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Originally Posted by ZZII 527
Anybody know the odds of this occuring randomly? I'm thinking roughly 6/1,000, but not sure. (1/10 * 1/10 * 1/10 for the three numbers that have to match * 6 different orientations of team numbers. This neglects repeated numbers and the fact that no two teams have the same number, as well as quadruple digit teams.)
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Freaky 3 X 3 square of SBPLI winning alliance team numbers that reads the same horizontally as it does vertically (originally pointed out by AIBob):
Soooo, I did a brute-force statistical analysis on this, and here are the results:
From a computer program that randomizes three 3-digit team numbers, eliminating any combinations with repeated team numbers:
Using 10,000,000 sample combinations, the computed probability of hitting three team numbers that could line up in any order to form the 3 X 3 square that reads the same horizontally as vertically was: 0.60086%. I'd give this an accuracy of roughly +- 0.02%. This is close enough to say it's 6 out of 1,000.
Using the team list from SBPLI gives an absolute answer:
There are 40 teams, which can be combined into alliances of three in 9880 ways. Of these, only 3654 do not have a quadruple-digit team in them. (Double digits are okay;they get a leading zero.) Of the 3654, only 21 could be lined up into a 3 X 3 square that reads the same horizontally and vertically. (This is 0.575%, right as predicted.) They are:
Code:
028 028 028 028 287 352 352
270 271 287 287 871 527 527
806 810 870 871 711 270 271
352 353 353 353 358 358 358
566 527 545 545 500 527 527
263 371 352 358 806 870 871
358 527 533 545 545 545 884
570 271 352 417 496 496 871
806 711 329 570 564 566 417
The OVERALL probability of an alliance forming at random at SBPLI whose team numbers can be lined up into the 3 X 3 square thingy is 21/9880 or 0.21255%.
Conclusion: If you don't believe in fate, then this matchup is merely a 1 time out of 470 or so coincidence. Factor in that our three seating sections were lined up immediately adjacent to each other (forming one massive cheering section) and that this year's field layout is itself a 3 X 3 arrangement, and you could make a pretty convincing argument that this alliance was meant to be.