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I still think y'all are crazy to fold here. I believe Hero can profit from a check/call of an all-in flop bet because he's ahead of villain's range.
Edit - I had some nonsense here.
Example: If the straight draws are in villain's range AND NOTHING ELSE WE LIKE, Hero has 52% equity here against K6-KQ and sets (boats). And KQ and KJ are in his likely 14% PFR range.
Stove: 2,816 games 0.005 secs 563,200 games/sec
Board: Ks 9c 7s Kd
Dead:
equity win tie pots won pots tied
Hand 0: 52.326% 46.41% 05.91% 1307 166.50 { Kh5h }
Hand 1: 47.674% 41.76% 05.91% 1176 166.50 { 99, 77, K6s+, T8s, 86s, K6o+, T8o, 86o }
Edit close
We can debate the likelihood of ranges, but Hero just doesn't need all that much non-Kx to be in the range to have 50% + equity here. Here's some interesting results you can verify (and you should - poker stove is acting quirky on me, so I've had to run a couple of these more than once - I stopped as soon as I got the same answer twice in row).
Bad News for Hero:
Hero has 21% equity against Kx (x>5), 77 and 99. (Note that Hero has 50% equity against Kx w/ x<6, so ignore.)
Good news for Hero
Hero has 89% equity against T8, 97, and 86 (all combos) Edit: 97 unlikely in extreme.
Hero has 98% equity against Ax (at least one card NOT spades - everything but AK is drawing dead).
Hero has 84% equity against Axs (spades).
Hero has 82% equity against Q9s, J9s, T9s & 98s (all spades), the best combo hands not covered above.
Hero's Equity
You can do your own estimates of equity by making a weighted average based on the % likelihood you feel each category is represented. When performing that averaging estimate, it helps (but is not mandatory) to know the following:
There are (6*4 + 2*3 = ) 30 combo's of Kx (x>5), and (2*3 = ) 6 combos of 77 and 99.
There are (3*9 = ) 27 combo's of T8, 97, and 86.
There are 10 combo's of Axs (spades only).
There are (9*16 =) 151 combo's of Ax (x not = K, 9, 7, 5).
There are 4 combo's of AK and 24 combo's of A7 / A9.
We then have to discount various portions of this range including some of the less likely Kx hands, like KQ and AK, for example, which are probably in his PFR range. It would be interesting to see what other folks come up with if they're willing to do the work involved. If you're not, at least say what's in your range and run it in PokerStove.
Hero Profits when calling a turn-shove
The turn got funky. Let's just compute what we'd need to see Hero with equity to make check/calling an all-in shove +EV on the turn. Hero is much further ahead when he's ahead, meaning the number of combo's of OTHER hands to make Hero have more than 50% equity is something like 30 - 32, depending on which you choose.
For Hero to profit from a check/call of an all-in shove to be profitable, he only needs 47.4% equity.
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