## Measuring Uncertainty
Standard deviation (σ) is the primary measure of variability in betting results. It tells you how widely individual results are dispersed around the mean.
## Calculating Betting Variance
For a series of n bets, each with profit p_i:
Mean (μ) = Σp_i / n
Variance (σ²) = Σ(p_i − μ)² / (n − 1)
Standard deviation (σ) = √σ²
For a simple binary bet (win or lose) at decimal odds d with probability p:
σ_per_bet ≈ √(p(1−p)) × d (approximate)
## The Variance of Different Bet Types
**Even-money bets (2.00 odds):** Low variance. Each bet is +1 or −1. σ ≈ 1 unit per bet.
**Long odds bets (10.00 odds):** High variance. Each bet is +9 or −1. σ ≈ 3 units per bet.
**Accumulators:** Very high variance. Four-fold accumulator at 16.00 has σ ≈ 3.9 units per leg.
## The 68-95-99.7 Rule
For normally distributed returns (approximately valid for large samples):
- 68% of monthly totals fall within ±1 standard deviation of the mean
- 95% fall within ±2 standard deviations
- 99.7% fall within ±3 standard deviations
**Example:** 100 bets/month, 0.05 units average profit, σ = 10 units:
- 95% of months: profit between −19.9 and +20.1 units
- A 15-unit losing month is within normal variance: no action required
## Why This Matters
Most bettors react to monthly results as if they are precise performance signals. Understanding standard deviation reveals that monthly results are extremely noisy. A strategy with genuine 3% ROI will have many losing months — this is not failure, it is variance.
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