Pre and postflop covariance--to raise or not?

Premise: We are trying to maximize EV of a given hand (while this may not be the best premise, it's a good starting place).


Let's say that you can separate the EV on various rounds (this is just some weird theoretical devise). Then the EV on the hand is equal to the EV pre flop plus the EV on the other rounds.


You gain preflop EV any time you raise and you are going to win more than your "fair share" (= 1 / number of players), and you give up prelfop EV any time you raise and are going to win less than your "fair share."


Unfortunately the matter is not so simple as to raise when you're going to win more than your fair share and don't when you're not because the way you play your hand preflop will affect your EV on the other rounds.


My question is how raising preflop will affect postflop EV.


In a recent post, two players limped in and the 2+2er choose to limp on the button with A10o. In a game I played a week ago, three players limped in and I choose to limp on the button with AJo. My question is the following: how would raising have effected our EV from the flop on? Both of these examples come from the category of big unsuited cards, but other categories of hands are interesting to discuss as well.


Tommy Angelo and Andy Fox (excuse me if I am wrong) often say that they would raise with a lot of hands and give as their reason that they think the hand will play better from the flop on if they raise preflop (I will intepret this as meaning that they think their EV from the flop on will be higher). I choose to *limp* on the button with AJo for the same reason, because I thought it would make my hand play better from the flop on.


To put it another way...When I looked down and saw AJo, I thought that I was going to win more than my fair share, but I also thought that there existed a negative covariance between my preflop and postflop equity by raising. On the other hand, I think Tommy or Andy would probably argue that I could both gain preflop and postflop EV by raising, i.e. that there exists a positive covariance. This is an important difference IMO. If my view is right, then it's just a question (not that it's simple!) of finding the correct fulcrum. But if Tommy's and Andy's view is correct, then lots of hands should be raised and a fulcrum is an irrelevant concept (because nothing is being balanced--the factors are working in the same direction).


What do you all think?


-Dan


P.S. I apologize to Tommy and Andy if I incorrectly inferred their opinions.

Against loose players limping with a lot of trashy hands, your hands like AJ make most of their money before the flop. Of course you will have EV after, but much of your money to be made with the big cards against these loose limpers is before the flop.


Plus the other benefit is to cover for your raises with your really big hands (AA, KK, AKs, etc). If you stop raising preflop with the other hands that warrant it, you will become much easier to read.


Against 2 or 3 loose limpers I'm raising with AT, KQ, probably even KJ and more. Am I a big favorite going in? Of course not. But will I win more than "my fair share" of the time? Absolutely.


Just my 2 cents.


-ActionBob

I think that ActionBob is suggesting a positive covariance and I would tend to agree. It appears to me that you limp with AJo because it makes your hand easier to play -- ie. its straightforward and you hit and bet/raise or you don't and release.


I think you need to better explain your reason for thinking that there is a negative covariance. I don't think that there is one. Perhaps if you (personally) can't check behind when you whiff or will likely bet and call a check-raise to take one off... But I think, for the reasons ABob gives and others, that it increases the EV on all streets.


You write:


"I choose to *limp* on the button with AJo for the same reason, because I thought it would make my hand play better from the flop on."


What does this mean? *Why* did you think that? What are some of the *reasons* you think raising might be plagued with a negative covariance on future EV? I think there are many things that contribute to a positive one (eg. free cards when it is checked to the raiser...) I can even think of a few reasons that a negative one might be created, but I think this will usually always be outweighed by the value of getting in two bets when you're relatively certain. Honestly, and perhaps I'm ignorant, how can you figure out the EV on future streets with any degree of certainty (as a value distinct from the PF EV)?


-CW

I played with AC Bob at the bellagio about a year ago and we had a discussion about raising before the flop. It mostly concerned when you were the opener but Bob gave a bunch of good reasons why raising before the flop is a good play in limit holdem and i think they apply to this situation. I don't remember them all so hopefully he'll comment on this thread. two of them are:

1) charge the blinds to play, why give week hands a chance to catch a good/great flop when they will often muck (with implied odds hands like 98s i can see the case for letting them in).

2) in limit holdem you generally want to be driving the action, not reacting. it is better to be the bettor and raiser than it is to be the caller. make the others react to you.


rob

"Tommy Angelo and Andy Fox (excuse me if I am wrong) often say that they would raise with a lot of hands and give as *their* reason that they think the hand will play better from the flop on if they raise preflop"


A subtle misquote. Change "their" to "a."


So many reasons I raise preflop. Foremost is to earn position. On the button this is not a factor and that's why I raise far more often from the cutoff and nearby seats than from the button.


Second is to give me the best change of winning the pot without a showdown. This statement has been misinterpreted to mean, "I plan to bluff 'em out." That's not what it means. It means that when everyone misses, someone has to win anyway, and typically the pot goes to the lone-preflop raiser who is also last to act. In heads up and three-way pots especially, if I'm in at all, I want to hold this advangtage. That's partly why I muck the blinds. It's not "bluffing," in that the cards don't matter. It's a routine situation where being last and being the aggressor equals profit, IMO.


Finally, to the point you mentioned, and it's huge. The phrase "play better" is often used, and it's another woefully vague wording. To me it means one and only one thing. Reads. If I raise from the cutoff with QJ and flop top pair and a guy check-raises me on the turn, I'm in a MUCH better spot to make the right play, laydown or not, than if I had limped in. The one small-bet investment preflop results in being able to save, or earn, one big bet later on. This happens a lot lot.


Putting pressure on the blinds sounds nice, and it is, but again, it really comes down to reading. Lots of guys at mid-limits don't willy-nilly call raises from the blinds, especially the small blind. When they call a raise, they got something. It might not be all that much, but I can safely elliminate the worst 1/4 of the hands when narrowing their range of holdings. This matters.


And then there's all the free turn cards, and free river cards after betting the flop. One of the advantages of raising from a late seat is reduced proportionally to whatever degree the field does not check to the raiser. In fields where checking to the raiser is routine, raising preflop is a fine investment for this reason alone.


On and on it goes. I raise!


Tommy