Math, EV and Middle Pair Options (long)

[PinkSteel]

Very thought provoking post. Thanks for taking the time on it.

In your progression of formulae for EV, you characterize average earn as a sum of earn on a set plus earn unimproved. It's this bi-modal characterization of the earn that especially got me to thinking.

So in a player's progression through skill levels and stakes -- as his postflop skills improve and as he faces more skilled players at the table -- the value to raising mid-PPs increases substantially. And a great deal of this value comes from the bi-modal earn character of the hand. First, you stand a better chance of taking down limps preflop, since you are ever more likely to face a tighter table. Second, even against a lone opponent postflop, you may stand a good chance to win the hand unimproved against a tighter opponent. Third, raising builds the pot for when you hit, which is all the more important against skilled players as they will be generally less likely than weak players to pay you off heavily postflop.

The mid-PP bi-modal earn profile also clearly distinguishes them from SCs, which are much more of a lottery ticket: worthless unimproved, with all the EV loaded into a much-less-likely jackpot. So as opposed to mid-PPs, where I have an unimproved earn potential, with my SC hands (1) limping will be generally more appropriate, given the -EV of much more frequent misses; (2) position, table tightness and skill will generally factor in preflop, where the important considerations are whether the hand will play multiway (table looseness helps greatly), and cheap (table passivity helps greatly). Postflop, a SC hand will be more likely to play itself than 77: you hit, you're drawing very live, or you let it go.

It stands to reason that as stakes increase, and generally so does aggression and postflop skill, the value of playing SCs at all drops, as opposed to the value of playing, and raising, those mid-PPs.

So my takeaway from this is: at lower stakes and tables of lesser skills, limp the mid-PPs more, play the SCs more and limp them, and limp the low PPs to boot. As stakes and table skills go up, raise those mid-PPs (with position), play them like the best hand, and be much more inclined to simply muck the low PPs (22/33) and the SCs. Sensible?