In previous work we have introduced a principled methodology for systematically exploring the space of bidding strategies when agents participate in a significant number of simultaneous auctions, and thus finding an analytical solution is not possible. We decompose the problem into sub-problems and then use rigorous experimentation to determine the best partial strategies. In this paper we clarify and extend our methodology. We also examine the Bayes-Nash equilibria for some of the design tradeoffs that arise when the problem is decomposed and each tradeoff is examined independently and provide some equilibrium strategies. Our agent White-Bear was created by using the results of this methodology and has consistently been a top-scoring agent in all the competitions.