 flop hand category is flush */ as COUNT1
from game='holdem', syntax='Generic',
     board='hhh',
     PLAYER_1='sh',
     PLAYER_2='*'

问题描述非常精确，谢谢提问！
通过计算我也学习了！三个对手至少有人trips概率高达一半，比我预想要高。

1. AAKQr  flop 227r，vs 一个、两个、三个对手（均为随机牌），至少有一个对手trip/full的概率%

对手：	一个	两个	三个
Exactly Trips	13.2	25.5	36.7
Exactly Fullhouse	4.9	9.7	14.4
At least Trips	18.8	35.3	49.8

2. AAK7r,flop 227r vs 一个、两个、三个对手（均为随机牌），至少有一个对手trip/full的概率%

对手：	一个	两个	三个
Exactly Trips	14.3	27.4	39.4
Exactly Fullhouse	2.8	5.6	8.4
At least Trips	17.7	33.6	47.7

回复7Sakuke在199楼的问题。

首先定义range。根据描述，“霍氏20BB战斗力大于等于1.1”，其range为：
77+, A*, KxQx-Kx2x, QxJx-Qx4x, JxTx-Jx7x, Tx9x-Tx7x, 9x8x, KxQy-Kx5y, QxJy-Qx7y, JxTy-Jx8y, Tx9y-Tx8y

共564 combo

下表中，Hero底牌: AK-A7
Villain的底牌【77+, A*, KxQx-Kx2x, QxJx-Qx4x, JxTx-Jx7x, Tx9x-Tx7x, 9x8x, KxQy-Kx5y, QxJy-Qx7y, JxTy-Jx8y, Tx9y-Tx8y】

Hero's Hands and Flop	Hero Flop Equity	How often hero has lower rank	How often hero equity less than 50%
AK @ A[Q-][Q-]	84.4	5.16%	5.77%
AQ @ A[K-][K-]!Q**	82.8	6.8%	7.45%
AJ @ A[K-][K-]!J**	81.3	8.47%	9.12%
AT @ A[K-][K-]!T**	80.0	10.1%	10.8%
A9 @ A[K-][K-]!9**	77.2	12.0%	12.8%
A8 @ A[K-][K-]!8**	75.9	13.5%	14.4%
A7 @ A[K-][K-]!7**	74.6	15.0%	15.9%
AK @ K[Q-][Q-]	83.4	5.63%	6.35%
AQ @ Q[J-][J-]	80.1	6.20%	7.18%
AJ @ J[T-][T-]	77.9	6.61%	7.81%
AT @ T[9-][9-]	76.0	7.35%	8.92%
A9 @ 9[8-][8-]	74.6	7.75%	9.75%
A8 @ 8[7-][7-]	72.9	8.62%	11.1%
A7 @ 7[6-][6-]	71.0	9.25%	12.2%

A[K-][K-]!Q** 表示Flop上有且仅有一张A，且没有Q。

超逸 发表于 2014-4-3 16:48
正好也有个问题求霍爷解答。

9人台，AAATT输给四条算BB,l理论上多少手牌能出现一次 ...

谢谢超逸提问，半年没人问，有提问的那必须当亲人看待

假设9人桌每个人都无条件打到showdown
假设both cards must play
假设四条不需要pocket pair（AJ在JJJT9 也算）
包括三家或更多都出现badbeat （67888 三黑桃，45黑桃 vs 9T黑桃 vs A8）

假设完了一堆东西，最后是坏消息：计算量太大，导致软件长时间停在0% 。。。

但是仍然有办法，因为网上有现成的，我作弊抄一下

http://wizardofodds.com/games/texas-hold-em/bad-beat-jackpots/

它是指的10人桌，不是9人桌。按9人桌算，要稍微调低那么一点点

Type1 不要求quads从pocket pair起步 （最宽松）
Type2 要求quads必须是pocket pair
Type3 要求quads必须是pocket pair，且fullhouse不能利用牌面的三条 （最严格）

Bad Beat Probabilities

BAD BEAT HAND	TYPE 1	TYPE 2	TYPE 3
Any full house	0.00203329	0.00050305	0.00049508
Full house, three 3's or higher	0.00189512	0.00046978	0.00046204
Full house, three 4's or higher	0.00175159	0.00043444	0.00042728
Full house, three 5's or higher	0.00160333	0.00039706	0.00039028
Full house, three 6's or higher	0.00144965	0.00035741	0.00035145
Full house, three 7's or higher	0.0012936	0.00031767	0.00031266
Full house, three 8's or higher	0.00113492	0.00027775	0.00027355
Full house, three 9's or higher	0.00097379	0.00023772	0.00023445
Full house, three T's or higher	0.00081113	0.00019759	0.00019503
Full house, three J's or higher	0.00064763	0.00015708	0.00015509
Full house, three Q's or higher	0.00048533	0.00011838	0.00011682
Full house, three K's or higher	0.00032561	0.00008130	0.00008033
Full house, three A's or higher	0.00016964	0.00004608	0.00004579
Full house, aces full of 3's or higher	0.00016004	0.00004350	0.00004322
Full house, aces full of 4's or higher	0.00014986	0.00004080	0.00004052
Full house, aces full of 5's or higher	0.00013898	0.00003797	0.00003763
Full house, aces full of 6's or higher	0.00012749	0.00003504	0.00003469
Full house, aces full of 7's or higher	0.00011580	0.00003233	0.00003203
Full house, aces full of 8's or higher	0.00010347	0.00002957	0.00002925
Full house, aces full of 9's or higher	0.00009067	0.00002673	0.00002645
Full house, aces full of T's or higher	0.00007714	0.00002383	0.00002359
Full house, aces full of J's or higher	0.00006286	0.00002064	0.0000204
Full house, aces full of Q's or higher	0.00004793	0.00001738	0.00001721
Full house, aces full of K's or higher	0.00003230	0.00001408	0.00001402
Any four of a kind	0.00001601	0.00001086	0.00001081
Four 3's or higher	0.00001437	0.00000996	0.00000992
Four 4's or higher	0.0000127	0.00000900	0.00000902
Four 5's or higher	0.00001099	0.00000805	0.00000804
Four 6's or higher	0.00000934	0.00000705	0.00000707
Four 7's or higher	0.0000078	0.00000613	0.00000611
Four 8's or higher	0.0000064	0.00000525	0.00000519
Four 9's or higher	0.00000519	0.00000439	0.00000435
Four T's or higher	0.00000414	0.00000359	0.00000357
Four J's or higher	0.00000317	0.00000287	0.00000285
Four Q's or higher	0.00000246	0.00000226	0.00000224
Four K's or higher	0.00000193	0.00000180	0.00000179
Four A's or higher	0.00000157	0.00000149	0.00000147
Any straight flush	0.0000012	0.00000122	0.00000121
Straight flush 6 high or higher	0.00000105	0.00000107	0.00000105
Straight flush 7 high or higher	0.00000089	0.00000091	0.00000090
Straight flush 8 high or higher	0.00000073	0.00000074	0.00000074
Straight flush 9 high or higher	0.00000056	0.00000059	0.00000058
Straight flush T high or higher	0.00000041	0.00000043	0.00000042
Straight flush J high or higher	0.00000028	0.00000027	0.00000027
Straight flush Q high or higher	0.00000012	0.00000012	0.00000012

这个数字是概率，是直接数字，不是百分数。

0.00002383 = 0.002383% = 1 in 41964

这是10人桌的情况，我估计9人桌大概要小15%左右。
也就是
0.00002 = 0.002% = 1 in 5万

再扣除一部分因为fold而错过的，大约打一个七五折。
实际概率大约是
0.000015 = 0.0015% = 1 in 66667

加入您的扑克室平均每天有  100 桌小时（qualified Texas Holdem Only），按照每桌小时30手牌算，两次badbeat之间的期望时间是：
66667/100/30 = 22天

起手最大为10（同花或者非同花）的连张、间1、间2、间3。
FLOP分别中2对、3条、天顺、天同花的概率

起手牌\Flop牌型	两对（无公对）	3条（无trips）	天顺	天花
98s	2.0%	1.35%	1.28%	0.84%
97s	2.0%	1.35%	0.97%	0.84%
96s	2.0%	1.35%	0.65%	0.84%
95s	2.0%	1.35%	0.32%	0.84%

除了造顺子能力不同，其他都相同。
造顺子能力，顶级连张是 1.28%。间隔增大，其能力以等差数列方式下降。

谢谢提问！

9人桌，UTG手持AJ，后面8人没有人持有下列牌的概率：22+、AK、AQ
9人桌，UTG手持AT，后面8人没有人持有下列牌的概率：22+、AK、AQ、AJ
UTG FOLD,UTG+1呢?
UTG和UTG+1 FLOD，UTG+2呢?

10人桌，UTG、UTG+1、UTG+2的上述情况下的概率。

10人桌UTG+1（枪口fold）等价于9人桌的UTG；
10人桌UTG+2（枪口和+1fold）等价于9人桌的UTG+1；

Probability of No Stronger Hand Behind Me Preflop

Hand and Position	Probality of No Stronger Hand
AJ with 9 players behind	47.8%
AT with 9 players behind	43.1%
AJ with 8 players behind	51.9%
AT with 8 players behind	47.5%
AJ with 7 players behind	56.4%
AT with 7 players behind	52.1%
AJ with 6 players behind	61.3%
AT with 6 players behind	57.3%