BB ante 50k/100k

Hero @ ~2.5 million chips, which is roughly the chip avg at this point.

We just sat down 3 hands ago, don't know anyone at the table, just left the TV table. 1st hand we call shortstack's jam w AJ and lost to J6

2nd hand at the table old guy opens 225 utg, folds to sb who overbet jams like 3 mil, utg calls w TT, sb shows QQ and holds. Utg is an older guy, gets all red and looks tilted, then our hand comes up :

Hero CO w AK , 2.5m effective
Folds around

Raise 250k

Folds to bb ( the old guy from prev hand) - call

Pot: 600

Flop : Ad Tx 5d

Check, Hero bets 375, Villain calls

Pot 1.35m

Turn : K (not d)

Check, hero bets 775, V calls

River : 2d

Pot : 2.85m

BB check. Hero ????

We have ~1.1 behind

I see merit in checking but also in putting his Ax to the test, especially since he seems grumpy and tilted after prev hand.

I size a bit on the bigger side on all streets, since no one knows me and how I play, however in hindsight I think I should've gone even bigger.

I dont know if it should affect our decision (appreciate thoughts on this too) but avg at this point is 2.5m and blinds about to go up.

So... Hero ?

This has to be very close but I think I'd be a nit and keep 11bbs when he got there thinking that I wouldn't bluff pretty much ever so no need to value super thin. Then again yeah he doesn't know you and looks tilted so shove makes a lot of sens but there's the "let's not bust" thing. Also on that particular turn he does have a bunch of xx dd able to cc even a large sizing because a lot of FDs become combo draws.

Do you have Kd ? Could possibly be the decisive factor.

I do not have the Kd

I understand whts you are saying here, do you think the fact that his KdXd and QdXd become combo draws is a reason to bet turn even bigger?

Also what about our flop sizing ?

(+ Jx dd and Tx dd is still a pair) I think your sizings are fine, flop is a little big if anything, turn we might go slightly bigger like 900K or something but doesn't change much.