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知其然不知其所以然
先赞一下windstormm的思路，非常清晰，论点也很鲜明。虽然是在反驳我的观点，但我必须要说我是同意并赞赏其中多数内容的。
mathematical models are all based on assumptions. Most of time they are not exactly the same in real cases.
I am guessing Howard averaged all odds against other hands to calculate the overall odds for each hand. This is assuming all hands in the list are uniformly distributed, meaning every hand has equal chances to call (he actually use a special case of that, 100% chance for each hand to call). This is clearly not an accurate assumption. A 7 A 8 will not call your all in all the time and 10 10, 9 9, 8 8 will not either but will call more often than not, because people over play small pocket pairs much more often. This is especially true when the pusher's stack is larger. Are you going to call off half of your stack with A 7 or 99 88? This is also why in my opinion KQ is much more appealing than 33. To compute an exact methematical model, you have to give out the probability of each hand that might call your all in and computer the weighted odds instead of the average of all odds. Is that easy? absolutely not. Because different people on your table will give you totally different probabilities.
In all, using a simple almost naive math model to rank the hand is not only inaccurate but also misleading. I would use this list with extreme caution.
我那篇《排名》所用的方法，的确如你所说，是先假定一个range，假定有且仅有一个对手，然后再假定他在这个range中100%会call，不在range则100% fold。注意这并不是说对手在这个range中uniformly distributed，因为我假设你是KQ的时候对方有16种可能AJ，却只有12种可能AQ。可以算作naturally distributed吧。当然最终赢率更不是针对单手牌算出来后再平均，而是考虑了这个naturally distributed的权重平均。
这些假设有一个问题，windstormm已经提出，就是不符合现实牌手的行为方式。他即使在range内，也未必要100%跟；即使不在range，也未必100%扔。他跟牌可能性的大小跟牌力有关，range里面AA/KK等牌，他一定要跟，AJ，99之类中等牌力，可能只有70%可能性，再弱一点到33，KJ，可能只有50%了；跟筹码绝对大小也有关，他跟一下只损耗他筹码的的10%，他跟的可能性就大，如果要伤筋动骨，就小；跟筹码相对大小也有关，他已经是绝望的最小筹码，他很可能跟，如果是中等大小，很可能就扔；跟他的风格有关，松就跟的多紧跟少；跟他上几次比赛的经历也有关，如果他连续3次比赛都是99最后一手牌，这次他再见了99可能有心理障碍会扔，88反而会跟；跟他对这场比赛的期望值有关，他只想混进钱圈，还是想争取夺冠；跟其他大量的随机因素也有关，比如他最近的心情，他老婆跟他的关系，他最近的经济状况，他的狗是不是生病。。。。
这些无数的因素，要都考虑进去才能做出“完美”的模型。有些因素是可以考虑进去的比如说筹码，但是有些因素根本无法量化。不过这并不妨碍我们做一大堆的假设，然后从最容易的角度入手考虑问题，就可以得到一个近似的结果，至少是一个方向。这有点像中学物理力学，总是假设光滑平面，空气阻力，摩擦力均为零，完美球体完美平面，任何弹簧/滑轮/铰链总是完美设计，现实中有这样的东东吗？没有。但是，这些假设是必要的，不做这些假设，就根本连分析问题的“入手点”都没有，只能“凭感觉”了。这些假设是不是“simple and naive”？我觉得也可以说是，但是我还真就喜欢这种naive的方法，呵呵，它毕竟是研究任何复杂问题都绕不开的第一步。
"I would use this list with extreme caution"，这个我是绝对同意的。我也觉得没有人会背诵这个list然后按照它行事，更何况list中也没有说你什么情况下应该推前百分之多少的牌。它只不过是针对特定range的排名而已。这个list有没有改进的余地？太有了。我做这个list的意图只不过想表明，在特定对手range下，你先push时的牌的好坏有时未必如你想象。比如，中等suited connector好于A-rag。
I also disagree with only trying to maximize your chip gain in touney like you do in cash. In cash, you go all in every time when you are with 51% chance vs 49% chance you will always be winning. Totally true. But in touney, totally not true. Let us assume you always go all in AA vs 22. you have 80% chance to win the pot. Great. Now if you do that 6 times in a touney (totally possible for large MTTS 1000 people because there is always bigger stack waiting for you out there), you have 0.8^6 time chance to stay after all in 6 times. What chance does that give you to still be in alive? 0.2621! did you imagine this number? If you always wait for good hand then go all in with it, you have small chance to make it to the end even with 6 AAs. Of course this model is naive as well because of the simple assumption but it gives you an idea. Now do you think it is still wise to go all in with 55% vs 45% all the time? I would be pushing with 45% of chance winning, but prefer not to calling with 55% chance winning if it is for my entire stack. Because this fold equity is so important in the game, it alters the touney play completely vs cash game.
你also disagree的这个论点我also disagree。如果你是在disagree我，我想可能是误会了，我从来没有说过maximize your chip gain是比赛中的要务，相反我在以前的文章中多次提到比赛合适机会甚至可以fold AA。我的模型是按照chip EV计算的，只不过是因为，money EV没法算，要考虑别人的筹码分布等等，可以说又是一个naive的假设把。
fold equity也是考虑到了的。如果你先推，首先有一点很明确，那就是无论你推72，还是推AA，对手给你的fold equity都是完全一致的。所以你不必考虑他fold的情况，只考虑他的calling range就够了。这也是为什么中等suited connector好于A-rag。因为他只要跟你，多半就大米呢特了你的A-rag，即使在单挑中，A-rag是比中等suited connector好得多的“hot-and-cold”的牌。 |
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楼主
