This invention concerns optimal ad selection for Web pages by selecting and updating an attribute set, obtaining and updating an ad-attribute profile, and optimally choosing the next ad. The present invention associates a set of attributes with each customer. The attributes reflect the customers' interests and they incorporate the characteristics that impact ad selection. Similarly, the present invention associates with each ad an ad-attribute profile in order to calculate a customer's estimated ad selection probability and measure the uncertainty in that estimate. An ad selection algorithm optimally selects which ad to show based on the click probability estimates and the uncertainties regarding these estimates.