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You have the nut straight, and you'd have to
split the pot with anyone else
holding AQ. Any (heart) on the river, however, will give you the nut flush, and the other player with AQ would get none of the pot instead of half of it.
This example illustrates the benefit of being suited: it gives you an additional out. For example, if you have and the flop is , you have the nut straight. If the turn card is another , then you have a draw to a backdoor flush, which will beat anyone else holding a 109, or anyone who made a straight on the turn.
How do you play your hand when you are freerolling? There are three things you must always do: raise, raise and raise. It doesn't matter if you don't make the draw; you still have the nuts. You'll get in extra bets with a winning hand, and that's the essence of winning poker. There is one situation that you should watch out for: when you're freerolling and it's four bets to go on the turn. With that many bets, if your freeroll draw isn't to the nuts, one of the other raisers probably has it.