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Balance?

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05-09-2019 , 10:39 AM

hyperknit

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Join Date: Dec 2016 Posts: 2,692

I’ve heard this repeated a number of times in different poker books:

“Balance is the result of taking the most profitable line with every hand in our range”

I know that many beginner players think that balance means playing a hand sub-optimally in order to prevent your range from being exploited (and I used to think that way too).

I’m just wondering what makes the above quote true? I’m sure it doesn’t just magically happen...

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05-09-2019 , 11:00 AM

plexiq

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Join Date: Apr 2007 Posts: 2,554

Quote:

Originally Posted by hyperknit

I’ve heard this repeated a number of times in different poker books:

“Balance is the result of taking the most profitable line with every hand in our range”

As quoted here it's not quite accurate, or at the very least misleading. Playing the most profitable line with every hand will NOT automatically result in balanced ranges.

It's true however that in a Nash Equilibrium, by definition, all hands are played with their most profitable line(s).

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05-09-2019 , 02:46 PM

hyperknit

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Quote:

Originally Posted by plexiq

So then according to you, a Nash equilibrium is not automatically balanced?

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05-09-2019 , 02:54 PM

plexiq

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Join Date: Apr 2007 Posts: 2,554

Nope, that doesn't follow from what I wrote.

Every Nash Equilibrium uses only the most profitable lines, but not all strategies that use only the most profitable lines are a Nash Equilibrium.

Last edited by plexiq; 05-09-2019 at 02:59 PM.

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05-10-2019 , 12:04 PM

hyperknit

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Join Date: Dec 2016 Posts: 2,692

Quote:

Originally Posted by plexiq

Nope, that doesn't follow from what I wrote.

Every Nash Equilibrium uses only the most profitable lines, but not all strategies that use only the most profitable lines are a Nash Equilibrium.

My mistake, I made a logical error.
I think I understand what you are saying. Just because the most profitable line need not be balanced- IE when the most profitable line is an exploitive line against a sub-optimal opponent!

Now would it be safe to say that against a maximally exploitive opponent, taking the most profitable line with every hand would result in a balanced range? (By maximally exploitive opponent I’m thinking of “the nemesis” from Mathematics of Poker)

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05-10-2019 , 12:59 PM

plexiq

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If you maximize against a nemesis player then that's going to be balanced, right.

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05-10-2019 , 03:00 PM

getmeoffcompletely

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Join Date: Aug 2012 Posts: 1,670

Balance is simply the end product of two agents maximally exploiting each other such that they reach an equilibrium where they cannot unilaterally improve their ev. A strategy is unbalanced when it allows an exploitative agent to unilaterally improve his ev such that it captures more ev than the equilibrium.

For a small game like RPS its easy to intuitively grasp how to be balanced (ie how to play a nash equilibrium). The confusion comes when someone tries to extrapolate that simple strategy to complex games like poker. Intuition with regards to balanced poker play does not get you very far.

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