It seems particularly promising as a way for the person on the street to estimate the number of significant digits in a floating-point value, and to experiment with the effect of changing the precision used in numerical computation. In computation with MCA, one can use either random rounding or random unrounding, or both. Using neither gives ordinary floating-point arithmetic. Random rounding can be used to produce rounding errors that are genuinely random, and that have zero expected bias. Random unrounding detects catastrophic cancellation, which is the primary way that significant digits are lost in numerical computation.
Randomization has various strengths, both theoretical and practical.
It can transform any floating-point computation into a Monte Carlo computation, and transform roundoff analysis into statistical analysis. Running a program multiple times measures the sensitivity of particular outputs to perturbations in the computation. Also, MCA gives a way to avoid some anomalies of floating-point arithmetic. Generally, MCA gives a different perspective on the study of error. Figures from this paper, showing how randomized floating-point arithmetic can both expose instability and find useful applications in numerical applications.