Jot your algorithm down in the simplest layman terms possible, and have a statistician look at it. It sounds like you're saying that you want a degree of randomness, but need tight control over the standard deviation of frequency of non-expected results. In other words, if you plot the frequency of non-expected results using a bell curve, you want a really steep curve with very short tails. This sort of thing is what statisticians understand best.

Without seeing the algorithm it'll be hard for us to suggest how to achieve a steep curve with short tails. And I'm not a statistician myself, so my helpfulness may be limited in that regard, though someone else may have the required understanding.

This also sounds a lot like the production / defect problem. Companies that use statistical analysis in their manufacturing will set a tollerance for defect, and a confidence interval which may be one or two standard deviations from their tollerance level. Once their test samples start falling outside of the predetermined standard deviation from tollerance, they have a high degree of confidence that not just the samples, but also the entire production run is edging toward unacceptible levels of defects. This is analyzed so that they will know when it's time to recalibrate machinery, rethink the quality of the raw materials being used, etc. Because this is a pretty advanced dicipline, you may find a lot of good info by searching for production statistical analysis.