Re: Head up with big-draw, 2 similar 20/40 hands
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hand 1 - given your comment on Stoxx, i believe there are a few hands in the villain's range that you beat now, K9, K7, K6, QJ, QT, JT...so i think its justified to call down---but given that calling down is okay, i think its even better to get those two remaining bets in on the turn, and perhaps win the hand now, or if called buy a free showdown if you don't improve. If he 3 bets the turn, fold. If you improve, raise (either flush, K, or T). If he calls and you don't improve, then he raises the river, fold.
hand 2 - your read on the villain is that he is aggressive preflop, but only shows down solid hands...your only pressure on him was preflop, and he pushed back to test you...seemingly he has the initiative; the most severe test you can put him to is to check-raise here--if he 3 bets, fold; if he calls, then check/fold the river...as you said he is aggressive but only takes to showdown his good hands...lets play it based on your reads...
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We have flush draws most likely to the nuts in hands 1 and 2. Any line ending with folding before the river is just not a good one. In hand 2 he can certainly be 3 betting w/good K's and might even do it w/any K. In hand 1 our turn raise might look suspicious enough for villain to 3 bet an overair when we raise turn. Either way get to the river with whatever line we choose.
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