Head Up Theory Question

[donkey69]

The unexpoitable strategy is not difficult to find. In fact its staring everyone in the face but they fail to realise it. Case of missing the forrest for the trees. The following strategy WILL DOMINATE ALL OTHER STRATEGIES in the long run. No ifs or buts. It will be EV+ against ANY other strategy. It will be EV=0 against itself.

Basically its a tight aggressive strategy:
If you draw 1: Fold
If you draw 2-999,999 check if you are first mover and if the other person bets call it.
If you draw 2-999,999 and are second mover, call the bet if there is one.
If you draw 1,000,000 raise infinitely until you are called.

Reasoning:
Folding the 1 is obvious since you are the dog with certainty.
Limiting the betting to maximum of 1 round for 2-999,9999: since you know you dont have the nuts but the other person may you try to limit your lossess as much as possible. On average you will beat your opponent half the time and he will beat you the other half. Should break even in the long run.
1,000,000 The Nuts: All bets made and reraises made are EV+ so you want as much action as possible.

I believe the above strategy will beat all the other strategies mentioned above. If both players are expert players betting should not proceed for more than 1 round.

[marv]

Why do people assume you never fold the 2nd nuts?

Here is an example where one can bet and fold to a raise with the 2nd nuts:

limit
ante 1 dollar
no blinds
10 cards
max 4 bets/raises
unlimited bankroll

This is small enough to solve exactly, and part of an optimal strategy is: with the second best card, bet 21% of the time and always fold to a raise. This strategy is unexploitable and loses 8% to the person who acts second.

We can solve the same problem with 100 cards, and you can also fold to the 4th raise some of the time with the 2nd nuts and be unexploitable.

I can even give you a 'preflop holdem' example where you fold one of the really big hands in case oppo has AA.

Marv

[Stephen H]

[ QUOTE ]
Why do people assume you never fold the 2nd nuts?

[/ QUOTE ]

I'm not assuming anything; I'm certainly open to the idea that you would fold the 2nd nuts in some small percentage. I do think that folding the 2nd nuts at a rate of 1/pot on the Nth bet is far, far too large, and I'd be interested in where the value actually is, or if the parameters of this game make it so you never fold it.

[Stephen H]

[ QUOTE ]

Limiting the betting to maximum of 1 round for 2-999,9999: since you know you dont have the nuts but the other person may you try to limit your lossess as much as possible. On average you will beat your opponent half the time and he will beat you the other half. Should break even in the long run.


[/ QUOTE ]

This strategy is easily exploitable and is an obvious loser. The statement "Should break even in the long run" is incorrect; the times you're calling a bet you'll be behind a lot more often than 50/50; the times you're ahead, the action will go check/check and you'll win less than you lose in this range, on average. The bets you win on the nuts hand will not nearly make up for the huge number of bets you lose here, one bet at a time. Calling a bet with this many low cards is terrible.
Also realize that a strategy tailored to exploiting this one will ALWAYS fold to any bet or raise, as that means you have the nuts, so you will make almost nothing the one time in a million that you have the nuts.

[diddle]

You have 9. You bet.

I am acting second. I have an unexploitable strategy for the second player which involves raising the first bet with 8,9, 10 every time.

How is folding a 9 ever part of a correct strategy?

Enlighten me

[diddle]

any strategy involving folding 999,999 is exploitable

[Jefzter]

[ QUOTE ]
Yes, as long as you are always dealt card 999,999 while your opponent is dealt a better card only one time in a million. Congratulations on devising a strategy that will give you positive EV under those conditions!

[/ QUOTE ]

Thanx but I didn’t really devise a clear strategy but instead debunked the, for lack of a better term, “bet for information system” that several other posters kept bringing up while insinuating I was idiotic for not taking it into account. Of course it only deals with getting the 999,999 card in the game Mr. Sklansky described.

[ QUOTE ]
Next, try to figure out how you can average $1 EV a hand playing 30/60 holdem when you are always dealt KK.

[/ QUOTE ]

I’m the first to admit that this is way out of my league. I have no idea how to add in table position, number of players in the hand, my relation to the betters, who has called and who has raised, the perceived betting personalities, and other pertinent information I might have in said situation into a standard formula that should give me an idea of what I can expect. If there is a way or an answer, please enlighten me.

[diddle]

which post is the sarcastic one?

[reubenf]

[ QUOTE ]
[ QUOTE ]
Yes, as long as you are always dealt card 999,999 while your opponent is dealt a better card only one time in a million. Congratulations on devising a strategy that will give you positive EV under those conditions!

[/ QUOTE ]

Thanx but I didn’t really devise a clear strategy but instead debunked the, for lack of a better term, “bet for information system” that several other posters kept bringing up while insinuating I was idiotic for not taking it into account. Of course it only deals with getting the 999,999 card in the game Mr. Sklansky described.

[/ QUOTE ]

You didn't debunk anything. And it's not betting for information so much as it's betting for value while taking all the information you can into account. And it's far better than betting and just ignoring all the information you're getting.

[ QUOTE ]
[ QUOTE ]
Next, try to figure out how you can average $1 EV a hand playing 30/60 holdem when you are always dealt KK.

[/ QUOTE ]

I’m the first to admit that this is way out of my league.

[/ QUOTE ]

It's out of your league to figure out how to make $1 at $30/60 with KK? Do you not get that this guy is making fun of you? Do anything but fold it. Anything at all works. He's comparing your strategy to realizing that you shouldn't be folding KK too often. But just like never raising and always calling with KK, your play with 999,999 is TERRIBLE even though it makes you money.

[M.B.E.]

What Marv and Stephen H said makes conceptual sense.

I'd be pretty surprised if the optimal strategy involves folding 999,999, but it is conceivable.