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Gambling Mathematics Academy

Standard Deviation

Standard deviation is the square root of variance and the most intuitive measure of how spread out outcomes are. For a betting strategy it answers, 'how big are normal swings around the average?'

Direct Answer

Standard deviation is the square root of variance and the most intuitive measure of how spread out outcomes are. For a betting strategy it answers, 'how big are normal swings around the average?'

Key Takeaways

  • 1 SD = ~68% of outcomes; 2 SD = ~95%.
  • Bankroll scales with SD, not EV.
  • Low-SD edges are more bankroll-efficient than high-SD ones.

Reading standard deviation

Roughly 68% of outcomes fall within one standard deviation of the mean; 95% within two. A strategy averaging $0 per bet with a $50 standard deviation produces $250+ swings (5 SD) routinely over thousands of bets.

Sizing for the standard deviation, not the mean

Bankroll requirements scale with standard deviation, not expected value. A small-edge / low-variance strategy can be more aggressive than a larger-edge / high-variance one.

Frequently asked questions

Is SD the same as risk?+

It is one component of risk. Correlation and tail outcomes matter too.

Educational only. Not wagering, financial, or legal advice. See our editorial policy.