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i think Btn's preflop calling range are mostly Ax, broadway cards and pocket pairs as well as some suited connectors. he's probably raising his big pairs.
i'd expect him to fold his pocket pairs lower than TT and maybe some weak Ax hands. Therefore his flop calling range are mostly 1) pair+drawing hands like AJ, AT, KJ, QJ or 2) two pair hands like KQ, AQ that he didn't want to 4-bet pre. trips are not impossible but unlikely. He could also be on a flush draw.
considering his range is heavily weighed towards pair+draw combos and he may pick up a flush draw on the turn, there's no reason to check and give him a free card. (unless he's aggressive then we can chk-raise and stick the money in on the turn) i'd keep betting at the pot. may be 2/3 of the pot. if he raises it's gonna suck....
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