This paper proposes a learning model of online ad auctions that allows for the following four key realistic characteristics of contemporary online auctions: (1) ad slots can have different values and click-through rates depending on users' search queries, (2) the number and identity of competing advertisers are unobserved and change with each auction, (3) advertisers only receive partial, aggregated feedback, and (4) payment rules are only partially specified. We model advertisers as agents governed by an adversarial bandit algorithm, independent of auction mechanism intricacies. Our objective is to simulate the behavior of advertisers for counterfactual analysis, prediction, and inference purposes. Our findings reveal that, in such richer environments, "soft floors" can enhance key performance metrics even when bidders are drawn from the same population. We further demonstrate how to infer advertiser value distributions from observed bids, thereby affirming the practical efficacy of our approach even in a more realistic auction setting.