Per-Trade Mode: Each trade either wins (+R × risk%) or loses (−risk%) of current balance. With win rate p and R:R r, expectancy per trade = p·r − (1−p) in R-multiples. Balance compounds after each trade.

Per-Day / Per-Month Mode: Each period applies a return drawn from a normal distribution with your specified mean and standard deviation. This is geometric Brownian motion in discrete form — the same model used for option pricing.

Monte Carlo: 5,000 random sequences are simulated. The chart shows the median, 10th, and 90th percentile paths. The deterministic curve assumes you hit your expected return every period (the fairy-tale version).

Prop firm mode: Drawdown is checked after every period. If equity drops below the max drawdown threshold, the account is marked as "blown" and that path is terminated. The blow-up % across all paths is your real risk of ruin.