How do ppl play this river, check call, jam, smaller size?

dunno what our 3betting range is, are we gonna have hands like 76s? if yes then shove here and shove the 76s as well. if we don't have much of a bluffing range then check/call and hope he has 76s

Hard to say, sometimes i have it, not sure if i bluff with it in this spot, dont think so. but was more thinking, can he have AJ, AQ, AT, float with JJ, set of 88, and its fine to shove for value

actually, i think we should bet/call 9. we're at the top of our range, our opponent has a straight less than 50% of the time, and the pot is bigger than our stack. we're not folding. we do want max value out of any bluffs he might have, as well as the 2pair/set hands that he wants to get to showdown with. we also want a betting range so we can bluff with some of our air. we have a lot of air, and a lot fewer nuts compared to villain, because most Kx and 9x hands have pairs on the turn and probably wouldnt bet).

mm he had straight, AK, but i dont think that matters, just thought, if i check, i just call and lose to straight, if i bet, i at least get called by shit i beat, was the thought process i think

haha i actually guessed he probably had AK, since he can have both suited and offsuit combos of it

btw first time doing this kind of range analysis, i hope i will make sense.

dunno if these ranges are accurate or not, but given how deep it is, his preflop calling range should be a lot looser than if it was 100bb

==IP's range==

straights:

AKo (12 combos)
AKs (4 combos)
KTh (1 combo)
KJ spades - K9 spades (3 combos)
9Js spades - 95s spades (6 combos)

= 26 combos of straights

2 pairs and sets:

All AQ (3 combos)
AJs (2 combos)
ATs (2 combos)
A8s (2 combos)
QJs (2 combos)
QTs (2 combos)
Q8s (2 combos)
JTs (3 combos)
J8s (3 combos)
T8s (2 combos)
88 (3 combos)

= 26 combos of 2pair/sets

one pair/air:

J7 spades (1 combo)
T7-T6 spades (2 combos)
87-84 spades (4 combos)
76 spades - 73 spades (4 combos)
65 spades - 62 spades (4 combos)
54 spades - 52 spades (3 combos)
43 spades - 42 spades (2 combo)
32 spades (1 combo)
72o (1 combo)

= 22 combos of air

(he probably has a lot less air, dunno if he should be raising 32s in CO)

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he has a straight about 35% of the time. let's say you go allin with your entire range every time and he only calls with straights. based on SPR:

65% of the time, he loses $35.10. (the pot)
35% of the time, he wins $65.46. (the pot + your stack)

the $65.46 should be a bit lower because sometimes it will be a chop and sometimes he will lose with the 9 vs K straight. generally he will win because when we shove our whole range we will have plenty of hands that are losing to straights

basically, he can just call with straights and fold almost all his bluffcatchers. it's important that we block top 2 pair (AQ) big time, which is probably the only bluffcatcher he needs to call with. because we have QQ, he only has 2 combos of AQo and 1 combo AQs, whereas normally he would have 12 combos of AQo and 3 combos of AQs. from 15 combos to 3 combos due to two blockers is pretty huge.

well this analysis was a lot of fun haha, i hope it was helpful. i'm high right now so i'm not sure if i'm actually making sense or not lol