How Randomization Can Improve the Performance of Greely?

I was wondering if we could return to some of the efficiency calculations. What you calculate is doing better than the greedy strategy, though admittedly not as good as the approach that uses bid shading. When we knew the true budgets, of course we're more blinded in this situation,. But where do our results come from? How is it that, even lacking the budget information, is there some corp kernel of truth of what we take advantage of to beat the greedy agarithm?"