Loading…
Reading the draws and working out what chance predicts.
Loading…
Reading the draws and working out what chance predicts.
LotteryOracle · F-50
Give fair numbers the wrong baseline and watch an innocent pattern appear.
Uniform integers from 1 to 49 · 2000 · Fair simulation
| First digit | Observed | Correct finite-pool expectation | Benford comparison |
|---|---|---|---|
| 1 | 453 | 448.98 | 602.06 |
| 2 | 458 | 448.98 | 352.183 |
| 3 | 455 | 448.98 | 249.877 |
| 4 | 429 | 448.98 | 193.82 |
| 5 | 43 | 40.816 | 158.362 |
| 6 | 34 | 40.816 | 133.894 |
| 7 | 43 | 40.816 | 115.984 |
| 8 | 35 | 40.816 | 102.305 |
| 9 | 50 | 40.816 | 91.515 |
Exact model: 1 → 11/49 · 2 → 11/49 · 3 → 11/49 · 4 → 11/49 · 5 → 1/49 · 6 → 1/49 · 7 → 1/49 · 8 → 1/49 · 9 → 1/49
The experiment samples 2,000 independent integers uniformly from 1 to N. Count the pool members beginning with each digit to obtain the correct expectation. Benford describes certain other generating processes; it is not a universal law of randomness or a fraud verdict. For 1–49, digits 1–4 each begin eleven integers, while 5–9 each begin one.
The experiment samples 2,000 independent integers uniformly from 1 to N. Count the pool members beginning with each digit to obtain the correct expectation. Benford describes certain other generating processes; it is not a universal law of randomness or a fraud verdict. For 1–49, digits 1–4 each begin eleven integers, while 5–9 each begin one.
Pfinite(d) = #{n ∈ [1,N] : first(n)=d}/N; PBenford(d) = log₁₀(1+1/d)
A famous formula is useful only when its assumptions fit. Moving the upper bound changes the leading-digit distribution of perfectly fair integers. The apparent anomaly comes from the comparison, not the generator.