Raising the river with less than 66% equity vs strong made hands

[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

[_D&L_]

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Yet, I think in either HPFAP or TOP it says that you only have to be a 55% favourite on the river to raise.


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This is just wrong, wrong, oversimplistic, and wrong. What you have to figure out from a game theory perspective is what % of their hands can they afford to fold, without making it profitable for you to just consta-bet. This depends on pot size (where is that variable? I don't see it...thats reason one why its wrong). And perhaps on relative distributions if they aren't symmetric.

Even if we simplified, and pretended that neither player can fold his hand, 55% equity is too aggressive on the river.

Let do some math:

.55 u have better hand and he calss: .55 * 2bb = + 1.1 BB

(think of a re-raise as a call + raise)
.45 u have worse hand he calls 100% of time: 45*2BB = -.9BB

So far we are + .2 BB

What percentage of the time must he raise for us to break even?

r*2BB = .2BB | r = 10%

Thus, even if an opponent calls with EVERY ONE of his worst hands, as long as he re-raises with 10% of his best hands, you will LOSE MONEY.

Most players are actually capable of folding sub-par hands, and will re-raise more than 10% of their strongest hands. THus, on both fronts the 55% proposition from that book, wherever i read it (is it one of skalansky's?) is wrong.

[_D&L_]

You can't just look at one card, its equity, and figure out the right course of action. I been thinking some more.

For instance, if 55% Equity was the lowest holding in the distribution your representing, and everything else lets say is "Ace Ace", your opponent would be folding most any hand. Yeah, an extreme example, but you get the picture, the right play depends on your distrbution, his distribution, and pot size.

We use this info to figure out how often he should fold to our raises. To raise a hand at 50.0001% (no rake) u need to know two things: (1) that he will call every hand, and (2) that either A or B is true: (A) he will never re-raise a hand, or (B) he re-raises, but its never a bluff. Only then do you have positive EV+ at 50.00001%. But assumptions (1) and (2) are unrealistic, thus percentages close to 50.00 are likewise unrealistic.

I'm eager to see if anyone has some good math / analysis as to what the proper cut off should be.

[elindauer]

d&l, your analysis is misleading. The 55% number is not talking about equity if you check it down. It's 55% to have the best hand WHEN CALLED, which of course is a matter of judgment as to what hands your opponent will call with. They are also only talking about value bets in position with this number... OOP is a different story. I think they make this pretty clear in the book(s), you may want to reread these sections.

good luck.
eric