Question

what value is used to determine whether your ad will show on a page and if so the ad's position?

Answer 1

Ad Rank is used to determine whether your ad will show on a page and if so the ad's position.

Ad Rank will be recalculated every time an ad is displayed and completes in an auction.

Hence, this will keep on fluctuating the position of the ad as per the competition, quality at the moment and even the context of a person search.