How Often Do Drawings "Coincidentally" Share Numbers?

Noticing two drawings share 2 or 3 numbers feels like a real coincidence — but the actual math (the same kind behind the "birthday paradox") says how often that should happen anyway, purely by chance. This compares that theoretical expectation against what's actually happened in the loaded history.

"Theoretical" here comes from the hypergeometric distribution — the exact math for "given two independent random draws from the same pool, what's the probability they share exactly k numbers" — not a simulation or estimate. Verified before publishing: the theoretical probabilities for all possible overlap counts sum to exactly 100%. Sharing 0 or 1 numbers between any two drawings is normal and expected most of the time; sharing 3+ becomes genuinely rare, which is exactly what the chart below should show if the game is behaving randomly. See how lottery odds actually work.