Head Up Theory Question

[reubenf]

[pokerrookie]

I had this exact same thing happen to me the other night. He turned over 1,000,000, and I no longer have unlimited money in front of me.

[thrillhouse7]

It would be very difficult to shuffle that deck

[bramj]

I don't believe the question is well-posed. What does expert mean? Does it mean that he knows which strategy you use for bluffing and what strategy to counteract his bluffing? Or does expert mean that he has some game-theoretic optimum against a variety of tactics?

Also the infinite amount of money is making the problem worse. Both players can raise for any finite amount of time *say 3 zilion times* and then they have exactly the same amount of money left.

Maybe we should learn from the question: in making analysis of poker situations, we should take in account "personal" factors, such as bankroll, risk aversion and willingness to bluff as well as specific assumptions about how people will bluff and deal with a bluff.
Or to pose this as a question: which variables are relevant to your decisions? in which cases does a game-theoretic unique solution with regard to bluffing and countering bluffing exists? What behaviour is relevant in opponent modelling? What are realistic assumptions?

[jthegreat]

[ QUOTE ]
If two expert players play the game then, they will play the "optimal mixed strategy" which is simply a probability density of how frequently they should play each pure strategy. Note: the optimal mixed strategy may not be unique, but the optimal value of the game will be.


[/ QUOTE ]

So what I said was correct, it just wasn't thorough. The optimal strategy depends on what the other player does, and without more information, you can only define that in terms of the probability of him playing certain strategies.

[NYCNative]

[ QUOTE ]
You and another player ante a dollar and both have unlimited money in front of you. You are both dealt one card from a deck where the cards are numbered from one to a million. You are dealt 999,999. You bet and get raised. How many times should you reraise, a dollar at a time before you just call against an expert? What about in Pot Limit?

[/ QUOTE ]I call shenanigans, Ms. Sklansky. You don't say what wins here. Maybe it's lowball! Trick question!

If it's not lowball, my earlier comments stand: I have literally a one in a million shot of losing this one so I am not stopping for anything.

If it is lowball, fold preflop. [img]/images/graemlins/smile.gif[/img]

[NegranuFan]

I agree fully with those who posted earlier saying that the answer does not exist...not even maththematically.

lets say someone eventually wins the pot of X dollars:
Infinity (+/-) X = Infinity

Therefore I quit waisting my time and go grab some low fat organic frozen yogurt.

Now if you each had a finite number of tournament chips and you were playing against extremely honest aliens to save the world... then its a different story...
How would stack size affect the answer?

[uphigh_downlow]

You can assume that playing against an expert implies, that you have pre-announced your strategy and your opponent knows what you are doing.

This only holds water however if there is a single optimal strategy. If there are 2 or more, then its a harder problem

[Ulysses]

Jefzter, what games and limits do you play?

[David Sklansky]

OK smarty pants, what's the pot limit answer?