Please help me understand this math problem

[HitNRunPoster]

Um, firstly, I'd like to use this hand for the basis of discussion: http://forumserver.twoplustwo.com/showfl...e=0#Post9000035

Here's my approach: We're up against {AA(1), KK(3), AK(6)} and we have AA on ~K54r and we're a 2:1 favourite. Ignoring small factors, we expect to have him slow down with AK if we put in a raise and keep up the betting with KK. However, we can't fold. Obviously, if we can fold, then raise/folding becomes correct, but we can't. So, then here's the math of raising:

As a 2:1 favourite, raising the river gives you: +1*6 -2*3 = 0 ev, and therefore this makes raising the river bad (it's zero EV, but it's increased variance).

Yet, I think in either HPFAP or TOP it says that you only have to be a 55% favourite on the river to raise. I have NO IDEA why they would say that, but I believe it may be because on average they assume that villain will not three-bet frequently. Comments on this would be appreciated.

Shill said that he'd stick in a raise on the turn or river, and he's basically always right, so it pisses me off a little because I don't understand it. How can you guys justify a heads-up raise vs made hands with little possible in the way of changing equity with less than 66% equity, or if you want to simplify this, how could you raise the river with less than 66% equity when the better hands will three-bet you and you must call?

I mean, I can't justify this, but clearly there are those that do... somehow... Please help me understand this.

FWIW, I thought Jaran's idea of donkbetting in a similar spot when OOP with AA was very cool (even though it was in jest), as an attempt to flatten the pot sizes by luring him into raising equally with AK as AA/KK, but it didn't work: http://forumserver.twoplustwo.com/showfl...e=0#Post9002887

[HitNRunPoster]

also, "equity" on the river is kinda useless... for example:

say you have 95% equity because the guy is bluffing 95% of the time with air and has you beat the other 5% of the time. Obviously in taht spot you would never raise, because the only hands he can call you with are the ones that beat you.

So equity isn't the entire picture.

[CrMenace]

Maybe you're not supposed to call if re-popped. Also, maybe the villain doesn't always repop KK?

Just taking stabs here.

[Absolution]

He's assuming you won't get raised in those spots or that when you are raised it's an easy fold. These are reasonable assumptions for river play. You assume you're going to call whe he raises, which means you must think that he is raising the river with a worse hand some time and you're not taking that into account in your math.

[HitNRunPoster]

I'm starting with the premise that people aren't going to fold AA for one bet in a 14 bet pot. No one in the threads that I mentioned ever suggested folding, and therefore I would assume this is true.

So, let's just pretend that I'm correct that no one is folding their AA to a 3-bet.

Now, should you raise with a 66% edge vs AA,KK,AK or not?

--Dave.

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edit:

Jaran:
[ QUOTE ]
My plan would be to trey, and no matter if he caps or not, lead the turn. If raised on the turn, I call down.

[/ QUOTE ]

Niedam:
[ QUOTE ]
If he has KK then it sucks to be you.

[/ QUOTE ] (I assume because he pays off.)

Buzz-cp:
[ QUOTE ]
I think any other line is more expensive when he does have it (such as raising the turn). Folding anywhere is just burning money.

[/ QUOTE ]

Benihana:
[ QUOTE ]
wel, you can 3 bet and see if he caps, which would narrow it down to KK proably, or you could call and rasie the turn, but when he 3 bets your turn raise you will have to swallow the vomit in your mouth.

[/ QUOTE ] Since i can't possibly imagine that beni would vomit after getting off cheaply, I must assume that he's calling down.

Finally, all of Absolution's math suggests calling down when villain puts in the last aggression, rather than folding.

...Interestingly, Shill doesn't respond to whether or not he would fold to a 3-bet. I assume that he would have to call down vs a good opponent (due to potentially being bluffed) and a bad opponent (due to potentially chopping).

So let's just assume that we're not folding, and evaluate the math based on that.

[Jaran]

Dave, What are the chances that he'll 3bet with either AK or the other AA here? And does that effect the math? Additionally, my initial reaction to the hand was to 3bet on the flop. I have since reevaluated and am not sure I like it, but how does a threebet on the flop change the numbers? (I'm a stupid classicist who is too lazy to do math [img]/images/graemlins/tongue.gif[/img])

-Jaran

[HitNRunPoster]

[ QUOTE ]
You assume you're going to call whe he raises, which means you must think that he is raising the river with a worse hand some time and you're not taking that into account in your math.

[/ QUOTE ]

No, actually. There's two flaws with this thinking.

1) He could sometimes raise with AA and so it's a call on the river, although that doesn't factor into the EV of the raise/call, since we chop when it happens.

2) We could theoretically say that he will ONLY put in further aggression with KK and also say that we will ALWAYS pay it off... If it's truth, it's an ugly truth, but this may very well be the case...

[HitNRunPoster]

Yes, him 3-betting AK does affect the math.

That's why I said "ignoring small factors". So he COULD 3-bet AK, though I'd say that it'd be rare.

He could also intend to call with AK but mouse-error raise it, or mouse-error fold KK, or disconnect fold or something.

Ignoring mouse errors, though...

Let's just say that he'll raise with AK 3% of the time (0.18 hands), KK 100% of the time (3 hands), and AA 10% of the time (0.1 hands but you only get half the pot).

Pot will be 13 bets and you need to win 1/14 of the timeish.

(7.4%?)

AK = 5.5%
AA = ....
(1.5%ish makes it about correct to call).

(to be continued... But yeah, it certainly does. As long as you call, the more often he three-bets AK even if its' a small % the better it is to raise)

like, now the math becomes -2*3 + (1*0.97+2*0.03)*6 now it's +EV rather than zero EV to raise.

[HitNRunPoster]

ANYWAYS, BACK TO THE MAIN POINT GUYS: IF WE WERE TO IGNORE THE SMALL STUFF, IS THERE A REASON TO RAISE WITH LESS THAN 66% EQUITY (EXCLUDING CHOPS)?

Just from a pure math standpoint, I'm trying to figure out why TOP and HPFAP say 55% requirement to raise, and the math seems to indicate 66% requirement to raise.

[Shillx]

Dave,

Sorry I haven't replied to your PM. I'm not ignoring it rather I don't want to think about it while doing 23 other things. [img]/images/graemlins/smile.gif[/img]

Brad