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If you are convinced that it's a bet/fold, try asking button for a free card. BB probably didn't whiff, despite his check. His stats tell me he has something solid, though it could be well be TT or AJs. The risk of giving a free card to those holdings isn't too great, and you'd love a free card against the rest of his range. Button may also have hit, and you'll find out for less by checking and re-evaluating than betting out.