Playing 1/2 HU 2-7NLSD vs a very loose opponent who knows very basic equities but generally is in it to gamble, making big bluffs that rarely work and paying off all my value bets.

We're in the last hand of a two hour session, my opponent starts the hand with $638, I cover. He makes it $38 blind on the button (he's been raising blind almost every button but never this big), I look down at T9322. Should I flat? Raise intermediate and fold to a shove (raising not all-in is very likely to induce a shove vs this opponent)? Shove for 17x as I have an equity advantage with a 1 card draw vs a random hand?

Maybe the place to start is if someone could please enlighten me as to what a random hand is in 2-7 predraw.

I don't know what average hand is, but I think odds of pairing your first 5 cards is around 70%, so u have well above average hand vs random.

If I know its last hand of session and I'm up pretty good, i like avoid playing a big pot for psychological reasons. I like to book wins, it aids my confidence. Because of that and opponents s blufginesz i like a flat, and let him bluff.

I'd fold for 19 bb the last hand.

I strongly suspect a jam here would be +ev. May not be the best play, though.

If you stack him will he rebuy? Is this hand an agreed upon last hand? I think all options have merit.

Yes agreed upon last hand, end of 2 hour session. Although if it weren't, he prob would rebuy. How so does that affect the hand? My opponent probably isn't playing any tighter or looser due to it being the last hand. I included that to explain why he was blind raising so big not that it really matters as far as I see.

Something important to note: if I call, draw 1, and check to him, he will almost for sure bluff. So idk if that helps or hurts us in this scenario.

Because then future equity is gained if he rebuys. Not just equity in the vacuum of this last hand.
And it for sure helps us.

It sounds like call is very profitable. Jam cannot be awful. If I were crushing poker I would probably jam it and gamble. If I were losing recently I'd probably fold quietly and quit lol

I was almost certain I had an equity advantage with a 1 card draw and just wanted to pick up the dead $38, so I ripped it in and was drawing dead vs a pat 96. If I'd had <$400, I wouldn''t even think much about it, but so deep I wasn't sure if it was a profitable shove in a vacuum let alone vs this opponent.