Lets start the discussion off with looking at a typical 3-bet. In this situation we're going to make the BB the 3-bettor, as it greatly simplifies the math by making sure no one yet to act has a chance to put in a 4-bet.

You're playing NL$100 6-max. It folds to you in the CO, and you raise it to $4. Button and SB folds, when the BB makes a pot sized raise to $13.

Before we even look at your hand or take a flop, lets notice how often the you must fold to the BB's 3-bet to have him show a profit with any two. The BB is risking $12 to try to win $5.5 ($1 blind, $.5 small blind, and your $4 raise).

$13 / ($13 + $5.5) = .702, or 70.2%.

What this number means is that if you're folding greater than 70% of your hands to your opponents 3-bet, he is showing an immediete profit and it would be +EV to raise you with any two. The number will be slightly different if your opponent doesn't raise a bit over pot oop or the 3-bet comes from somewhere other than the BB, but it's usually around 70% so we'll stick with that number.

You look down and see you have [9s]. You muck it to the BB's 3-bet without much thought.

Was this a mistake? While it is very complicated if not impossible to show if folding here was correct as an isolated situation, we can see that we are exploitable if we are folding 70%+ of our holdings here. If this is the case, we need to either open are 3-bet calling range or shrink our CO opening range.

In a vacuum, I raise about 30% of time it's folded to me in the CO. If I'm 3-bet from the BB, I usually fold anything that's not 99+/AK/AQs. Why? Because I read 2+2 and that's what they tell me to do. After I started 3-betting light, I think most regulars have a similar 3-bet calling range. The problem is 99+/AK/AQs make up the top 4.2% of the hands you can get dealt preflop! I'm folding over 85% [(30-4.2)/30] of the time, much less 70%!

This is (was?) an absolutely huge leak. I'm giving my opponent immediate profits, not to mention all the times I call with QQ and he flops an A with AJ or stacks me with 55 on a 225 flop.

We know folding 85% of my range here cannot be optimal. Either I am being exploited too easily, or I am exploiting my opponent's too narrow of 3-betting range by folding almost anything other than the nuts (folding this easily is correct against a range of QQ+/AK). Back in the day, I would agree 3-betting ranges were so narrow folding this easily was correct, but now (on Stars/Full Tilt) this is no longer the case. It's time to start fighting back.

Before you muck the [9s], you realize you're being exploited by your opponent as you are folding over 70% of your opening range. Should we still fold?

We know that by calling or 4-betting with 99+/AK/AQs, we are playing only the top 4.2% of the preflop hands. Since we're opening 30% of the hands dealt to us on the CO, we need to at least play be playing 9% of our hands for opponent not to show a immediate profit. It should be obvious 9% alone still can't be right as then our opponent will be breaking even with raising any two and seeing free flops, but for now lets just worry about getting to 9%.

One option is to call with the strongest 9% of preflop hands, similar to the way we are always calling with the top 4.2% of our preflop hands (99+/AK/AQs). The advantage of this is we are playing with our strongest hands that have the best equity against his 3-betting range. The disadvantage is our 3-bet calling range is so clearly defined that a good opponent will know exactly how often we have a hand and how to play against us.

A better option is to start calling with suited connectors, lower pocket pairs, and hands like ATs/AJ some but not all the time. By doing this we can call his 3-bet a higher percentage of the time, and our range will be wider but still weighted towards stronger hands which are being called or 4-bet 100% of the time. For example, our opponent will know there are 6 combos of QQ when identifying our range, but can't say for sure if and how many combinations of 89 suited, 55, or JJ there are.

K that's enough for now lets get some discussion and I might add more later.

Double post, took like 10 minutes for it to go through.

bah this one is not the double post

Nice post, Dr. H. I think I remember reading somewhere that Townsend raises any two in the blinds when someone steals. Apparently it's very profitable, as you demonstrate.

I think you've also identified the two proper responses as well. You define one of them as a calling range, but against a light 3 bettor, a 4-bet would be preferable, right? Particularly with a hand like , I think a 4-bet is better.

Second option is to tighten up your pfr range so that you are continuing more frequently than 30% of the time. You note that a weakness here is that the BB will know our range, and be able to play against us, but I don't see how this follows, unless we stipulate that we're playing under certain conditions of clairvoyance. It is eaiser to play against a narrow range as opposed to a wide range, perhaps that's all you mean here.

You identify the first option as preferable, and I tend to agree with you. Okay, so what hands should we be 4-betting with. Similar to the profitability of 3-betting light, you just calculate what you need to show a profit by 4-betting light. The BB's raise to $13 makes the pot $18.50. How often do we expect the BB to fold to a decent 4-bet? I think it would be very narrow for a typical light 3-bettor, which means we should be 4-betting a lot. On to the math: if we 4-bet to $40 then we have 40/(40+18.50) = 68.4% and following percentages for other amounts:
$35 = 65.4%
$45 = 70.9%
So, a light 3-bettor needs to call with 29%-35% of his/her range to prevent us from an immediate profit. Thus we need to identify a 3-bet range and specify what portion of that range continues with the hand. I'm going to leave it here for now, and let Dr. H or someone else add some comments/thoughts/specify various 3-bet ranges.