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However, once YOU know the ENTIRE BOARD with 100% certainty before the flop is even dealt, you completely eliminate your need to rely on probabilities.

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You still need to put your opponents on a probable range of hands.

Now that I think about it, the advantage to seeing your opponents hole cards is even bigger than it first seems. It's been said on here before, but knowing an extra 18 cards is a huge advantage in calculating your outs. There will be only 29 and 28 unknown cards on the turn and river, repectively, instead of the normal 47 and 46. In addition to the fact that you can play better against your opponents, you can also better determine the odds of you hitting your hand AND knowing which of your outs are live.

(Slightly off-topic for my post: you still can't be sure what to do if you know that a flush draw on the flop will be completed on the river, and you are holding top pair top kicker against two calling opponents.)