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Simultaneous, separate ascending auctions are ubiquitous, even when agents have preferences over combinations of goods, from which arises the emph{exposure problem}. Little is known about strategies that perform well when the exposure problem is important. We present a new family of bidding strategies for this situation, in which agents form and utilize various amounts of information from predictions of the distribution of final prices. The predictor strategies we define differ in their choice of method for generating the initial (pre-auction) prediction. We explore several methods, but focus on emph{self-confirming} predictions. An agents prediction of characteristics of the distribution of closing prices is self-confirming if, when all agents follow the same predictor bidding strategy, the final price distributions that actually result are consistent with the utilized characteristics of the prediction. We extensively analyze an auction environment with five goods, and five agents who each can choose from 53 different bidding strategies (resulting in over 4.2 million distinct strategy combinations). We find that the self-confirming distribution predictor is a highly stable, pure-strategy Nash equilibrium. We have been unable to find any other Nash strategies in this environment. In limited experiments in other environments the self-confirming distribution predictor consistently performs well, but is not generally a pure-strategy Nash equilibrium.