While I agree with Jimmy's observation I don't agree entirely with the math.

If we are called here I have a hard time seeing us continue in the hand. If we want to be complete we should probably do calculations for the 3 different scenarios here:
1) A comes on turn after the call (we're now ahead of many Kx hands but behind AK)
2) Diamond comes on turn (we now have more equity and may decide to hang around for the non-nut flush)
3) Anything else

That said - on a superficial level it's true to say that 11% may be our hand equity but the value we realistically realize if called is closer to zero. 11% would be the number if and only if we went all in with the flop bets.

If we calculate with 0% chance of winning if called we find the following:
If he folds we win $72.
If he calls we lose $68.
If he folds 68/(68+72) = 48.6% of the time we are breakeven on fold equity alone.

Ok, let's go back to Goat's analysis now with the above in mind. I'm going to make some more gross assumptions to make the math simple.

The entire 3betting range (73 combinations) c-bet this flop 100% of the time (assumption).

Let us further assume that if he continues with his hand he calls (this may also not be true - there could be a 3bet) with the 21 hand combinations listed by Goat.

For the purpose of this analysis let us assume that if an A comes the villain will bet turn with AA, KK, AK (we fold) and check KQs and KJs, folding to a bet. This means if we get an A on the turn (3/47) we lose 15/21 of the time and win 6/21 of the time. For any other card we just lose. I'm going to ignore the flush draw option and say we fold or check down and lose any non-A turn.

EV(flop villain fold): $72 * (73-21)/73 = +$51.29
EV(flop call - A turn - villain fold): $108 * (21/73) * (3/47) * (6/21) = $108 * (3/47) * (6/73) = +$0.57
EV(flop call - A turn - hero fold): -$68 * (21/73) * (3/47) * (15/21) = -$68 * (15/73) * (3/47) = -$0.89
EV(flop call - non-A turn - hero fold): -$68 * (21/73) * (44/47) = -$18.31

EV: $51.29 + $0.57 - $0.89 - $18.31 = +$32.66

Now, let us assume that if the A comes the villain is clever enough to throw away KQs and KJs as above, but we're not - we hit our A and we foolishly end up going all-in on the turn. Of the above only the third EV changes but becomes three lines. Against the AA, KK, AK range we have 0% hand equity with As and Ac and 19.545% equity with Ad.

EV(flop call - As/Ac turn - both all-in hero loses): -$175 * (15/73) * (2/47) = $-1.53
EV(flop call - Ad turn - both all in hero loses): -175 * (15/73) * (1/47) * 0.80455 = -$0.62
EV(flop call - Ad turn - both all in hero wins): +$215 * (15/73) * (1/47) * 0.19545 = +$0.18

EV: $51.29 + $0.57 - $18.31 - $1.53 - $0.62 + 0.18 = $31.58

$1.08 less EV if we foolishly go all-in on any A that we hit.

This is all more example math than anything else - because our assumptions are not really realistic. The minute differences in EV come mainly from me calculating only the extreme example of an A coming on the turn which occurs 6% of the time.

An interesting exercise to do here would be to change the 3/47 number as a chance to hit the A on the turn based on us having decided that our opponent range is AA, KK, AK, KQs, KJs - of these 21 combinations 9 have one Ace and 3 have two Aces. This would mean there is 9/21 chance to have 3/47 chance to hit an ace, 9/21 chance to have 2/46 chance to hit an ace and 3/21 chance to have 1/45 chance to hit an ace. This gives us an ace on the turn 1 time out of 20.3 - slightly more than 2 effective outs because our opponents (known) narrow range counts as discounts. I could do the above maths with this in mind but won't.

Let's play another dream scenario here. This time our opponent does not cbet his entire 3betting range 100% of the time. This time he checks QQ, JJ, TT, 99, AQ, AJ, QJs some of the time. That's 45 combinations out of the 73 in the above computations and ... something struck me as wrong, so I added up combinations a couple of times. The mentioned combinations do come out at 45 - but I note that 73 for the 3betting range is actually 75 hand combinations. I'll ignore the error in the above and correct it in the below. And the bet/calling range should be AA, KK, AK, KQ, KJs - 30 hand combinations.

Hand combination list/table (one A, K and J accounted for - for KJs which is the only suited hand in the range 3 are possible because the known K and J are both diamonds - if they were different suits 2 would be the number):
AA: 3 combos
KK: 3 combos
QQ: 6 combos
JJ: 3 combos
TT: 6 combos
99: 6 combos
AK: 9 combos
AQ: 12 combos
AJ: 9 combos
KQ: 12 combos
KJs: 3 combos
QJs: 3 combos

It's probably not completely fair to state that the 45 combinations check every time - surely they will sometimes check and sometimes bet. Let's assume that two times out of three they check, and one time out of three they bet - I'll calculate that as if 30 hand combinations check and the 15 of these hand combinations bet along with the 30 hand combinations in AA, KK, AK, KQ, KJs.

Everywhere in the calculations where it used to state 21 it will now state 30. Where it says 15/21 it will now say 15/30 - where it says 6/21 it will say 15/30. Where it says 73 it would be fixed to 75, but since this calculation is based on some checks this calculation will use 45 in that spot as those are the hand combinations that bet - 30 hand combinations check.

And I won't do the "if A on turn" series - just the basic one where we either fold out the villain on the flop or lose the hand 100% of the time.

EV(flop villain fold): $72 * (45-30)/45 = +$24
EV(flop call - hero folds): -$68 * (30/45) = -$42.67

EV: $24 - $42.67 = -$18.67

Same calculation - this time the 45 combinations that can check or bet is the other way around - 2/3 they bet, 1/3 they check - this gives us effective 15 checking hand combinations and 60 betting hand combinations.

EV(flop villain fold): $72 * (60-30)/60 = +$36
EV(flop call - hero folds): -$68 * (30/60) = -$34
EV: $36 - $34 = +$2

I think the basic conclusion here is that if our opponent is wary of wa/wb and pot control and does not simply auto-cbet every chance he gets raising small here is not profitable for flop fold equity alone. He doesn't need a whole lot of caution to make it pretty universally unprofitable to raise small here.
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