Variance & Bankroll Calculator

How this is calculated

Each bet is treated as a two-outcome event: win with probabilityp (profit = stake × (odds − 1)), or lose with probability 1 − p (profit = −stake). From that, the expected profit and variance of a single bet follow directly from the standard formulas for a discrete random variable. Betting n independent bets multiplies the mean by n and the variance by n (not the standard deviation — that only scales by√n, which is the entire reason variance shrinks proportionally as a sample grows).

The "chance of being in the red" uses the normal approximation to this distribution (reasonably accurate once you're past ~30 bets; treat it as a rough guide, not an exact figure, for very smalln).

Why this matters: plug in a real, modest edge — say 55% at 1.91 odds, close to what a genuinely good process might sustain — and run it at n=50. The red-zone probability is uncomfortably high even though the strategy is profitable in expectation. This is the same variance that makes any single week or month a weak signal on its own — see is value betting profitableand why we default to flat stakingrather than sizing up on perceived edge.