Helmuth - Ferguson Head Up Match Theory Question

[Michael Davis]

In real life nobody gives a crap that they have to waste an extra day or two to win the match. Besides, even if they wrap the thing up early, some wellknown poker pros will just spend the extra time blowing the money on streetwhores and horses. It's like reverse implied opportunity cost.

-Michael

[Shandrax]

All-in EV is all about how often you get called and win and how often you don't get called and steal the blinds. Winning chances against total random hands don't tell you anything.

[Lee_C]

I would set a more aggressive image as to make my opponent feel that I might be loose, but in the end I would continue to play my game plan.

[StregaChess]

"For the sake of this question we will assume that both you and your opponent are tough players of approximately equal skill and playing styles."

That being the case my pushbot plan is not as valid.
I’m sure Mr. Sklansky would prefer some sort of mathematical reasoned out response, sorry can’t oblige you there (just don’t have the skills).
What I can do is reason this out a bit, so if I’m a weak player in the larger scheme of things (which is true) a pushbot would be the best approach.
Since the opposite is true we are actually peers I’m leaning towards the opposite approach and playing tight. If we are equals playing tightly would force him to come to me and decrease my chance of losing five matches in a row. So without proof per say, that’s my gut…

[alanbrown]

I'm not sure I can claim to know you well but I think I know why you didn't like Busto's answer...

Busto's reference to the binomial distribution was unnecessary. It doesn't enter into the logic required here and therefore only served to confuse. Throwing in unnecessary equations changes the landscape of the discussion to Why Is This Equation Unnecessary, rather than What Is The Answer To The Solution. That is what is to be disliked about his answer.

[ QUOTE ]
variance is maximized when your winrate is 50%. so people who think they can lower variance by playing less optimal are mistaken.

[/ QUOTE ]

I have no idea what this is trying to communicate.

[ QUOTE ]
play as optimal as you can and you will maximize the probability that you win that leg of the match and the match itself.

[/ QUOTE ]

Agreed. Though the question we're trying to answer is does Play As Optimally As You Can change as you accumulate more wins.

The simple key here is 'independent events'. If each game is an independent event with the same starting conditions (chips, who deals, randomness of cards, rules) and the same goal (win the other's chips), then the optimal strategy must not have changed to succeed at it.

Let's imagine that the villain has amnesia and has no memory of previous games we've played or what the current scoreline is. His game is optimized to win This Game. Not a series of games. There is no 'series of games' to him. Just this one. And our strategy that is optimized to win This Game can not be improved upon by knowing we won't need to win another one afterwards.

All the points Busto made about variance and probability are unrelated to this issue. And unrelated points are harder to refute than false ones. I think that's why you hated his answer.

[CityFan]

I know, that's why I said it was so unscientific.

Still, it's a horrible strategy

[CityFan]

[ QUOTE ]
All-in EV is all about how often you get called and win and how often you don't get called and steal the blinds. Winning chances against total random hands don't tell you anything.

[/ QUOTE ]

Winning chances against random hands ARE important (well, it depends on the question), because they dictate the strategy that your opponent will take. It's you who has the random hand, and he has to decide which hands to call with.

[alanbrown]

That is Indeed the question. But the answer is the same for game 10 as it was for game 1. Pushing with the right SC number is never wrong, but it may not be optimal. As to what to do if he moves in on you, well, what you need there is the Reverse SC Number [patent pending! [img]/images/graemlins/wink.gif[/img]]. This number would say that if you have holecards H and for an opponent that was pushing the top x% of his hands, you should call any all in up to $Y. Turns out this numbers isn't hard to calculate.

As an example, let's say you hold 23o and you're the BB for 2k and the button goes all in 2/3 of the time. You should call if the call requires less than 4.5K. If it's more then you should fold.

If you have Q5s in the same situation, then you should call any AI raise of up to 23.5k.

Of course, these numbers aren't the answer to optimal strategy. Just a way to find and plug some of the more severe leaks.

[StregaChess]

[ QUOTE ]
The simple key here is 'independent events'......

Let's imagine that the villain has amnesia....

[/ QUOTE ]

The first part is true, the second never is....

This scenario has a real world corollary in Chess. In their first battle together for the world championship Karpov – Kasparov squared off in 1984, Karpov jumped out to huge lead of 4-0. What followed was 17 consecutive draws and Karpov pushed the score to 5-0, one more win and match is over. The match turned bizarre after the 5th win, strange early draws, and psychological pressure and finally after a total of 48 games the match was stopped with the score 5-3 and neither player declared the winner.

[alanbrown]

That's a fair point. The idea that the optimal strategy remains the same, assumes a rational opponent. Psychology is a much bigger part of poker than chess, so optimal strategy might change for that reason. But in that case it would change based on the specific opponent and no general advice could be relevant.