Logistical challenges in modeling marksmanship outcomes: striking a balance between reliability and efficiency

There is little guidance in the literature concerning the number of simulations required when performing stochastic marksmanship duels to balance obtaining a reliable answer against obtaining that answer quickly. The present research fills this gap by investigating the reliability and computational efficiency of stochastic marksmanship duels with different numbers of draws. We simulated a stochastic duel using a Markov chain with Monte Carlo methods modeling the transitions between behaviors. The simulation was run five times each (100 draws, 1000 draws, 5000 draws, 10,000 draws, and 100,000 draws) to estimate the probability of victory, variation in this estimate, and required runtime. Assuming these efforts are run using comparable hardware, a simulation with 5000 draws will take approximately 1 min to complete (M = 01:09), but the estimated probability of victory is likely within ±1.25% of the mean, and theoretically true, probability. If a simulation with 10,000 draws is conducted, it takes several minutes (M = 02:19), yet the estimated probability of victory is likely within ±0.88% of the mean probability. Fewer than 5000 draws were more unreliable, and greater than 10,000 draws were more time-consuming. The present research is novel because it provides guidance on this trade-off between reliability and efficiency for a variety of use cases ranging from operational to scientific. Practitioners of marksmanship modeling performing stochastic duels should conduct simulations with 5000–10,000 draws to balance reliability and efficiency.