关于期望的一个疑问

回复 10# greatsunkai


    这个问题里比较微妙的一句话是：
如果你判断对手听同花，然后通过巧妙的设计，C-R对手allin了。

说的是你判断对手是同花，而不是对手亮出牌来让你看同花。
check-raise是什么，是开弓没有回头箭。
对手的bet，可以是同花兆，也可能是两对以上的好牌。所以，这样的move重复100次，可能有50次你遇到的是同花兆，25次遇到他比你弱，但是他扔了，25次遇到他比你强，你没有退路了。
所以，总算下来，似乎同花兆比你打得更加合理。

这里没有给stack的对比情况，所以，不太好算。

我假设一个具体点的。
假设主角AA，锅底100，两个人手里都是300。
翻牌出来，278，两红桃。
主角观，对手上100，主角回手300 all in。

我们假设对手是这样一个对手。如我上面说的。
他只有好于2对的成牌会靠主角的300，以及合理的兆牌。而任何差于2对的牌会扔掉。
这些情况的分布比例大概如下：
50%的时候，他扔掉了1对，25%他拿8个outs以上的抓牌跟你拼命，25%的时候拿2对或者暗三和你拼命。
现在计算一下谁吃亏呢。
不用仔细算，肯定是AA吃亏。

因为对手知道，我无论如何还有约1/3赢的机会。
而AA自己不知道深处何处。如果他冒冒失失先all in了。要么人家扔了只赢100。要么人家靠了把300全输了，要么人家还有1/3的机会来赢。

所以，这牌同花兆的处境要比AA好得多，而且有位置。

难道说，我的AA就这么啥也不是，怎么打怎么不对？
对手的问题出在翻牌前。
如果他没有足够的计划就去靠了AA的翻牌前的raise，他几乎是白白送钱。
我们假设翻牌前主角搞到50，他大大咧咧的靠，除了去中牌，没有任何计划，那就等于他白送了AA50元，至少白送40。
同花兆上的机会不过1/10，多数时候中一小对，根本没有战斗力。

而当真的同花兆上后，你对对手的了解，你们的stack对比就非常关键。
如果你知道他是AA，你有没有信心翻牌打不走转把他打走，你的筹码是不是足够完成这些计划，如果转你的同花就到了，你到底能赢他多少钱。河如果来了J或者6，你有没有信心打走之。
所有的这些equity都考虑进去，才是你打这手牌的根本。
如果上面说的这些方案都不可行，对手是个拿了AA，打死不放手的人。那你的同花就多于靠了。

除非他有10000筹码，翻牌前搞到50，而且你也有10000，这种情况太少见了。
所以，你去靠别人的牌，要计划在先。

回复 11# 伟大的墙


    其实我这个疑问主要是针对Phil Galfond的理论，而不是具体的一手牌。
In the previous paragraph, we touched on a subject that is commonly referred to as GBucks.
G-Bucks was originally pioneered as a concept by Phil Galfond (AKA OMGclayaiken, a
top-5 player in the world currently). The idea is relatively simple—whether or not you make the
correct decision against someone’s hand is relatively unimportant (this type of decision is called
a Sklansky buck decision, i.e. if you put in 100 dollars at 20% to win, you win a theoretical 20
dollars). Galfond’s idea, though, was that even if you get the money in at 20% to win, if you’re
60% to win against his range, you actually win 60 dollars in the long-term, even though the
results of the hand led you to a 20 dollar expectation.

回复  伟大的墙


    其实我这个疑问主要是针对Phil Galfond的理论，而不是具体的一手牌。
In the previo ...
greatsunkai 发表于 2010-11-24 14:37

   
没看懂

easy game里面的一章
Chapter Twelve: A Brief Understanding of G-Bucks
In the previous paragraph, we touched on a subject that is commonly referred to as GBucks.G-Bucks was originally pioneered as a concept by Phil Galfond (AKA OMGclayaiken, a top-5 player in the world currently). The idea is relatively simple—whether or not you make the correct decision against someone’s hand is relatively unimportant (this type of decision is called a Sklansky buck decision, i.e. if you put in 100 dollars at 20% to win, you win a theoretical 20 dollars). Galfond’s idea, though, was that even if you get the money in at 20% to win, if you’re 60% to win against his range, you actually win 60 dollars in the long-term, even though the results of the hand led you to a 20 dollar expectation.
A moment ago, we were talking about how people don’t do a good job of evaluating the strength of draws in the context of equity. They assume that if a person has a draw more often than 50% of the time, they should go all-in. This ignores the fact that range equities are what matter—a person with a range that looks like sets 40% of the time and draws 60% of the time usually is a big favorite against our range, even though they have a draw more than half the time.This is a pretty basic understanding of G-bucks in terms of equity.
This also is a pretty decent argument as for why we shouldn’t overly concern ourselves with math when trying to play poker at a table. The math is either very simple (we have the nut flush draw and thus have around 45% equity) or extremely complicated (against an estimated 10% of his range, we are 75% equity, against an estimated 35% of his range, we have 20% equity, against an estimated 55% of his range, we have 45% equity, balance out the range equity and compare to pot odds to determine our G-bucks). Even in the complicated scenario, it relies on deductive analysis to determine his likely range. In general, we’ll instead rely on the basic math and a generalized “feel” approach to the complicated stuff. But, it’s important to know that G-bucks defines a structural poker concept.
Since writing this chapter in for the initial release of “Easy Game”, it has come to my attention that G-Bucks, as originally written, refers not to our hand’s strength against our opponent’s ranges but the opposite—our range against our opponent’s holding. In terms of understanding the concept, this is somewhat beside the point. What matters is that we’re focused on identifying our equity against our opponent’s range first and foremost. It’s a rather more advanced skill to identify our range’s equity against our opponent’s range (and one that we won’t really need to emphasize until we play against the same strong players every day). Until we hit the nosebleeds, we can take advantage of the practical uses of G-Bucks and focus on range equities.

c-r对超对不适合吧，考虑自己是set的情况。如果对手100%bet flush draw的时候，这么的C-R不是相当于套住了么。

回复  Howard


    那您认为主角的check-raise是不是正确的选择呢？
greatsunkai 发表于 2010-11-24 14:00

    是否正确的选择取决于怎样定义“正确”。如果主角认为对手range偏弱，fold概率大于特定值比如30%，即使他跟自己的牌也有40%以上赢率，这个C-R就是正确的。但是对手恰好是暗三条，不但绝不可能fold，而且希望主角C-R，这里主角就正中对手的奸计。但主角的估计也没错，只不过对手恰好处在他range的顶端而已。

下一次对手同样行动的时候，说不定就是仅有8 outer甚至更少。仍然可以把主角的的C-R看作正确的。

回复 16# Howard


    嗯，大概有一些思路了，谢谢。

回复 14# greatsunkai


    这篇文章里的弯子我没绕过来，谁能结合例子给解释一下子，如下：
easy game里面的一章
Chapter Twelve: A Brief Understanding of G-Bucks
In the previous paragraph, we touched on a subject that is commonly referred to as GBucks.G-Bucks was originally pioneered as a concept by Phil Galfond (AKA OMGclayaiken, a top-5 player in the world currently). The idea is relatively simple—whether or not you make the correct decision against someone’s hand is relatively unimportant (this type of decision is called a Sklansky buck decision, i.e. if you put in 100 dollars at 20% to win, you win a theoretical 20 dollars). Galfond’s idea, though, was that even if you get the money in at 20% to win, if you’re 60% to win against his range, you actually win 60 dollars in the long-term, even though the results of the hand led you to a 20 dollar expectation.
A moment ago, we were talking about how people don’t do a good job of evaluating the strength of draws in the context of equity. They assume that if a person has a draw more often than 50% of the time, they should go all-in. This ignores the fact that range equities are what matter—a person with a range that looks like sets 40% of the time and draws 60% of the time usually is a big favorite against our range, even though they have a draw more than half the time.This is a pretty basic understanding of G-bucks in terms of equity.
This also is a pretty decent argument as for why we shouldn’t overly concern ourselves with math when trying to play poker at a table. The math is either very simple (we have the nut flush draw and thus have around 45% equity) or extremely complicated (against an estimated 10% of his range, we are 75% equity, against an estimated 35% of his range, we have 20% equity, against an estimated 55% of his range, we have 45% equity, balance out the range equity and compare to pot odds to determine our G-bucks). Even in the complicated scenario, it relies on deductive analysis to determine his likely range. In general, we’ll instead rely on the basic math and a generalized “feel” approach to the complicated stuff. But, it’s important to know that G-bucks defines a structural poker concept.
Since writing this chapter in for the initial release of “Easy Game”, it has come to my attention that G-Bucks, as originally written, refers not to our hand’s strength against our opponent’s ranges but the opposite—our range against our opponent’s holding. In terms of understanding the concept, this is somewhat beside the point. What matters is that we’re focused on identifying our equity against our opponent’s range first and foremost. It’s a rather more advanced skill to identify our range’s equity against our opponent’s range (and one that we won’t really need to emphasize until we play against the same strong players every day). Until we hit the nosebleeds, we can take advantage of the practical uses of G-Bucks and focus on range equities.

回复 16# Howard


    老霍，我一直搞不太懂，这个range的顶端时什么？

這個論點的出發點就錯了。

怎麼去「判斷對手聽同花」??，在 flop 我們怎麼能去判斷對手 100% 是聽同花呢???，除非你能通神看到對手的牌，否則只憑對手一次的下注就判斷他是聽同花??哪有這種事~~

如果對手會拿同花兆，看到你 check 之後下注，當然，他也有可能拿著第二大的對子或頂對這樣做，甚至他什麼都沒有，只是看你沒下注示弱想下注偷 pot，這時被 c-r 他多半會扔，我們就多贏了，而且這裡的「多贏」是 70% 以上會發生的狀況。

然後當然，他也有可能認為你拿著同花兆 c-r 而拿比我們落後的牌 call，這對我們來說也是增加 ev 的情況。

不去考慮 80% 以上的情況下會發生的事，會讓我們能增加多少 ev，而去考慮 20% 以下的情況下，我們會損失多少 ev，這不是很沒意義嗎??

所以這樣做，重點不是期望值，而是我們希望要達到的目的，當我們認為我們領先的時候，我們會希望投入 pot 裡面的 $ 越多越好，既然目的已經達到了，還去談對手最後的 call 的期望值??；他之前已經做了二三次 -ev 的舉動，就算最後一個動作是 +ev，也無法改變他要輸錢的事實。