Although I think results are immaterial, for those that are interested, V1 flips JT, V2 flips T4, you know what hero has.

River is the A

This is actually lower EV than the situation I computed since only 2 of your chop outs were live.

The "FTOP correct" play is to fold. I suspect folding is the correct play against the total combined ranges of V1 and V2 as well.

I think when he says bound it refers to a best or worst case scenario. It's 100% of something. For instance the upper bound is we have 100% equity.

The lower bound, for EV, is someone has a ten and the three other cards the Villains have are three of our outs. I'm not sure how you're proposing to put a percentage on what's worst case (lower bound).

Worst/Best case is 100% of one particular scenario -- that's a "bound".

For a simple example if you have kings perflop worst case is assuming you're against aces 100% of the time. That's the "lower bound" of EV.

I know, he was putting 100% on the lower bound of 11 outs. That's not the worst scenario. TcXc and TxXc gives us only 10 outs. That is not a ridiculously unlikely scenario. It's 1/2, XcXc and TcXc isn't impossible either, that's 9 outs. So saying the worst scenario is 11 outs is a terrible lower bound.

__________

Lower bound

V1: 5c6c
V2: Tc9c
OP: AcQc

To call V2's shove it costs $398, that's what we can lose.
Chopping gets us 1/3 of the $162 = $54 in the pot once we go to the turn.
If we win we get the $162 + V1's $350 + V2's $398 = $910.

We're 21.43% here to win and 7.14% to tie.

(.2143*910)+(54*.0714)-(.7143*398) = -$85.4228

__________

Upper bound

V1: 5c6c
V2: 3c4c
OP: AcQc

We're 92.86% to win and the same 7.14% to chop.

(.9286*910)+(.0714*54) = $848.8816

__________

So our interal is (lower bound, upper bound) = (-85.4228, 848.8816). Since the lower bound is negative, there are times where it's a fold, and to get a point estimate, we'd need to attach weights to every possible scenario.

CMV was fortunate that his lower bound was also less than zero. So while he came to the correct conclusion of there being times where this is a fold, his lower bound wasn't an accurate lower bound. For example, had the 11 out scenario given an EV of +$2, CMV would have concluded that even in the worst case scenario, the EV is positive, so it's always a call. But the 10-out or 9-out [correct] lower bound would give an EV less than zero and in that case the conclusions would be different.

But my original point was to attach weights to each EV scenario and get a point estimate, not an interval estimate. If you do go with an interval estimate, the lower bound actually needs to be the worst case scenario, and the 11-out scenario wasn't the worst scenario, just a less than ideal one.

FWIW, I woudda made an insurance bet with anybody at the table that they both had tens, but nobody would have taken it. It was truly obvious. V1 does NOT want V2 to draw out on him, so he shoves, V2 has no wiggle room left, he will never call less than a str8 here (his game is pressuring people, not hero calling draws without knowing the final odds).

The smirk on V2's face told me he was freerolling clubs also. The look on V1's face was priceless when I told him V2 was freerolling clubs, while I was tanking. He never even considered that possibility, lol.