1/3 game Friday night. One background hand with one of the villains, then on to the main.

Background Hand

Hero raises to 10 UTG
Four callers including V2 on the button

Flop A 5 3

Hero bets 30
Three callers including V2

Turn A 5 3 K

Hero checks
Cutoff bets 60
V2 calls
Hero calls

River A 5 3 K 8

Hero checks
Cutoff checks
V2 shoves for 140ish
Hero folds
Cutoff folds

V2 shows 55 for a flopped set.

Hand In Question

Hero has just over 300
V1 (MP) has about the same. Late 20's white guy. Fairly loose PF and post flop, has bet some thin value.
V2 (Cutoff) covers. Early 50's black guy, seems relatively tight PF but can reach showdown with third pair depending on the board.

Four limpers including V1 and V2
Hero checks in the BB with 102

Flop: 10 Q K (Pot after rake - 14)

Hero bets 12
V1 calls
V2 calls

Turn: 10 Q K [Blank] (Pot after rake - 43)

Hero checks
V1 bets 40
V2 calls
Hero calls

River: 10 Q K [Blank] 3 (Pot after rake - 163)

Hero?

Hero has about 250. Comments on the turn and river as played are welcome.

I'm curious as to why you lead with a draw, then c/c when you hit. I'd prefer to lead the turn once I hit.

AP, I'd lead the river for $75ish.

The turn was a blank, I hit on the river.

Oh. My bad. Disregard my comment about the turn.

I would probably cr this flop looking to gii on all turns except for black/heart JQKA. Unlikely the flop gets checked around imo, but I don't think leading is bad.

As played I would lead river for $125ish. I'm probably calling a shove too.

In the background hand, AQ/AJ is a c/f on the turn. I think if you're c/calling turn, it's very hard to fold river getting almost 3:1. I know the turn bet is somewhat small, but it's a losing play re: reverse implied odds to call it because of the great odds and then fold the river with great odds. I also think bet/fold half pot on the turn followed by a check/fold on most rivers is by far the best line so you can get value from worse on the turn with a mid-sized bet and then fold on rivers as I don't expect people to bluff worse Ax, 22, 44, 5x, etc. The only likely bluff at that point is really like 6c5c. When you go into c/decide mode, you will run into A3, A5, 42s, 55, 33 far more often than if you're value betting yourself.

On to the next hand.

Please don't bet the flop. What's your goal? You don't get a better hand to fold - you already have 3rd pair. You generally don't get worse hands to call. Being multi-way magnifies those issues because when people continue they very likely have better hands in ranges. And you cannot really "barrel" any turns on this board. You're also oop multi-way, and you don't really want to build a large pot - the best way to try to accomplish that is to check, not bet. You also have a non-nut draw, which is a consideration. I think c/assess the flop is best. If someone bets close to pot, I would say you to have very little fold equity, and I would c/c with my weak made hand + draw.

As played, well, you need to win quite a bit more on the river (you're getting 3:1 vs a bet of 40, and you're a 5:1 dog at best, so you need at least 80 more = 40*(5-3) in order to justify the turn call. And by the way, with a bet and a call in front of you, you almost always have the worst made hand (V1 easily has a straight or 2-pair) and possible but not likely you have the worst draw. More likely V2 has something like KJ, QJ, JT, T9, etc.

Long story short, bet/fold 125 on river imo.