[Ribbo]

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I probably would not have raised from the BB with that hand as you are out of position, but others would.

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Position is far less relevant 3 handed, raising the best hand is far more relevant. Raise, if you get reraised, raise them back, they don't have AA and will fold.
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On the turn, I'd probably check. Once you are raised, you have to fold.

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You will get chewed up alive in shorthanded games playing like this. Check folding a queen high flush 3 handed to any bet from the button? Do you even know how to play the game? Bet the pot on the turn and fold to the reraise. The chance of one of the other 2 players having the suited ace of hearts is around 1 in 10. If they have a king of hearts suited then you want to put pressure on them to fold.
But just checking the turn and folding to ANY bet is quite frankly weak and utterly terrible 3 handed. If I had the button I would be betting any flush if checked to me, even 3 high, since it's likely good at this point against 2 checkers.