20. A method for maximizing page yield by optimizing display depth of advertisements displayed to searching Web users, the method executed by a server having a processor and memory, the method comprising: (a) tracking click activity, by the server, on a plurality of sponsored advertisements by a plurality of users via a set of hierarchal search results pages delivered in response to a search query for a keyword by a search engine; (b) tracking bidding activity, by the server, of a plurality of advertisers related to the keyword and corresponding advertisements of the plurality of advertisements; (c) calculating, by the processor, an optimum number of advertisements (k*) to display on a particular search results page of the set of hierarchal search results pages in response to the search query such that a probability that a total share of click volume being greater than that of any of the plurality of advertisers is less than or equal to a predetermined business tuning parameter (β), wherein the probability values are obtained from a probability of click distribution based on the tracked click activity from at least one query; (d) executing, by the processor, a Monte Carlo randomization procedure to include: (i) randomly sampling a different probability of click distribution than that of step (c) based on at least one different query; (ii) recalculating k* as per step (c); and (iii) repeating steps (i) and (ii) to calculate potential multiple optimum numbers (k*) of advertisements; and (e) serving, by the server, to the particular search results page at least some of the plurality of advertisements according to at least one calculated value of k* in response to the search query for the keyword.
20. A method for maximizing page yield by optimizing display depth of advertisements displayed to searching Web users, the method executed by a server having a processor and memory, the method comprising: (a) tracking click activity, by the server, on a plurality of sponsored advertisements by a plurality of users via a set of hierarchal search results pages delivered in response to a search query for a keyword by a search engine; (b) tracking bidding activity, by the server, of a plurality of advertisers related to the keyword and corresponding advertisements of the plurality of advertisements; (c) calculating, by the processor, an optimum number of advertisements (k*) to display on a particular search results page of the set of hierarchal search results pages in response to the search query such that a probability that a total share of click volume being greater than that of any of the plurality of advertisers is less than or equal to a predetermined business tuning parameter (β), wherein the probability values are obtained from a probability of click distribution based on the tracked click activity from at least one query; (d) executing, by the processor, a Monte Carlo randomization procedure to include: (i) randomly sampling a different probability of click distribution than that of step (c) based on at least one different query; (ii) recalculating k* as per step (c); and (iii) repeating steps (i) and (ii) to calculate potential multiple optimum numbers (k*) of advertisements; and (e) serving, by the server, to the particular search results page at least some of the plurality of advertisements according to at least one calculated value of k* in response to the search query for the keyword. 21. The method of claim 20 , wherein each value of k* represents a display depth on the particular search results page, wherein calculating k* in step (c) further comprises: (f) computing class cardinality of the plurality of advertisers based on price bid elasticity of each advertiser for the keyword, wherein the class cardinality includes classes comprising at least market maker, market follower, and market neutral; (g) decrementing k* by 1 if the class of the advertiser at the display depth corresponding to k* is market neutral; and (h) repeating step (g) until the advertiser at the given depth is determined to be a market maker or a market follower.