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How Many Unknown Cards? How Many Unknown Cards?

11-13-2018 , 05:11 PM
There hasn’t been a posting in this forum for over 6 days so to get the ball rolling (maybe), here’s one:

You hold KT on a board of K 4 8 T, three hearts. You are almost certain villain has a flush when he goes all-in. You have 4 outs for a full house win (kings and tens) ignoring the extremely unlikely one-outer for a straight flush. What is your equity?

The 2x rule says 2*4 =8%, but we know that is a simple approximation. The “exact” answer is 4/R where R is the remaining unknown cards. So, what is R?

6 cards are precisely known, the two in your hand and the four on the board. That leaves, at most, 46 unknowns. But, we also stated that villain has a flush (almost certainly), so we can infer that villain doesn’t have a king or ten for if he did he could not have a flush. That confirms that our four outs are in the deck, but what does it tell us about R?

Should we reduce the 46 unknowns to 44?
How Many Unknown Cards? Quote
11-13-2018 , 08:32 PM
How is a straight flush relevant?
A heart can not pair the board giving us a full house. We know all of the relevant information about villain's cards. It makes no difference whether we know villain has specifically QhJh or that we only know he has a flush. The answer is 4/44.
How Many Unknown Cards? Quote
11-13-2018 , 08:40 PM
I'd say yes, it makes sense to do so, because an inference here is as good as seeing the cards. But it almost certainly won't change your decision about whether or not to call. Unless his all-in gives you well over 10-1 odds, you have to be folding. And if his all-in does give you that good of odds, then it would be a very small shove, and you couldn't be sure he has a flush.
How Many Unknown Cards? Quote
11-13-2018 , 08:54 PM
Quote:
Originally Posted by browni3141
How is a straight flush relevant?
It isn't. I don't know why I put that in at the last minute.
How Many Unknown Cards? Quote

      
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