How Monte Carlo simulation works
A Monte Carlo simulator lets you simulate possible outcomes by sampling one result for every match from the probabilities supplied to the model. The sampled outcomes are compared with every card in the plan, payouts and costs are calculated, and the resulting profit or loss is recorded. Repeating this process thousands of times produces an empirical distribution rather than one point estimate.
Inputs determine the meaning of the output
The model needs outcome probabilities, card definitions, decimal odds or payout rules, and allocations. If matches are treated as independent, it also assumes one result does not change the probability of another. Poorly calibrated probabilities, stale odds, missing costs, or unrealistic independence assumptions can make a precise-looking output misleading.
- Probabilities for all modeled outcomes should sum to one per match.
- Payout calculations should use the same allocation basis across cards.
- Dependencies should be modeled or acknowledged where they are material.
Outputs that matter for profit
Average simulated profit estimates the model-based expected result, while median profit describes the middle run. Loss frequency shows how often the plan finished below its cost. Percentiles reveal the range of outcomes, and maximum loss shows the downside represented by the simulation. These measures are more informative together than a single maximum payout.
How many simulation runs are enough?
More runs reduce random sampling noise but cannot repair weak assumptions. Start with enough runs for the main statistics to stabilize, then repeat with a different random seed. Rare outcome paths require more samples than common ones. If key metrics move materially between repeated runs, increase the sample count before comparing plans.
Stress-test probabilities and correlation
A useful robustness check changes the input assumptions rather than rerunning the same model. Lower confidence in favored outcomes, widen uncertain probabilities, and test plausible dependencies between matches. A plan whose estimated profit remains comparatively strong across these variations is more robust than one that succeeds only under one narrow estimate.
What simulation cannot tell you
Simulation does not prove that a plan will profit, discover true probabilities automatically, or turn a negative expected-value setup into a positive one. It shows the consequences of the model you supplied. Treat results as a structured comparison tool, keep assumptions visible, and compare simulated expectations with later recorded outcomes.