Ontario · Probability
Probability Basics Every Lottery Player Should Know
2026-06-13 · 7 min read
Independence, expected value, variance and the law of large numbers — the four ideas that explain almost every lottery question.
1. Independence
Each draw is independent. Nothing that happened in previous draws changes the probability distribution of the next one. This single fact invalidates most 'systems' sold online.
2. Expected value
Expected value is the average return per dollar wagered over the long run. For essentially every lottery product it is negative, typically returning 40 to 60 cents per dollar in prizes. That is the cost of the entertainment, and it is why a lottery ticket is a purchase rather than an investment.
3. Variance
Variance measures how far individual outcomes scatter around the mean. Lotteries have extraordinarily high variance: almost every ticket returns nothing, and a vanishingly small number return enormous sums. High variance is what makes short-run frequency data look patterned when it is not.
4. The law of large numbers
Over enough draws, observed frequencies converge toward their theoretical probabilities. Crucially, this convergence happens because later results swamp early deviations in the average — not because the process corrects itself. Nothing 'balances out' in the short term.
Important: This website does not guarantee winning numbers. AI-generated suggestions are based on historical statistics and probability analysis for informational and entertainment purposes only. Lottery results are random. Need support? Call ConnexOntario at 1-866-531-2600.