Let's say you are demanding at least 10 to 1, due to the possibility of your set losing.

If you get an average of 14 bets from your first bet and 11 more from your raise, you would be right. Your implied odds would decrease but it is still +EV to raise.

But if you get an average of 14 bets from your first bet and 7 more from your raise, you would be wrong. The second bet would be -EV.

And I suspect scenario 2 is almost always true, for several reasons we can get into.

You don't need 20% to raise profitably. You flat out stated we have 20%, and we don't. If we're set mining and playing some of our straight draws, we're continuing on the flop like 12%-14% of the time. We have implied odds with flopping a set, but we don't have 20% hot/cold equity from a 5 card runout.

We have plenty of odds to call. You can make an argument about 0EV spew for fun and profit raising small PP. However, boldly stating makes this the clearest raise ever. It isn't. ArronW did a nice 2+2 magazine article as a proponent of this thin raise, and it was hotly debated.

I think 66 is a style thing. You're probably losing a tiny bit raising it, but do as you like. 77 is probably meh, whatever. 88 is just clearly profitable. You remember the Harrington thing about beating half of your opponent's Ax with your kicker? If people raise TT+ or JJ+ but cold call a bunch of other PP, 88 is more dominating in those second set vs third set spots.

Again, my objection is your painting this spot as an easy raise when it clearly isn't. If you said "we're close to about even equity and why not spew for free?" I'm cool.

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In the SL, NL case, maybe you make a case for a teaser raise tying people to the pot. As long as you don't get squeezed or LRR. Again, you're naming your price. Why do you want it to be $20 instead of $3? You're 6x-ing your investment because? On 12% of flops you're happy and hoping to cooler someone? I guess if you're playing with the wisdom of the masses of "don't go broke in a limped pot", you're making more people willing to go broke?

I think it's a slam dunk limp in NL (and a close/whatever raise in FL), for whatever it's worth. The risk of getting squeezed and the fact that we can much more easily realize our implied odds post flop strongly cuts in favor of limping in NL.

In FL, it's really pretty close to breakeven preflop, you rarely if ever get punished that badly when you are behind, and it does some good things to your range to have stuff like 66 or J9s in your range when you raise a bunch of limpers. I get the concern about cutting into your implied odds, but I think that's counteracted by: (a) building a pot so big that people will chase even when they have virtually no equity; and (b) getting in a bunch of action because people figure you missed a 6xx flop after you raised PF.

Link?

With the caveat that that my model is likely to be far inferior to a well written 2+2 article, here's the 30 minute analysis.

1. We declare we win the pot if we have an overpair or straight on the turn or a set on the flop or the turn. (This model does not include the possibility of someone limping a better overpair.)

2. We fold flop if we don't have a set, overpair, or a straight draw. I've counted the OESD where we have the low end to be a gutshot for this model. We always pay on the flop (that is, we never get a free turn).

3. We count the eventual size of the pot excluding our contribution as the win size.

Under this model, when limped, every pair 88 to 22 shows positive WR from 4 BB+ and 88-77 from 3 BB+. That is, as long as the pot gets to be 4-5 BB, limping all hands is EV+.

When we raise, this bar goes up. 22-33 now needs a pot (excluding us) of 8 BB, 44-66 7 BB, 77 6 BB, and 88 5 BB. The key thing here is that there's a pretty big difference here between 77 and 44 - raising forces smaller slicing. 44-66 will need a total pot of 8-9 BB.

If you keep the pot size constant, raising looks terrible. A 10 BB unraised pot would bring +0.89 BB for 66, but only +0.48 in a raised pot.

The exact numbers are not huge important. The goal is to identify the trends and sensitivity.

It's easier to get a 10 BB pot by raising 66 than by limping it. The comparison is really between a pot of X in the unraised system and X+n for the raised system, where n at least includes the extra money preflop and should include more as people chase larger pots.

Unraised pot, X = 6 and X = 8 pot size (baseline)
88 0.66 1.00
77 0.47 0.76
66 0.37 0.63
55 0.32 0.57

Raised pot, n = 4
88 0.97 1.32
77 0.66 0.95
66 0.48 0.74
55 0.40 0.65

Raised pot, n = 3
88 0.80 1.14
77 0.51 0.80
66 0.35 0.61
55 0.28 0.52

Expressed differently, this is the n required for each of the pairs so that raising is justified:

88 2.2 2.2
77 2.7 2.8
66 3.2 3.2
55 3.4 3.5

If you have 4-5 limpers and 1-2 blinds, the n solely from preflop would be 2.5-3.5.

This model isn't perfect but here are the key takeaways:

1. The extra bets you gain solely from preflop very likely outweighs the cost of raising for 77+. Everyone pretty much agrees we raise these.

2. If people are likely to chase larger pots, 66 and even 55 should be considered. The additional bets they bring in likely but not very likely outweighs the cost.

3. The dropoff is steep below that. 66 and 22 are pretty different and should not be lumped together.

I forgot to mention that I've excluded the possibility that we see a free turn. It's important to note that even a small percentage of free turns dramatically improves the equation. Even a 1% chance at a free turn can drop n by 0.1 or so.

Here are the numbers with a 1% chance at a free turn:

88 2.1 2.1
77 2.7 2.7
66 3.1 3.1
55 3.3 3.3

The smallest hands benefit the most (because they basically derive all their value from binking), and at high flop check-through percentages, I think it's worth considering raising 44-.

Is raising 66 thin, in the sense that it relies on a few assumptions? Yes. Is it thin in the sense that it's the worst hand I consider raising and only under the most optimistic of scenarios would I consider it? No.