1/2 NL live full ring table:
Stacks are $700 effective
After everybody call blinds The Villain, TAG old guy player, raised to $20 from CO. Hero at BTN calls $20 with pair 10s.
SB calls, BB calls 4 players are going to see the flop.
Flop: 7,8,9 rainbow Pot: $80+
Villain bet $60 Hero calls $60. SB and BB fold Pot: $200
Turn: 10 (still rainbow board)
Villain bet $150 Hero calls $150 Pot: $500
River: Blank and Villain bet $250 ($200 left behind)
Hero action with $450 behind? Any other suggestions?

Raise flop. AP call down turn and river, TAG old guy isn't likely bluffing but could easily eb overvaluing KK/AA. Not sure where the question is.

lol @ old guy triple barreling KK/AA on this board. If V doesn't have JJ or TJs I'll be surprised.

If he has value that we beat its more likely to be 88 or 99 than KK/AA.
I wouldn't fold, but hey i'm a pay-of wizard .

V's check this turn like 95% of the time with a set

this and this.

He has JJ everytime here.

as played, call and boat up on the river

Fold river.

I'd mix it up between calling and raising flop. Against and older TAG who's weighted to mostly larger overpairs, I'd call in this spot. Calling turn is very standard. I'd fold river. This board should hit your range a lot harder than his, yet he's triple barreled anyways. Can't see an old TAG doing that with AA/KK, and they're probably c/c most sets OTT/OTR. With a V as described, feels like JJ almost always.

I think raising flop is really bsd

3-bet preflop. Why just calling? - Do you plan to set mine, that's why you called preflop?

Raise flop, shove turn and get it over

Well played preflop, flop and turn.

River is a close one, but I lean towards a fold without any live reads suggesting otherwise, since I think that villain is unlikely to bet QQ+ on this river (he will once in a while, just not often enough to make calling profitable).

I disagree that villain *never* bluffs this river. Bad live regs often just bet when they don't know what else to do and 4 straight boards are often bluffed, so villain certainly can show up with QQ+ here. But not always.

Hero actually shoved all in and the Villain called with the rest of his $200. He had Ace Jack off suite (turned J high straight)

Ouch. Shoving is the worst option. We fold out sets/2pr we beat and get called by str8s.

Why?

Agree that with particularly this old TAG player the fold on the river was the correct choice. I guess the Hero just malted
and convinced himself that Villain is having overpair QQ+ or smaller set.

Even if V has those hands, he's not calling a river shove with them. That was the nut low decision to make.

Why are people advising to raise the flop? Given this V, you have very little fold equity when raising on the flop. He's just going to shove over your raise and then you get pushed off your equity. Calling can hopefully induce a call from the SB or BB improving your odds as well as not bloat the pot against a nittish range that you are likely to be behind right now.

If V is nitty old guy that is folding anything but the nuts, I'm raising the flop to get him to fold AA/KK. If V is not nitty old guy that won't fold AA and KK, then I'm calling flop and raising turn.

If I'm a hero convinced that old guys can only have the nuts, I'm going home.

Because this board smacks our range, and completely missed an old TAG guy's opening range. And no, he's not going to shove $700 with KK/AA if we raise flop to about $200.

I guess I just don’t understand what we’re trying to accomplish with a raise?

-Are we raising for value because we think V is going to call with worse? What worse hand do we think he’s going to call with?

-Are we raising to try and get him to lay down better? Surely this can’t be it? Maybe my ranging sucks but when an old man opens for $20 in a 1/2 game and then bombs a four way flop for 3/4 pot a neon sign starts to go off.

-Are we raising to thin out the field and pick up some equity? Don’t we want SB and BB to come along for the ride and improve our pot odds to draw to our straight?

-Are we raising to try for a free card on the turn? I guess I can maybe see this argument if we are reasonably sure V won’t come back over the top of us or donk the turn.

I’m not trying to be difficult, just understand and learn how to properly think through these things.

Quoting your post:

I guess I just don’t understand what we’re trying to accomplish with a raise?

-Are we raising for value because we think V is going to call with worse? What worse hand do we think he’s going to call with?

Not really. It's a multi-street play value-wise.

-Are we raising to try and get him to lay down better? Surely this can’t be it? Maybe my ranging sucks but when an old man opens for $20 in a 1/2 game and then bombs a four way flop for 3/4 pot a neon sign starts to go off.

Yes - but not just on the flop. Given Hero's range and this board, I don't expect V to lay down QQ-AA on the flop, but there's tons of turn cards where we can shove and get him to lay down one pair.

-Are we raising to thin out the field and pick up some equity? Don’t we want SB and BB to come along for the ride and improve our pot odds to draw to our straight?

This too. We likely have the best hand right now but it's vulnerable if we don't spike the straight. There's also not a lot of turn cards that are "good" for our hand value-wise if it stays 4 ways. Coincidentally,
the hand V showed up with here is exactly the kind we want to fold out because it still has significant equity against us.

-Are we raising to try for a free card on the turn? I guess I can maybe see this argument if we are reasonably sure V won’t come back over the top of us or donk the turn.

If we get it HU, then yes that's a possibility.

I’m not trying to be difficult, just understand and learn how to properly think through these things.