V1 is a winning player, fairly aggro.
V2 is a loose calling station fish.

Hero has $770, V2 has $500, and V1 covers both.

Table agrees that the winner posts straddle for the next hand.

MP straddles to 10, V2 calls in HJ, hero raises to 45 in CO with AK, V1 calls in EP, MP folds, HJ calls.

Three to the flop: A J 7 (pot:155)

EP and HJ check, Hero bets 70, EP and HJ call.

Turn: 8 (pot: 365)

Check, check, Hero bets 150, EP calls, MP calls.

River: 8 (pot: 815)

Check, check, Hero bets $505 (all-in).

Thoughts?

I think calling ranges are just too strong for a 3rd barrel on this runout, including the overcalling fish.

V1 is a winning player, so I think we can agree he's almost never calling unless he has us beat. So we are risking $505 on this river to win $235 from V2 based on V1 not having a hand, then after V1 folds I'd say it's a decent proposition since V2 is a calling station fish.

This changes the value betting math greatly. Let's say V1 calls & beats us 15% of the time, but the rest of the time he folds. When V1 folds, V2 will call.

So, 15% of the time we lose $505 (-75.75$); The other 85% of the time we get called by V2, let's say we are 65% to win -> (0.85)(-235 * 0.35 + 235*0.65) = $59.925.

Based on these somewhat generous assumptions, a river shove loses us almost $16. The risk/reward is just too difficult to overcome here IMO, as we're risking more than double against a caller that will always have us beat to try to get value from a different player that still will have us beat at times too, and V2 will find some folds too.

You're pretty much laying poor odds on a three leg parlay: A parlay of V1 not having us beat, V2 calling, and V2 not having us beat.

Part of why ranges are stronger than normal is V1 should also be aware of the fish behind which makes an otherwise aggressive player very call-heavy-strong. I mean, at least that's what his range should be doing. The fish guy isn't necessarily betting his 78/98/T8 either.

I’d look for max value on the flop and turn. Sizing up the river 3-way with the 8 still out there seems dicey. Basically praying V1 has AQ and V2 has busted diamonds.

I certainly respect your POV / analysis, and you might very well be correct, but allow me to offer some alternative assumptions for arguments sake:

A) I think getting called here by V1 isn't quite as high as 15%, probably more like 5-10% (he's beyond capped on this texture multiway when he doesn't raise flop/turn or lead river -- only something like 86dd/98dd/T8dd that rivered us can/would really x/call).

B) The idea the passive station has us beat more than 1/3 of the time is pretty pessimistic. Yes, because he's passive he's far less capped on this river, but even then he will raise us on flop or turn w/ a big hand some % of the time on a wet board multiway, or just lead out on river themselves w/ a full house, straight etc. Not to mention his Ax count should be quite high relative to the stuff that beats us (T9/98, etc.) and he should be calling down w/ most/all of it. So let's say instead we're only beat 20% of the time because of this.

So . . .

(.10) * -505 = -50.5
(.90) (.20 * -235 + .8 * 235) = +126

With these assumptions in place, the shove represents +75.5 $EV.

However, say neither of us is correct, & the truth lies somewhere between our two calculations. Say I'm correct about the regs calling frequency, but you are correct about how often loose passive has us beat, we are still +13 $EV. And if you are correct about the reg, but I'm correct about the station, we are around +46 $EV. It seems both of your assumptions need to be very close to correct for this to be -EV.

I'm doing alot of mental arithmetic here well past midnight, so if my my maths are ****ed up anywhere, plz let me know

Shouldnt we check turn here for potcontrol?

Can we assume:
V1 - x/r flop with hands like KQdd/JTdd/98dd? Maybe not oop?
V2 - AI ($235) on river with 8X?

I'd size up flop/turn 3-way for value, then smaller on river to target AX.

I was writing something much longer than this last night that basically was only saying this, and then I got too busy to finish.
I would have sized up on the turn to $225-ish here and checked back the river.
Edit: yeah, size bigger on the flop is good too.
Shove river is too optimistic imo.

Phil Me Up:

Your maths are good, but one thing to understand is that V2 is never calling 100% frequency when V1 folds. Even the worst of the worst can still have missed draws, or find a "good fold" with QJ. That's part of why I said my assumptions were generous, as I was giving full frequency to V2 calling.

It's more likely that V2 calls somewhere around two-thirds of the time when V1 folds. With your "80% when called assumption", our bet would be worth:
(0.1)(-505) = -50.5
(.9)(2/3)(.2 * -235 + .8 * 235) = +84
+33.5

I think V1 has a pretty restrictive range OTT after calling our 3-way bet. AQ, ATs/A9s, FD + Pair/SDs, likely a few hands better than AK playing it coy trying to bring in V2.

AQ/ATs/A9s are 12 combos together. {KQ-KTdd, QJ-QTdd, JT-J9dd} comprises 7 combos of draws. T9s is likely 2 combos (T9dd/T9hh). T8/98dd are 2 combos of trips.

If V1 has a range like this, 4 combos beat us OTR, and the other 19 combos fold. This would mean we're beat by V1 17.4% of the time.

I think this is a reasonable range. It excludes hands like AJ/77/JJ that beat us & could sometimes take V's line, even if rarely. The presence of the fish likely incentivizes V1 to play his combo draws passively, rather than semi bluffing with them.

Checking certainly isn't a bad option (and it's definitely the safest), but a lot of players don't win as much as they could, because they don't get full value out of the hands they're winning. The draws have missed the board, and 8s shouldn't really be in the villain's range, so all we're really scared of here is a slowplayed set, or maybe someone playing AJ conservatively. I think there's thin value to be gained from betting.

I mean, it just gets wildly complex doesn't it? 2 ranges that also interact with one another+our sizing choice, etc.
Also, did you calculate the EV of Checking against the same ranges compared to betting all in?

After the river bet, V2 cursed and flashed J7 to my side of the table. V1 then went into the tank and eventually had clock called on him before calling at the last second. We were good and V1 never ended up showing. I guess AQ is his most likely hand. I think if we're only polarizing with FHs then we're repping such a thin range that he can profitably bluffcatch with some of his AQ (no Q).

My EV calculations with regard to betting/shoving river are the EV compared to checking back, and are based on certain assumptions outlined in my previous posts, namely V1 not calling equal/worse, both opponent's calling frequency, and how often we win against V2 when he calls us.

For example, if we're on the river with a medium hand, we know we always have the best hand, but also that villain is never calling any bet. Odd assumptions, sure, but under those assumptions, betting river and checking river have the same EV. That's the same type of math I used with my calculations.

Rofl that is so awesome