$.25/$50 on Global
VILLAIN Cutoff: $87 174bbs
HERO Button: $50 100bbs [HOLE CARDS 56]

Preflop: LoJack limps, HiJack limps, Villain raises to $2.75 from CutOff, Hero three bets to $7.50, folds to villain who calls.

[Pot $17.50] Flop Q 8 3

Villain checks, hero bets $7.25. Villain calls.

[Pot $32] Turn J

Villain checks, hero bets $13.50, villain raises to $87 and is all in, hero calls.

I miscalculated my pot odds on the river because I looked at the amount in the pot even though I didn't have villain covered and $37 of the pot wasn't in play for me. In reality I was calling $23 into a pot of about $79. I need 22.5% equity to continue and I'm probably a hair short of that. I'm right around 20% equity against top pair hands, but if he had a pair with a club or a set then I'm drawing thinner, and if he happens to have a bigger flush draw like A10 then I'm in really bad shape. So as played I think I need to find a fold on the river.

This lead me to believe I made a big mistake as I have heard time and again it's horrible to put yourself in a position where you get jammed on and have to fold your equity. But in reviewing this hand I wasn't sure where that mistake was.

Maybe the turn should be a check back? I thought villain might have to fold some more hands on the turn, and I was getting a good price on my bet. But the pot got so bloated preflop that for me to get stacks in by the river required 40% pot sized bets on all three streets, and maybe that gives him too good of a price.

Should I be sizing bigger on the turn? Giving up on the turn?

In this case Villain had 8-8 and held. I walked away feeling like he kinda sucked out on me because he wasn't getting a great price to set mine, and he's going to have to be defending a marginal hand out of position against a lot of pressure. My gut tells me that when he makes a set he's usually getting 1-2 streets from me (often just one), and when he doesn't he's going to have to fold most of the time and occasionally pay me off when I have him beat.

I just think he's risking a lot of his stack pre and post flop either set mining or hoping for a cheap showdown or a bluff catch. I think had this been a standard 3x open and 10bb three bet it's a pretty easy call, but due to the limpers the bets got bigger and I think it was too wide. Or is 8-8 a standard defend since we're CO vs Button?

In thinking about it maybe 8-8 is a good call, and with the pot this bloated and the smaller bet sizing he just needs to call down light a lot or he is just over-folding. For some reason I'm really struggling with this spot for both positions!

Don't 3b pre, hand selection is too wide (56s is too weak). Post seems meh. Generally you want to be sizing up your bets OTT - flop cb's can be small bc we are continuation betting wide OTF, turn barrels can generally utilise a larger sizing as we are doing it with a more narrow range. This is a tricky spot in terms of sizing, as you said we can comfortable GII by betting small on each street, although with our value we may be letting hands out draw us, and when bluffing we gain little fold equity.

Your remaining stack OTT should be around $35 (pot $32) - have you considered moving AI for just over pot w/ entire betting range OTT? This makes some sense to me, as we gain good FE with bluffs in comparison to line taken.
This way, we are the ones putting V in the cage, not the opposite way around

AP fairly trivial fold OTT.

56s is fine bluff selection imo, can't flat, has decent equity and playability but I wouldn't 3B this after two limpers unless I know they won't flat this 3B light.

Size larger flop to set up more comfortable SPR on turns, which you should just jam.

I'd rather call preflop and hopefully play a multiway pot in position against 2 fish.

I'm not really liking the flop and turn sizings. I think jamming the turn as played is still better than leaving an SPR of ~1/3 OTR when villain calls, and torching any fold equity you might have had. Turn's a fold when villain jams. Even if villain plays all top pair combos like this (which is unlikely), you still don't have enough equity to call with the sets/2 pair/better flush draws.

88 is a standard call in CO versus a BTN 3bet. Even with ranges possibly being a little tighter, I think it's probably still a defend for CO.

I think its totally fine to 3 bet here - you take control of the hand, and the limpers are unlikely to flat. However I really don't like flatting because of your position. If you call here you're investing 5.5bbs pre, and you're not even sure that the original two limpers are going to call, which is really what you want with your hand in this situation. For me personally, it's 3 bet or fold.

I'd also 3 bet slightly larger, around $8.5 or $9. On the flop, I'd bet slightly larger so SPR is even and you can jam the turn if you choose to. However, the turn hits his range, and for that reason I would check and try to realize your equity on the river.

I would put him on this range pre: 77-QQ, AQo, A8s+, 89s, 109s, 10Js, Q10s, KQo, KQs, and so on......in this hand, the turn hits a lot of that range - or at the very least gives him reason to continue when you bet the turn.

I would shove any turn that gives you equity and doesn't favor his range (low clubs 2-6, and gutters or open-enders). Otherwise, I check to avoid him jamming like he did.

If you do jam favorable turns and you run into a set, whateves. Sometimes you get stacked, but more often than not - he folds and you win not having to realize your equity.