Turning a -EV draw into a +EV lead (micro theory)
 

I was thinking about a principle that I stumbled across a few years ago in my initial micro days. I dont recall ever reading about this principle in any books, but I'd be surprised if it isnt out there somewhere. For some of you this will be old news, but for others it might help your play out of position.

So we can most easily understand this principle, I'll set a very small stage: a 9 handed micro limit holdem game where hero is in the big blind. Often times in this sort of situation, some unfamiliar player from early or middle position will open limp (this occurs less frequently in tougher games). Also, imagine that all other players after the limper fold to you in the BB and you check. You are now heads up, out of position, with a preflop limper and a 2.5SB pot.

Say you have a hand like J[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] and the flop is Q[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/heart.gif[/img]. Whats your line?

1) check/call
2) check/fold
3) lead
4) check/raise

In this example lets assume that your opponent will always (correctly) bet when checked to, and the two of you are otherwise unfamiliar with each other.

Option 1 (check/call) is obviously wrong, since we will be getting 3.5:1 on an inside straight draw where we need 10.5:1 to call. Even if we count a Jack as a partial out we're not getting the proper odds to call. So we have a -EV draw.

Option 2 (check/fold) at 0 EV is a better option than the -EV option 1, but we're getting bluffed or giving up a pot that could be ours far too often. Our opponent will bet with a lot of hands that we beat currently or have odds to draw against. 56o, A3s, and 44 are examples.

Option 3 (lead) I claim is better than option 2. In the cases that we are ahead or actually have +EV draw we are spending the same amount of money as option 2, but we are adding fold equity to the value of option 2. Now our opponent folds all of his bluffs (which we cant profitably call) and might even fold hands like A3s and 44 which have us beat.

Option 4 (check/raise) is worse than option 3 for two reasons. First, it offers our opponent better odds to call, thus reducing our fold equity. Second, it's easier to fold after leading than it is to fold to our opponent's 3bet because of the increased pot size.

So... thats how to turn a -EV draw into a +EV lead. Im not sure if I've chosen the best example or circumstance to illustrate this principle, but hopefully the micro gurus can fine tune the idea. Also, some might have a problem with my proof, because I say the draw is -EV, when it might be slightly +EV depending on our opponents hand. I cant really think of an elegant way to explain this problem, but since our J8 isnt really a bluff catcher, we have to consider our hand to be a straight draw when we check/call, when it might be stronger. Obviously calling all the way down to see if he really has 56 is horrible. So any critiques or suggestions to make this explanation better are much appreciated.

If youre inspired, let me know cuz my ego needs a boost... naturally.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

Lots has been written and said about the power of being "first to the pot" in situations like this. The two points that you have to keep in mind in most micro online games is:

1) your fold-equity against most unknown opponents is zero;
2) see 1.

Slightly less important is that the board needs to be at least this uncoordinated to have any hope of it working. Make the 9 a jack, and you're getting called by any ace, king, ten or 9 out there.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

It depends on the villain; I don't want to bet this into a calling station (I hope you can see why).

Re: Turning a -EV draw into a +EV lead (micro theory)
 

If your opponent is unknown to you, you are most likely unknown to him. And as was already mentioned, unknown micro players (especially the type that open limp) aren't exactly world reknowned for their ability to fold postflop.

This hand is a bit of an exception, though, because we did at least flop a draw to a very strong hand. As you mentioned, depending on villain's hand when he does call, we could very well be looking at 10 outs twice, which makes us just a little worse than a coin flip assuming we're going to the river. Make his hand an underpair to our 8 & we actually have a bit more equity as we can win with running Q9. So anyway, yeah, I will often bet out with a hand like this (as well as when I believe I have the best hand, even if that "best hand" is something like 32 or ace high). As you sort of alluded to, the equity of our draw plus our (limited) folding equity turns this into a +EV play.

Incidentally, I don't think check/call is always a bad play here, as we're often going to be given a free card on the turn when our opponent is betting with air, and may also be able to steal the pot with a river (or even turn) lead when we miss. But I would not assume that any of those moves would work often enough against an unknown micro opponent.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

Agree with boz that fold equity is almost null in micros. I will only lead out on the flop in such a situation if I have my reads firm on the villian. He's gotta be really weak tight, with his postflop aggression below 0.6-0.8. Or else, leading out would be just spewing my chips away. And if he called me on the flop, most of the time I wont' try leading again on the later streets to bluff him out. My first attempt to steal has failed with a SB, in a small pot, and I won't wanna spew again on a BB street.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

[ QUOTE ]
Agree with boz that fold equity is almost null in micros. I will only lead out on the flop in such a situation if I have my reads firm on the villian. He's gotta be really weak tight, with his postflop aggression below 0.6-0.8. Or else, leading out would be just spewing my chips away. And if he called me on the flop, most of the time I wont' try leading again on the later streets to bluff him out. My first attempt to steal has failed with a SB, in a small pot, and I won't wanna spew again on a BB street.

[/ QUOTE ]

I also agree with boz, but i think in this situation (with a draw and an uncoordinated board) leading is better than conceding the pot 100% of the time by checking.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

I check/fold this almost everytime. I don't think our hand has a lot of equity against an EP preflop limper in this case. I also might bet out against someone who plays against me regularly.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

[ QUOTE ]
I also agree with boz, but i think in this situation (with a draw and an uncoordinated board) leading is better than conceding the pot 100% of the time by checking.

[/ QUOTE ]

So, when do you give up? Do you c/f the turn if your flop bet gets called? Do you fire again?

I agree that conceding the pot 100% of the time is bad, and I never said that you should. (fwiw, doing ANYTHING 100% of the time is bad.) The problem is that you're making a generalization, which is also almost always a bad idea.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

In a live game, I check-raise the flop and fire out on the turn. Then I hit a ten on the river where I check so that I may tarp him with another C/R. When he bets and sees my hand after calling my check-raise. he goes to the kitchen to grab a blunt knife and tries to stab me in the stomach. I sue him making this situation +EV and all my bets for value.

Re: Turning a -EV draw into a +EV lead (micro theory)
 

Since no one has yet, I'd like to at least mention pot size, since it should be a consideration. Here it is small. So by virtue of that alone, I almost always check and fold and look for other opportuities.