I wanted to open up some discussion on something I didn't cover in my Beating Spin and Go Poker videopack: limping in the SB when the BU folds. I believe that it's quite close in terms of readless EV to min-raising with most hands so it's something that you can often get away with not using. However, in some places it may be a very good option for us. What kind of hands and in what situations do you guys believe limping may be be better than min-raising?

To give us a starting place I did a little bit of math to help us compare the two options. First let's look at limp/folding. Let's look at the EV of limp/folding assuming that open folding is 0bb in EV:
EV(Limp/fold) = -.5bb*R + EV(when villain checks)*(1-R)
Where R is villain's raise frequency versus our limp. We can expand the new EV term by thinking about a number F which represents the fraction of the pot we expect to win on average post-flop. This lets us write:
EV(when villain checks) = 2bb*F - .5bb
This is simply the fraction of the limped pot we expect to win minus our investment in that pot from our decision point.

Now with some algebra we can solve for the F we need to make limping better than folding. I'll spare you the gory details and just post the result, which due to some cancellation ends up simple.

F = .25/(1-R)

A common raise frequency I've seen is 30%. This would lead to F = .357. To give you a reference point, when you flat a min-raise OOP in a HUSNG you need F = .25. However, in this case ranges are quite different since a min-raising range is uncapped but also doesn't have some bottom hands, while a check back range will be capped and include more junk.

To look at min-raise/folding we need to know how often villain raises and folds. We can write the EV the same way as for limping in terms of a new F term. R is the 3b frequency and C is the calling frequency.
EV(minr) = 1bb*(1-R-C) – 1.5bb*R + (4bb*F – 1.5bb)*C
Solving for F gives a slightly more messy:
F = .375*(1/C)*R - .25*(1/C)*(1-R-C) + .375

Let's again plug some numbers into this. A common raise frequency I've seen is 20%, and a common call frequency I've seen is 45%. Then we get F = .347, so a bit lower than for limping. It's important to remember though that hand villain's range will be stronger than when he checks back, so it may be harder to win a higher fraction of the pot. We can now see why limping and min-raising are likely pretty similar in EV in many situations. We can now start thinking about hands that maybe benefit from the larger pot post-flop caused by min-raising, or that have similar equity versus both the flatting and check back range and so appreciate not needing quite as much F to make the min-raise profitable. You can also examine other frequencies and see how F will vary in each case given different player types.

Try to work out some combination of min-raise and limp ranges for different player types. What kind of results are you getting? Post them here and we can all discuss them and build the best SB range we can.