Variance

Variance is the statistical measure of how widely actual results scatter around the expected average (EV) over time. High variance means large swings — big wins and big losses in clusters — even when the underlying expected value is unchanged; low variance means outcomes cluster tightly around the average. It is the mathematical reason a positive-edge bettor can still endure long losing runs, and why a negative-edge gambler can run hot for a while: the edge governs the long-run destination, variance governs how bumpy the road there is. Worked example: flip a fair coin 10 times at even money, £10 a flip. The expected result is break-even, but you might easily see 7 heads and 3 tails and finish +£40, or the reverse and finish −£40. Flip it 10,000 times and the proportion of heads converges toward 50%, dragging your result back toward break-even. The per-flip edge never changed; only the sample size tamed the variance. The same logic explains why a high-volatility slot, despite a fixed RTP, can drain a balance fast or deliver a sudden large hit. Why it matters for bankroll management: the higher the variance of your chosen games or bets, the larger the bankroll you need to survive the inevitable downswings without going broke before your edge (if any) asserts itself. The common mistake is reading short-term variance as a trend — believing a hot streak proves skill, or that a cold streak is 'due' to end. Independent trials have no memory; the gambler's fallacy is precisely this error. Size stakes for the variance you face and never chase. Compare with the house edge, slot volatility and the cold streak.