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In LLSNL I find it better to stop worrying about the mistakes your villains are making and start thinking about your own.
Why would they be mutually exclusive? A mistake is a mistake, and learning from others mistakes is much cheaper than learning from our own. Additionally, if you can't put him on a range besides possible KK, how do we even know what a mistake is?
This phrase is overused so much, and no it literally cannot be burning money to bet in this spot. 3 pure outs to the nuts, a spot where villain cannot c bet with air very often, a board that hits my preflop overcalling range in this spot quite well which affords me the ability to bluff with some frequency, and we can represent the flush on turns and rivers.
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The HJ could likely have KK, too.
Villain "could" have the current nuts seems very lazy. He could have KK, could have checked the flop with AQ/AJ/AT/88/77/66/55/QJ/JT. Additionally, if he does have KK, it seems like when stacks get in on the turn or river it's likely that we will be favorites.