Playing 1/3 NLHE. Eff stacks $300

3 players open limp.

Villain 1 is a WG in 50's, with long beard and glasses. Recently pushed us off a pot, and needled us about it. He is in the CO
Villain 2 is about 40-50 WG guy. Been relatively quiet. He is on Button
Villain 3 is 30-40, and he is steaming from a couple of hands prior where he was sucked out on. Been complaining vocally. He is in the SB.

Hero is in the BB with T9o and checks.

$12 Pot
Flop is a T97 rainbow.
SB checks
Hero leads for $10
V1 calls, V2 raises to $60, and V3 calls.
$152 in the pot.

What do you think these guys have? What would you do in this spot? Would you have done anything different if you were hero?

Fold, and I probably play it the same.

unraised pot

facing real aggression from multiple spots


easy fold

I'm fine with preflop.

I bet slightly less on the flop. Two pear (even top two pear) isn't nearly as good a hand as everyone thinks it is (especially in games where most people don't go nutso/broke with TP) so I'm not looking to build a huge pot at this point, so I simply bet smaller.

I fold to the flop action (and likely would have folded even without the call). A quiet guy just raised the flop. Quiet guys don't raise the flop with one pair (and overpairs would mostly have raised on the Button). We only beat a handful of worse two pairs, but we lose to all sets and straights. And on top of that we still have to worry about the SB taking this big raise cold to the face.

GcluelessNLnoobG

V2 has you crushed. muck it.

Unless you hit your 4 outer, you're going to have no idea where you're at on any street so fold.

So what ended up happening was that Hero folded, and V1 called.

Turn card was a Jack.
V3 bet the turn.
V1 called
V2 folded

River was a 6. All the money went in.
V3 showed down QJ
V1 showed down K8o for the winning straight at the end

This was what I have been asking myself after the hand was played, as we do block a lot of sets, but we also block a lot of the hands that we want to be called by (other two pair). We don't block straights, or straight draws.

Whatever else we may think, this is a very clear shove or fold spot. Calling makes no sense at all. So what do we get called by if we shove? I cracked open an equity calculator and plugged some numbers in. Here is what I found.

For starters, assume I shove for $300, and get called by just one player.

1. Get called by made straights, and sets only
No surprise here, we have miserable 17.568% equity in the pot.

2. Straights, sets, and all Two Pair combos
36.144% equity. Better, but still not what we want.

3. Straights, sets, all Two Pair combos, and all pair plus 8 combos
46.966% equity. Still not what we want, although now we can start talking about the money in the pot already, maybe making this worth it from pot odd POV.

4. Straights, sets, all Two Pair combos, all pair plus 8 combos, and JT, QJ 88
52.405% equity.

5. Straights, sets, Two Pair combos, all pair plus 8 combos, and some other 8's
By other 8's I mean all combos of A8 and K8, plus 88, Q8s, 82s, 83s, 84s, 85s. Fish do like any suited cards.
Here we have 56.127% equity.

6. Straights, sets, Two Pair combos, all pair plus 8 combos, JT, QJ, 88, and some other 8's
57.82% equity

There was $137 (after rake) in the pot by the time the action got to us. If we push for $290 there is $427 in the pot.
V2 and V3 need to call $230 so they are getting about the right price to call with their open enders.

Its a complicated spot with multiple players. If I assume that V1 calls with range #5, V2 calls with Range #2, and V3 calls with Range # 4 then we have only 18% equity.... but that's if they all call.

If V2 always folds, then we have 35% equity.

So I am guessing that from a pure math POV this is always a shove, since we must have some fold equity (where all 3 fold, or two fold), and get called wide enough to be in a +EV spot, especially with the chips already out there. But I have no idea how to factor in fold equity with this many players.

Does anyone know how to work out the full math ie plug in each players calling range, and folding %, and calculate all the different scenarios?

Pokerstove knows what's up if everyone calls.

Anything else is better the more folds we get.

You make a good point about simplicity here. We spend a lot of effort in this forum measuring with a micrometer and cutting with a meat axe.

(ETA: I got chided recently in another thread for focusing on what I thought was the most-likely holding of a V and using that as the fulcrum of my analysis for a river decision. What the hell else can you do on the river in real time at the table? Integral calculus of V's range probability distribution function?)

In this case on the flop, your equity and probability assessments are important, but so is your FE estimate. So we can measure the former pretty carefully, but the latter is subjective and highly prone to error. That said, since our weakest FE generally is on the flop, it's important not to over-estimate it.

But I liked your idea of getting the math within a sand wedge/lag putt of the hole and then focusing on the FE/subjective issues. Normally our FE/subjective errors are way larger than our math errors in real time.

This post definitely took a dramatic turn for the better.

It went from suggestions of "easy fold" to figuring out the math to figuring out a reasonable approximation that can be used at the table. Using the latter, it's nice to see that an AI is likely +EV. Nicely done.