Head Up Theory Question

[reubenf]

You're stopping at 110 raises with KK if your opponent hasn't looked at his cards yet?

[scottgiese]

I never studied much game theory, but the answer seems clear enough to me: none. Same for pot limit.

Why?

Because here you've got unlimited money, and yet you're playing an ultra-low-stakes version of the most boring card game I've ever heard of -- one where you only get one card in the first place and it's going to take the dealer like a week to shuffle the deck between hands. Ever seen a 1,000,000-card deck? It's as big as a house!

Come on! Why do you care? Just fold and go play Parcheesi or something.

I didn't need me no fancy equations to figure this one.

[diddle]

[ QUOTE ]
oh wise david, please tell us the answer!

[/ QUOTE ]

i don't think this game has been solved yet

[Shoe]

20 bets is still way too low, IMO. I agree 900,000 bets or whatever is wrong.

[reubenf]

[ QUOTE ]
20 bets is still way too low, IMO. I agree 900,000 bets or whatever is wrong.

[/ QUOTE ]

Have you backed that up with any math or reasoning or anything at all other than that it feels wrong?

[David Sklansky]

To answer these questions more easily, just assume that any bluffs be done with a frequency minutely below optimum. Then there is no folding. Most game theory questions can be answered this way. The simplification is especially useful when analyzing the pot limit variety.

Also in the original question I shuld have said that you are playing an expert who knows that you are also an expert. Just in case that changes anybody's answers.

[PairTheBoard]

Why is there no folding if bluffs are done at a frequency minutely below optimal?

PairTheBoard

[cheapsuit]

well, it would seem that mathematically if you put in more bets past that point youre setting yourself up for a big let down if he has aces. just playing the odds it figures that thats the maximum amount of bets you could safely put in. what i mostly mean with my example is that you cant raise indefintely unless you have the nuts--this is how it leads back to sklansky's question.

on the other hand, i cant tell if youre being sarcastic. its like 4am and i am not asleep like i should be so i may just not be picking up on it.

[bigjohnn]

I dont usually post on forums, but I've found this debate so interesting that I thought I'd throw my ideas into the hat.

I only have an answer for the first part of David's question, not the pot-limit part. Furthermore, I dont claim that this is definately the correct answer- I've just tried to put my thoughts down. I'd appreciate any comments about it. Also, I am still not sure where people such as reubenf are getting the figure 20 from. They may well be right, but I've not seen a post detailing the full logic behind their answer. Again, it would be great if they could explain it.

And so to my answer:

Both players have a strategy, S1 for the player (us), and S2 for the expert we are playing against. As a player, we want to devise a strategy such that it maximises our expected value from the hand. Maximising the EV of this hand is equivalent to maximising the size of your bank-balance once the hand has been completed i.e.

The player chooses strategy S1 to maximise:

BankBalance(Before Hand) + EV(S1,S2)

Where EV(S1,S2) is the expected value to player 1 given strategies S1 and S2.

Now, we know that the bank balance before the hand is played is infinity, therefore the player is choosing S1 to maximise:

Infinity + EV(S1,S2)


It is the case that Infinity + X (where X is any real number) equals Infinity. Therefore, whatever strategy player 1 plays (i.e. however many raises he makes) the expected value of his bankroll at the end of the hand is the same.

I therefore belive that it really doesnt matter how many raises you put in.

Feedback appreciated.

[reubenf]

[ QUOTE ]
what i mostly mean with my example is that you cant raise indefintely unless you have the nuts--this is how it leads back to sklansky's question.

[/ QUOTE ]

If your opponent doesn't look at his cards, why not? What has changed after you put in 110 raises that you suddenly thing the 111th will not be for value?