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Check the turn and evaluate

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Won't that give a flush draw an oppurtunity for a free card?

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The reality is that half the time you're already beat by JJ or QQ. Against A-Ks or A-Qs with the draw, you're not that great anyway. You don't have a big hand. Check the turn to control the pot and reevaluate based upon his action. You can fold this overpair if he bets the turn strong. I repeat, your hand is very marginal.