Helmuth - Ferguson Head Up Match Theory Question

[marv]

[ QUOTE ]
-Knockwurst

i agree with your position on the snyder match.

example for people who don't think so.

person A has stack of 9 chips
person B has stack of 1 chip

blinds are 100/200

there is no skill. its a coin flip test no matter what. the contention that person A has higher than 90% winrate is wrong obviously.

[/ QUOTE ]

You're right that once the small blind exceeds the number of chips in play that all skill is removed.

But you're wrong about the probability of the large stack winning. With 90% of the chips he will win the tournament *exactly* 90% of the time.

Prop bet?

Marv

[almostbusto]

[ QUOTE ]

You're right that once the small blind exceeds the number of chips in play that all skill is removed.

But you're wrong about the probability of the large stack winning. With 90% of the chips he will win the tournament *exactly* 90% of the time.

Prop bet?

Marv

[/ QUOTE ]

reread. i am saying what you are saying... i think you missed the word 'higher'. that or you don't realize that 90% is not higher than 90%.

[marv]

[ QUOTE ]
[ QUOTE ]

You're right that once the small blind exceeds the number of chips in play that all skill is removed.

But you're wrong about the probability of the large stack winning. With 90% of the chips he will win the tournament *exactly* 90% of the time.

Prop bet?

Marv

[/ QUOTE ]

reread. i am saying what you are saying... i think you missed the word 'higher'. that or you don't realize that 90% is not higher than 90%.

[/ QUOTE ]

Ah yes, sorry. My mistake.

Marv

[David Sklansky]

"answer is super easy if you have taken a 100 level stats class.


the result of a heads up match is a binary variable (1 = win, 0 = loss). this means the results of a heads up match follows the binomial distribution. moreover, standard deviation of a binomial variable is sqrt(n*P*(1-P)) where n is your sample size. this means that variance is maximized when your winrate is 50%. so people who think they can lower variance by playing less optimal are mistaken. play as optimal as you can and you will maximize the probability that you win that leg of the match and the match itself.

so in short: maximize your edge over the other guy and you will maximize your chances of winning AND minimize your standard deviation (that is to say its the min standard deviation you can achieve while still being a winning player, i add this caveat because everybody could have a standard deviation of 0 if they forfeited every match).

so if you were maximizing your edge the first match, and he hasn't changed, then you shouldn't change."

I hate your answer.

[Karmic]

You have 4 matches you can afford to lose, he must win every single match. It is difficult to accept that he wouldn't vary his play at all, but even assuming that is true I believe you want to maximze the number of decisions he has to make that put his tournament life at stake. Playing more aggressively will do this. He can correctly call you and win the hand 4 times before you are in danger of losing. One mistake, or even a correct call that you win anyway and he's out.

The situation is really only slightly different than a large stack vs small stack situation. However, if you fall behind on one of the tournaments you can push hard and if you happen to lose you get to start over the next day with even stacks.

[almostbusto]

-David Sklansky

1st, why do you hate my answer? is it wrong?

i mean if its right there is nothing to hate, unless you hate truth. are you jealous that my answer is way more elegant that all the poker mumbo jumbo you were going to pull out to prove a simple truth through a complex argument?

or (and this may be more likely) have i used some fallacy myself?

[alanbrown]

Each game is a completely independent event. The optimal strategy that would win the first game is therefore the same as the optimal strategy that would win the nth game. The key term here is 'independent'. Each game starts off with the same conditions. Each game has the same goal - win that game. Of course, 'strategy' here encompasses the myriad different ways of handling different situations.

And, David, I'm glad to hear you you didn't actually need a few days to go away and think about this. Very Glad!

[Karmic]

The games are certainly not independent. If you are saying we play 5 games and the best 3 of 5 wins each game is technically independent but still may be influenced by play during the earlier games. Also, winning the first game doesn't necessarily mean you played under the optimal strategy to win the game, only that you won.

Maybe I'm throwing in too many outside influences into a philisophical problem but I think the conditions set forth allow that not only should you not play each game exactly the same way, it might be correct to play each of the 5 games in a decidedly different way to maximize your chances of winning at least 1 more of the 5.

[David Sklansky]

"i mean if its right there is nothing to hate, unless you hate truth. are you jealous that my answer is way more elegant that all the poker mumbo jumbo you were going to pull out to prove a simple truth through a complex argument?"

Are you talking to ME?

[almostbusto]

[ QUOTE ]
"i mean if its right there is nothing to hate, unless you hate truth. are you jealous that my answer is way more elegant that all the poker mumbo jumbo you were going to pull out to prove a simple truth through a complex argument?"

Are you talking to ME?

[/ QUOTE ]

yes.

it just sounds weird to hate answers. answers are either right or wrong. that usually how they are classified. so is my answer right or wrong in your eyes?

if its right then its just as good as your answer. assuming yours is correct. if your answer requires talking about poker though, it suffers from a defiancy that mine does not, since my is generalized to any binomial contest.