The formulation of a fractal procedure for estimating exploration success ratios using the Cantor set theory can be derived by using information from discovery history or discovery sequence. This new procedure is illustrated using discovery history information from the Devonian Rainbow sub-basin of the Western Canada Sedimentary Basin. As exploration proceeds, success ratios of discovery history fluctuate, but with a non-linear declining trend. An observed clustering of success ratios, attributed to the predominance of a single factor that decides well location, prevents universal predictions of success ratios. Rather, it appears possible to make suitable predictions of success ratios for groups of 30 exploration wells using the fractal procedure proposed here and the sample data set. Considering this clustering, we predict a post-1993 success ratio for the Rainbow sub-basin of about 43% for the next 30 exploration wells to be drilled.