Tbh I'm fairly new at constructing balanced ranges and this is my first post on the subject. I thought this was an interesting spot to work through.

Hero is playing a $0.25/$0.50 cash game at a university poker club, approx 7 handed. I don't think reads on V are relevant since this question is about good range construction not exploitable play.

The game is paying deep-stacked, Hero is ~$150 deep (300bb), V covers.

Loose-passive villain limps from the HJ, Hero raises to $2.50 from the CO, BTN calls, main V in the BB makes it $8, HJ folds, Hero calls, BTN calls.

3 Players ($24.75) - Flop T83
V bets $12, Hero calls, BTN folds.

HU ($48.75) - Turn (T83) J
V bets $32

What does our shoving range look like on this turn? In particular, what bluffs should we use? Do we need to have any pure bluffs or can we just use semi-bluffs here?

In a seven person home game? Reads are everything, including on you

Also, you're discussing shoving like 3 times the pot or something absurd like this, which means your range is generally a mix of nutty hands being played like you're scared + semibluffs.

I feel like you might lean towards draws because your big hands could raise smaller and/or call to extract a river bet from them. Which is also a reason why I'd simply bluff for less with my semibluffs. Make a similar raise to what you'd make if you had JT or 88

Hero's stack on the turn is about $130 after the preflop and flop bets have gone in, so a raise here would be less than pot-sized. I would never raise any hands on the turn that I would not be shoving.

But I do agree--reads are important.

Villain’s post flop line is weak but your shove reps little besides JTs.

QJ likely raises flop.

^We definitely rep/have JJ/TT/88 also. And personally i'm flatting my whole continuing range on this board texture, unless V is reeeeeeaaally exploitable.

Anyway, sets plus JTs, thats 11 value combo's. Given pot odds we should be bluffing a balanced range at a roughly 2:3 ratio, so with about 16 combo's.

That means if we shove all our draw combo's, we are overbluffing a lot. I probably select combo's with the least showdown value, like KcQx or AcQc, and flat pair+draws like QcJc and Td9d that don't block AcKc.
Vs his shove-calling range i'm not even sure those two hand groups differ that much in equity, so feel free to select combo's by other criteria. It probably doesn't matter much.

Having said all that, you can probably shove your entire range profitably vs a 25c/50c player who has a fold button.

I'd say JTs, 99, A9 clubs, JJ, KQ clubs. It doesn't make much sense to have a pure bluff in this spot.

It totally depends on your estimated fold equity, i.e, P(fold)

EV(shove) = P(fold)*(80.75) + (1 - P(fold))(P(win)*178.75 - ((1 - P(win))*98.75)

We can model this with WolframAlpha using x for P(fold) and y for P(win) by

Solve(80.75*x + (1 - x)(y*178.75 - ((1 - y)*98.75))==0,{x,y},Reals)

We can generate a nice contour plot with the following:

ContourPlot(80.75*x + (1 - x)(y*178.75 - (1 - y)*98.75)=0,{x,0,.6},{y,0,.4})



So to answer your question...we can pure bluff if and only if our fold equity is over ~56%

If we have say 9 nut outs, we have P(win) = y = 9/46 ~ .2 and can see from the graph we need about 38% fold equity.

If we have 15 nut outs, we have P(win) = y = 15/46 ~ .33 and can see from the graph we need about 11% fold equity.

This works for range vs. range equity estimates also when some of our outs are non-nut outs but beat much of villains' range, and sometimes villain is on a draw and we can win unimproved. Such is often the case when we have a hand like the NFD + two overs. (Technically this is a slight simplification as villain could theoretically bluff catch with K high vs an Ace high draw and still win by spiking a K).

Finally, note this implicit plot shows the break even solutions. If we ever have more than about 56% fold equity OR more than about 36% real equity we can ship profitably regardless of the other variable.

So if we have an Ace high with some draws and estimate its equity is over 36% against villains' range OTT, we can ship profitably regardless of whether he ever folds.

Hope this helps. Constructing a shoving range is straightforward once you know your estimated FE and your RE. For instance if villain folds one time in three we need about 22% real equity so we can shove anything with 9 outs or more. If he folds half the time we can shove super wide including gutshots.

I don't think I made any errors here but it's always possible with this kind of tedious work so if anybody spots anything please point it out

This is the GTO answer to the question essentially. This makes the assumption that the villain will be indifferent to calling or folding. In reality, the villain's actual range is more important. If he's only got strong hands here (as he defines), then you don't bluff. If he can have a wide range, you can bluff the first time a lot. However, once everyone sees your hand, they will adjust.

I think reads on V are very important here. If he's a calling station or only betting for value, don't bluff. If he's a LAG and is betting turn with his entire range, bluff away. How much you bluff (semi, total, etc.) depends on reads, too.