That truly is an unpleasant run of cards, but I'm not seeing any line that is systematically better. No quarrel with the way you played it. Most other lines risk other headaches that aren't any better. To answer your questions:
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Originally Posted by Summer Is Coming
QUESTION #1: Should I always be betting this flop?
Put me in the yes camp. Against one opponent you could get cute and see if Tx, A-rag or a busted draw gives you more action if you check. But against two Villains, the range of free cards that could give somebody 2 pair or a straight is too darn big. Bet to protect your equity.
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QUESTION #2: If we do decide to bet, what kind of bet sizing are we using here?
I'm fine with our sizing, though clearly if you bet bigger (pot? 1.5x pot) you probably could kick out the flush draws and OESD draws. On the other hand, you're telegraphing your Ax pretty clearly then ... and you're very vulnerable to a real or bluffed two pair/flush.
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QUESTION #3: After it's checked around on the turn, are we ever calling villain 2's river bet?
If this were heads up, it's borderline. There's maybe a 30% chance he's trying to buy the pot with a busted draw. Three-way, though, there's the added risk that the SB is slow-playing ... and if so, you can't beat them both.