Unsure whether to c-bet?

[MadMojoMonkey]

Example: We have A T and X-ray specs. Villain has 22. We get into a blindwar and end up 5bet shoving with 51% equity for 100bbs.

Q1) Are we hoping he calls or folds?

Q2) Is it possible for him to fold a better hand, or call with a worse hand?

Q3) What type of bet is this? e.g. bluff/valuebet

Q4) Are there any other reasons to make a bet besides folding a better hand, or getting value from a worse hand?

1) Hope he calls, 'cause our 51% equity is more than his 49%.
2) It is not possible for him to fold a better hand, because we have x-ray specs and know that our hand has more equity. It is possible for him to call with a worse hand for the same reason.
3) This is a value bet, Hero has the most equity.
4) No.*

*caveat: meta-game against a tough reg, but this is really just because we're playing ranges, not hands.

[Pelion]

I strongly suggest you work out the EV of:

100bb stacks

Villain raises to 3bb.
We 3bet to 9bb.
Villain 4bets to 22bb
We shove for 100bb.

EV of villain folding vs Calling when we have 51% equity.

[Micro2Macro]

1) Hope he calls, 'cause our 51% equity is more than his 49%.
2) It is not possible for him to fold a better hand, because we have x-ray specs and know that our hand has more equity. It is possible for him to call with a worse hand for the same reason.
3) This is a value bet, Hero has the most equity.
4) No.*

*caveat: meta-game against a tough reg, but this is really just because we're playing ranges, not hands.

we'd prefer he folds because folding would be a mistake.

[MadMojoMonkey]

You need to make sure you are calculating EV from the same point in each case. Either both from the start of the hand, or both from the point of the decision.

I should have known something was amiss when things came out like that, but !@#$ migraine headaches do weird things to my thought process.

From the moment of Villain's decision:
If Villain folds, Hero's EV is:
100bb + 22bb = 122bb
All of the chips in the middle.

If Villain calls, Hero's EV is Hero's equity times the size of the pot:
51%*200bb = 102bb

Also note that the first of these is an EV calculation. The second is an equity calculation. The two are not the same and you can't draw a direct comparison between these numbers.

The sum of all probabilities (equities) times their associated outcomes (profit) is the EV.
51%*200bb + 49%*0bb = 102bb

When villain calls, our EV is the difference between what we expect to end the hand with and our stack at the moment.

Hero's stack at the moment when he's all in is 0bb.

I see that you consider Hero's stack to be 91bb in the following analysis, which is Hero's stack prior to the shove.

so EV if villain folds is +31bb.

EV if villain calls is 102 - 91 = +11b

You can also work this out as a 109bb (pot + villain stack) win 51% of the time, or a 91bb (our stack) loss 49% of the time. 0.51*109 - 0.49*91 = +11bb

31bb > 11bb so we want him to fold

This is, of course, all true.

We both show a spread of 20bb in favor of Villain folding.

we'd prefer he folds because folding would be a mistake.

Yes. I see it now. Thanks.