Overview

Variance is the bettor's true opponent, even more than vig. The Variance Calculator runs a Monte Carlo simulation of your betting profile — bankroll, average edge, average odds, bet size, number of bets — and shows you the distribution of possible outcomes, including risk of ruin and 5th/95th percentile bankrolls.

The Math

For a sequence of N independent bets with edge e and average decimal odds o, expected return is N × e × stake. But the standard deviation is roughly:

σ ≈ stake × sqrt(N × o × (1 − p))

Where p is the win probability. Risk of ruin for a fixed bankroll B with flat bets follows a random-walk approximation:

RoR ≈ ((1 − e)/(1 + e))^(B/stake)

The simulator runs 10,000+ trials of your sequence and reports the actual percentile distribution rather than relying on the closed-form approximation.

When To Use It

Use it before scaling stakes, when deciding how much bankroll you need to support a strategy, when evaluating whether a losing month is variance or process failure, and when sizing bets via fractional Kelly.

Example Walk-through

You have a $5,000 bankroll, place 500 bets a month at average +3% EV, average odds -110, flat $100 per bet. Expected monthly profit: 500 × 0.03 × $100 = $1,500. Sounds great. But standard deviation per bet at -110 is roughly $99, so over 500 bets total σ ≈ $99 × sqrt(500) ≈ $2,213.

The simulator shows:

• 5th percentile monthly result: −$2,140 (below your bankroll — you bust 1 in 20 months at this stake)
• 50th percentile: +$1,500
• 95th percentile: +$5,140

Risk of ruin in a single month is materially nonzero. The fix: drop stake to $50, halving variance, while expected profit drops only to $750 — same edge, half the variance, near-zero RoR.

Second example, a 1% edge grinder placing 2,000 bets/month: expected profit $2,000, but σ ≈ $4,427. The 5th percentile is roughly −$5,300. With a $10,000 bankroll, RoR is meaningful. The simulator suggests fractional Kelly sizing of 0.25× full Kelly, which trades 25% of expected return for an 80% reduction in tail risk.

Common Mistakes

• Ignoring variance entirely. Most bettors size to expected return and bust on a normal downswing.
• Using full Kelly. Mathematically optimal in theory, brutal in practice. Fractional Kelly (0.25× to 0.5×) is the standard for real bankrolls.
• Assuming independent bets. Correlated bets compound variance. Treat correlated days as fewer effective trials.
• Confusing variance with edge. A 12-month losing stretch at +2% EV is rare but not impossible. Track CLV alongside results.