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Reading the draws and working out what chance predicts.
Loading…
Reading the draws and working out what chance predicts.
LotteryOracle · F-51
From a 1767 paper to every possible arrangement of consecutive runs.
| Run lengths | Combinations | Probability |
|---|---|---|
| 5 | 86 | 0.0002% |
| 4 + 1 | 7,310 | 0.01663% |
| 3 + 2 | 7,310 | 0.01663% |
| 3 + 1 + 1 | 307,020 | 0.69858% |
| 2 + 2 + 1 | 307,020 | 0.69858% |
| 2 + 1 + 1 + 1 | 8,494,220 | 19.32733% |
| 1 + 1 + 1 + 1 + 1 | 34,826,302 | 79.24205% |
A profile is the multiset of consecutive run lengths in a sorted draw: 3+2+1, for example. If there are r runs and m_j runs of length j, its exact count is r!/∏m_j! × C(N−k+1,r). Every combination belongs to exactly one profile. This modern reconstruction is inspired by Euler’s 1767 paper, not a transcription of his notation.
A profile is the multiset of consecutive run lengths in a sorted draw: 3+2+1, for example. If there are r runs and m_j runs of length j, its exact count is r!/∏m_j! × C(N−k+1,r). Every combination belongs to exactly one profile. This modern reconstruction is inspired by Euler’s 1767 paper, not a transcription of his notation.
P(profile) = [r! / ∏ⱼmⱼ!] × C(N−k+1,r) / C(N,k)
Euler published his investigation of sequences in the Genoese lottery in 1767. This desk begins with five numbers from ninety, then lets you change the rules and see a complete partition of the possible draws.