Patent ID: 8099326

Claim:
A computer-implemented method comprising: receiving, by a server system from a client system associated with a user, criteria for media play placement in a media feed; generating a list of available ads based on the received criteria; for each one of the available ads on the generated list, selecting, by the server system, an overspending cost per thousand (CPM) bid and an underspending CPM bid for the one of the available ads, defining, by the server system, a bid interval that includes the overspending CPM bid as one endpoint, and the underspending CPM bid as the other endpoint, iteratively, until the bid interval has converged within a threshold range: applying, by the server system, a reguli falsi process to the bid interval until the bid interval converges, then, when a range of the converged bid interval is larger than the threshold range, applying, by the server system, a bisection process to the converged bid interval for a predetermined period of time, and outputting, as an expected CPM bid for the one of the available ads, a result of applying the reguli falsi process and the bisection process; and generating, by the server system, bids for the available ads on the generated list as the corresponding expected CPM bids that have been output via the reguli falsi process and the bisection process.