[TheRenaissance]

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What hand would fold here that beats you?

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None. If I do this it is purely for value.

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And what hands that you beat would call?

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Villain is getting about 5:1, so he should call me with any flush or straight draw. I think there is a decent chance he will call me with Jx as well, having put in so much of his stack.

Note that I showed weakness on the turn by timing out when the ace fell, so I think (semi-)bluffs are a significant part of his range. Also, there is no real reason to think villain has an ace here except specifically AJ/A9/A5/AK/Adxd. That is quite a few hands, but I believe MOST of the hands villain gets to the turn with DO NOT contain an ace.

Now consider our alternatives on the turn:
Check-fold is terribly weak tight.
Check-call commits us.
Bet-fold is meh, as now we will be the ones gettting 5:1.

Also, and perhaps most importantly, if we do lead out on the turn we limit villain's range to almost exclusively hands that beat us. So bet-call does not seem like a good option either.

I know my line is not standard, but I think there some value in it. If anyone thinks another line is better, I would like to see the reasoning in more detail than what I've seen so far.