Does applying earlier to UK universities increase chances of admission??

<p>I am an american looking to apply to U edinburgh, U st andrews and U aberdeen ....</p>

<p>Will putting the application in asap increase my chances of getting in??...is that how the rolling admissions work? (i assume its rolling)</p>

<p>Also if im accepted unconditionally to all my schools, how long do I have until I have to choose to accept one, and is it binding?</p>

<p>also does anyone know statistics on how difficult it is for americans to get into these schools?
Please help me out here ( :</p>