Calling off with QQ on KXXccc flop

Hero raises in CO with QhQs, Villain (51/13/1.9) limp/calls UTG.

Flop is Kc4cJc, the pot is .58 and the effective stack is 1.31. Villain mindonks and I make it .48 (this cbet may have been too large, but let’s consider what happens next). Villain shoves and we’re getting 2.86 to 1 to call. Hero needs 26% equity against Villain’s range for the call to be profitable.

I don’t expect Villain to have KK, JJ, KJ, AK or KQ because he will usually raise these hands. So, the value hands we’re behind are 44, K4s, J4s and VcWc. How many flush draws does Villain need to shove in order for the call to be profitable?

Villain’s NFDs are flipping with us. We have ~60% equity against FDs that don’t have the Ac.

hand type combos equity
9 made combos 44, K4s, J4s 13.5%
X flush combos VcWc ~2.8%
Y draw combos VcWx > 50%

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This linear function says to call the jam when Villain has at least 5 more draws than value hands. This is a conservative estimate granted that many of his draws have less than 50% equity against Hero’s hand. How many flushes v FDs do we expect Villain to have?

Let’s assume that Villain is playing every suited hand (remember, 51/13/1.9); this means that he has (10 choose 2) = 45 flush combos. This is a conservative estimate for 2 reasons, 1) we expect Villain to open raise AcQc/AcTc/Ac9c and 2) he might fold trash like Tc2c/9c4c/7c2c/etc.

Consider Villain’s best draws (assume Villain open raises A9+),

# combos range
21 Ac2x-Ac8x
12 Qc8x-QcJx
6 Tc8x-Tc9x

We expect villain to have ~39 3rdnut+ FDs.

Using the function we derived earlier, how many draws does Villain need to be shoving if he is playing/shoving every XcXc?

.962(45) + 4.562 = 47.852

47.852 > 39, calling is possibly a small mistake if he only shoves 3rdnut+ FDs.

 What # of flush combos makes calling profitable when Villain shoves 3rdnut+ FDs?

39 = .962X + 4.652

X = 35.704

Calling is profitable when Villain has less than 36 XcXc combos (top 80% of suited hands).


 How does Hero’s equity change when he has the Qc (the draw to the 2nd nut flush)?

hand type combos equity
9 made combos 44, K4s, J4s 43%
W nut flush combos AcVc 2.8%
X small flush combos: VcWc ~32%
Y nut FD combos AcV ~50%
Z small FD combos VcW ~98%

Hero’s equity has drastically increased against flushes and draws where Villain doens’t have the Ac. On the flip side, we also know that Villain won’t have any 2ndnut flush draws to shove on us, so we should expect him to shove less draws.

Let’s make a conservative estimate of how many FDs Villain needs to have in order for calling to be profitable. We will assume that Villain is playing all XcXc combos; also assume that Hero only has 50% equity against all draws (the same as in the original case).

hand type combos equity
9 made combos 44, K4s, J4s 43%
8 nut flush combos* AcVc 2.8%
28 small flush combos* VcWc ~32%
Y draw combos VcW ~50%

* sanity check: 8 + 28 = 8 + (8 choose 2) = (9 choose 2) = 36

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At minimum, we need villain to shove a negative number of FDs; thus we should always be calling as he will always shove more than a negative amount of FDs.

Does this make sense, considering that we need 26% equity to call? What is our equity against his range when he doesn’t shove any FDs?

(9/45)(.43) + (8/45)(.028) + (28/45)(.32) = .29 = 29%

29% > 26%, so this seems to check out. In other words, when Hero has the Qc (2ndnut FD) he doesn’t need Villain to shove any draws for calling to be profitable. It seems clear that we should be more inclined to call when we have the Qc.


 What is the minimum # of small flushes Villain must shove when he shoves zero draws for calling to be profitable?

Continue considering the case where Hero has the Qc.

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Hero should always call when Villain shoves at least 6 small flushes and has less than 8 NF combos.

 
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