Failure is Also an Option

The Nijmeegse Vierdaagse (http://​www.​4daagse.​nl/​en/​) is the world’s most famous walking event. The walk is known to be challenging and each year about 10 % of the participants drop out. In 2016 the Vierdaagse will celebrate its centennial anniversary. In the walker community there is a frenzy about participating in the centennial walk. 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 are also granted tickets to the walk. Finally, 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 organizers. We never got an answer but the rules were subsequently changed.