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Statometrics
Calculator · from Lesson 1.4

Why do "impossible" results keep happening?

What it’s telling you, step by step: Lesson 1.4: Fat tails: when the bell curve lies

Try it · Tail comparison
010203040
━ Bell curve▮ Exact count━ Clumpy▮ 25 or more
P&L at 25 winners
−£1,035
Bell curve
1 in 186
Exact count
1 in 118
Clumpy
1 in 12
As percentages: 0.54% · 0.85% · 8.2%. Expected P&L £163 (£0.82 a bet). Average winners: 15.0, SD 3.72 (clumpy 6.44). Clumping 0.010 means the true rate itself wobbles by about ±2.6%.
The bell curve says 1 in 186. Allowing for clumping, it's 1 in 12, about 15.3 times as likely.
RunBellExactClumpy
23+ (2 SD)1 in 451 in 361 in 7.9
27+ (3 SD)1 in 9901 in 4481 in 19
30+ (4 SD)1 in 20,1671 in 4,4171 in 40
The bad count is the number of bets that go against you: winners for a lay. The bell curve assumes a smooth, symmetric world; the exact count is right for independent bets; the clumpy line lets the true rate wobble from week to week, which is what real bets do.
18+ only. Educational content, not financial or betting advice. Past results do not guarantee future returns. If gambling stops being fun, get free, confidential help at BeGambleAware.org.
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