Exact calculation vs. simulation
Know when to use exact combinatorics and when to use a Monte Carlo estimate.
Exact calculation
A simple opening-hand condition with no effects can be calculated with the hypergeometric distribution. The same input always produces the same answer with no sampling error.
Simulation
When draws, deterministic searches, top-N selection, mulligans, and action order interact, the state space grows quickly. The simulator estimates the success rate by running many virtual games.
Simulation results include the seed, trial count, and a 95% confidence interval. The same seed and settings reproduce the same result.