[Aaron W.]

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does anyone bet this flop, figuring BB will raise and protect our overcards?

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I don't. Even if villain raises, the likelihood of BB folding out anyone holding a hand that bothers us (AK/AQ) is incredibly remote. There's no way any one pair hands are folding in this gigantic pot.

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You should toss in some value bets on this turn--you have lots of outs to a straight or flush here, and will win a lot.

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With the aggressor on the flop acting immediately after hero, checking is better. If villain bets and a bunch of people call, then a check-raise would do well. If hero bets and villain raises, then hero is sad because everyone gets shut out of the pot.