Why was Saratoga and the Hudson River strategically important during the Revolutionary War?

Ascientist successfully predicts the outcome of an experiment. you watch carefully and know he didn't cheat. the scientist's success shows that: a) the scientist knows absolute truth about this experiment; success is not possible unless you know the truthb) the scientist was just lucky; no one ever knows what's going on, so successful predictions require luckc) the scientist may know the truth, or at least know something that is close to the truth, or the scientist may have gotten lucky this time; you can't be absolutely sured) the scientist really was cheating, even though you didn't see the cheating; no one can get things right, except by cheatinge) the scientist spent the night at a particular hotel chain and go a free breakfast, giving the scientist the ability to do amazing things