Four Days Marches lottery inconsistency proven by maths

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Lottery-4daagse

Using probability theory, four students at the Institut Mines-Télécom in Paris penned a paper entitled ‘Failure is Also an Option’ to prove that the best chance of being allowed to participate in the 100th edition of the International Four Days Marches Nijmegen (aka ‘Nijmegen Vierdaagse’), which was held from 19-22 July 2016, was if one failed that year’s event.

The world’s most famous walking event attended by some 40,000 participants from around the world and featuring international armies and hardcore walkers alike, has a drop-out rate of about 10%.

Initially, the rules governing participation were the following: A walker who succeeds the n-th walk is admitted to walk at year (n + 1). Walkers who fail a walk enter a lottery. If they win the lottery, they get tickets to the walk. Walkers who fail two successive draws are admitted to the walk following the second lottery failure. In 2013, while computing our chances to be admitted to the centennial walk, we noticed a rather counterintuitive fact: By purposely failing the 97-th walk, walkers can actually increase their chances to attend the centennial walk.

We notified this inconsistency to the organisers and never got an answer, but the rules were subsequently changed.

(Link: www.improbable.com, image: www.ens-paris.fr)

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