Another AA hand

[danzasmack]

i got this pm too. so much for feeling special.

[Municipal Hare]

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i got this pm too. so much for feeling special.

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Sorry. I'm such a whore. I sent those three AA hands to ILP, kapw7, and you, becuz y'uns guys are my favourite posters. May I make amends by writing you a haiku? Limerick? Trope?

[rzk]

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whaaaaa???? how's that possible that in a two-person game with limited raises that there's no Nash equilibrium???? either you are really drunk or i'm missing something very fundamental. btw, i didn't take classes in GT, just read some stuff on my own so i might certainly be missing something. but i still think you are just too drunk

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Doesnt matter for this post that much.

But in a 2-person game with "limited" (finite) strategy sets there is not necessarily a Nash equilibrium in PURE strategies.

Thres is always at least one in MIXED strategies.

For one to ALWAYS exist in PURE strategies you neeed a compact and convex strategy set for each player and quasiconcave payoff functions for each player.

Since the strategy sets in LHE are not convex that result does not hold and you can have spots where pure Nash equilibria doesnt exist.

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sorry i didn't see you were talking about _pure_ strategies. i guess i didn't notice it because it really doesn't make sense to talk about pure strategies when we were discussing playing against a perfect opponent. i thought you were saying that for some reason a truly perfect strategy doesn't exist, which would of course be really weird.

anyway, doesn't matter now. so you agree that against a perfect guy c/c is the best? if so, what assumptions are we making about the imperfection of the actual guy that make us want to b/f or b/c c/f or do anything other than c/c?

[Oink]

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anyway, doesn't matter now. so you agree that against a perfect guy c/c is the best?

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I need to see some formal proof of that to be convinced

[rzk]

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anyway, doesn't matter now. so you agree that against a perfect guy c/c is the best?

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I need to see some formal proof of that to be convinced

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ok i'll give it a shot. suppose both opponents put each other on AQ, QQ,KK,AA and let's say you decide to bet. if he has AQ and knows that you will fold AA then he has a profitable bluff-raise. however, if you know that he _always_ bluff-raises AQ then you have a profitable call-down with AA. this shows that there exists some fraction of the time for which he should bluff raise AQ to make you indifferent between b/f and b/c and there exists some fraction of the time for which you should call a raise with AA to make him indifferent to bluff raising AQ.

because of the large pot size the fraction of time he has AQ when he raises is rather small, usually he'll have you beat but you are still indifferent to calling down. this shows that in the b/c down or b/f line (doesn't matter which since he made you indifferent) you lose almost 3BB starting from the turn if he raises.

now, suppose you decide to check. similar arguments show that he will adjust his bluffing with AQ to make you indifferent to calling down. but this time you lose a little less than 2BB starting from the turn if he bets when you check.

so for the times he has you crushed OR decides to turn his AQ into a bluff you lose 1BB more if you bet than if you check.

the only time when betting might be better than checking is when he has AQ _and_ he doesn't want to turn it into a bluff. if you bet he'll call down and if you check, he'll check. so in this case you win 1BB more with the bet line.

but because there are more situations of the first type than of the second type, overall you would be losing with the bet line compared to the check line.
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but frankly, i don't care much about the perfect guy, the perfect strategy is only a default starting point. i'm much more interested in what assumptions you are making about the actual live guy.

[Oink]

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the only time when betting might be better than checking is when he has AQ _and_ he doesn't want to turn it into a bluff. if you bet he'll call down and if you check, he'll check. so in this case you win 1BB more with the bet line.


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But this is whats happening most often when he has AQ, right?

Still not convinced.

From what I read you are only treating his bluff frequencies. Not his call down and check behind frequencies.

It should be pretty clear that bet gains on check whenever he checks AQ but calls a bet.

So far you just fifured out that ckeck is better than bet when he bluffs?

[rzk]

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It should be pretty clear that bet gains on check whenever he checks AQ but calls a bet.

So far you just fifured out that ckeck is better than bet when he bluffs?

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but the quote you quoted deals precisely with that situation, so let me quote it again [img]/images/graemlins/laugh.gif[/img]

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the only time when betting might be better than checking is when he has AQ _and_ he doesn't want to turn it into a bluff. if you bet he'll call down and if you check, he'll check. so in this case you win 1BB more with the bet line.


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as for
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But this is whats happening most often when he has AQ, right?


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if you count the combos you'll see that there are more situations where betting loses 1BB than those where it gains 1BB. that's what i meant with

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but because there are more situations of the first type than of the second type, overall you would be losing with the bet line compared to the check line.


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but the clearest way to see it is to realize that you are an underdog to his range. this is the same as saying there are more combos when you are behind than those when you are ahead. plus of course, you have to take out some fraction of combos where you are ahead and add them to the combos where you are behind since he'll turn them into bluffs.

[Oink]

yes but since he doesnt bet AQ everytime and to make hero indifferent between calling down and since he doesnt bluff raise AQ every time it happens fairly often that he calls a bet with AQ and checks behind AQ.

As said. You need to consider those as well. Not just how much it cost to get bluff raised and bluff bet.

Either I misunderstand you, or you are way off. Prolly the first

[rzk]

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As said. You need to consider those as well. Not just how much it cost to get bluff raised and bluff bet.


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but the quote above (where i made some stuff bold) deals specifically with those situations, it doesn't deal with bluffs. bluffs are dealt with earlier in the argument.

sorry if i'm being hard to follow. also, i have a stupid habit of editing my posts in an attempt to make them clearer when somebody has already read it and is writing a reply. i really need to stop doing that [img]/images/graemlins/grin.gif[/img]

[Oink]

ok so we agree.

Sounds probable. Altho I am always suspiciuous untill I am presented with formal proof