Helmuth - Ferguson Head Up Match Theory Question

[alanbrown]

I certainly didn't intend rudeness. I think I tried too hard to interpret what you meant. I was trying to state that there were some red herrings in your explanation that served to confuse the fact that your conclusion was correct and that your premises didn't lead to your (correct) conclusion.

[almostbusto]

w/e no harm no foul.


but i still maintain i pwned this problem. i am pretty sure i am the first poster to correctly answer the question (other people said independent but nobody said IID) and i was the first to show directly why "being more aggressive" would hurt your chances of winning the match.

further brag, my first example in the snyder post is the most simple proof of snyder being wrong that i have read yet by far. of course its one of the least useful proofs. like i give a [censored] though [img]/images/graemlins/tongue.gif[/img]

[David Sklansky]

Goodness. What is wrong with everybody? The question was simply how should you change your strategy in a five game match when you have to win one game compared, to a one game match where you have to win one game.

And the answer is that unless your opponent changes his strategy, the strategy that works best for one game works best for all five. I don't care if its poker, chess or tiddliwinks. If you insist on math, you simply need to minimize the other guys one game chances, taken to the fifth power. x to the fifth gets smaller as x gets smaller. Duh.

[almostbusto]

[ QUOTE ]
Goodness. What is wrong with everybody? The question was simply how should you change your strategy in a five game match when you have to win one game compared, to a one game match where you have to win one game.

And the answer is that unless your opponent changes his strategy, the strategy that works best for one game works best for all five. I don't care if its poker, chess or tiddliwinks. If you insist on math, you simply need to minimize the other guys one game chances, taken to the fifth power. x to the fifth gets smaller as x gets smaller. Duh.

[/ QUOTE ]

um its not true if the legs of the match aren't IID. the legs of this match obviously are IID but the whole reason why what you say is true is because they are IID. thats the whole proof. you need to establish that its IID. i established it by saying its a binomial variable...


whatever, this is my last post in this thread. this question was probably the easiest that i have seen sklansky post yet even the people who knew the answer didn't seem to have a grasp on why the answer was the answer.

[Piers]

[ QUOTE ]
Goodness. What is wrong with everybody? The question was simply how should you change your strategy in a five game match when you have to win one game compared, to a one game match where you have to win one game.

And the answer is that unless your opponent changes his strategy, the strategy that works best for one game works best for all five. I don't care if its poker, chess or tiddliwinks. If you insist on math, you simply need to minimize the other guys one game chances, taken to the fifth power. x to the fifth gets smaller as x gets smaller. Duh.

[/ QUOTE ]

Despite this appearing to be another of your flogging the bleeding obvious posts, I have to be impressed at the number of people you have found to disagree with you.

[CityFan]

[ QUOTE ]
OK. I am now ready to hear explanations on your answers. And a guess as to why I see an analogy with the Snyder head up situation. And a theory about what is going on in the heads of the people who are screwing this up. It seems like there is a specific fallacy operating and it should have a name. And forgiveness for lying when I said I have to think about this.

[/ QUOTE ]

Go on then... what is your theory?

I think I would call the fallacy something like "paradigm worship" (thanks, thesaurus).

People are very attached to the idea that they can play individual hands in ways that will have higher or lower variance but similar expectation. They therefore don't see that the only important statistic about a binary trial (e.g. winning or losing a HU game) is the probability of success. They try to transfer their ideas about variance.

The Snyder analogy is because, in that case, the optimal strategy is to maximise your expected chip gain on each hand by playing poker rather than trying to somehow harness variance by going all in. That's only true because of the linear heads up equity result.

And it was so obvious you were lying it isn't even funny.

[diddle]

[ QUOTE ]
Goodness. What is wrong with everybody? The question was simply how should you change your strategy in a five game match when you have to win one game compared, to a one game match where you have to win one game.

And the answer is that unless your opponent changes his strategy, the strategy that works best for one game works best for all five. I don't care if its poker, chess or tiddliwinks. If you insist on math, you simply need to minimize the other guys one game chances, taken to the fifth power. x to the fifth gets smaller as x gets smaller. Duh.

[/ QUOTE ]

Whyd you ask the question? The answer is trivial. Was this some sort of practical joke to make the people using complicated math look pompous and stupid? Congratulations on using your position to make people look dumb.

[George Rice]

[ QUOTE ]
Poker is closer related to Backgammon than to Chess. Comparisons should only be drawn to games of incomplete information.

[/ QUOTE ]

Backgammon is not a game of complete information?

[Bantam222]

If my opponent isn't going to change their playing style, you should play it exactly the same. If you played the first match to the best of your ability, playing the same game will give you the best chance of winning.

[Shandrax]

[ QUOTE ]
I don't care if its poker, chess or tiddliwinks. If you insist on math, you simply need to minimize the other guys one game chances, taken to the fifth power. x to the fifth gets smaller as x gets smaller. Duh.

[/ QUOTE ]

In chess this simply doesn't work. By minimizing the other guys chances you minimize your own chances also and the game will end in a draw. Since draws don't count in a match you will play on forever this way, just like Karpov did.

Even though Karpov had a huge lead, it was similar to a must win situation for him (with some sort of safety net). In order to win in chess you have to unballance the position. That may lead to an unclear position with equal chances or an unclear position that's either won or lost, but you cannot apply normal distribution and standard deviation on it, because from this point on it's all about better judgement.

Also there are factors outside the game that may have a huge impact on the result. In the Kramnik-Leko match, Kramnik lost a game, because he didn't have his computer analyze a specific position long enough. Now try to incorporate this into Leko's expected winning percentage. Still such little things are the reasons why chess matches on the highest level swing one way or the other.

If you visit the Kramnik camp and tell him something about 0.5 to the 5th power, he would smile, pat you on the back and send you back home.

The reason why your advice works for poker is the blind structure. There is no draw in poker. If it wasn't for the blinds going up, your imaginary players of equal strength would be pushing chips back and forth forever.