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few applications of random walks for random human walkingI've heard a hypothesis that an advantage of dubious fortune-telling techniques (entrails, tea leaves, etc.) for hunter-gatherer societies is that random choice of prey and direction each day keeps them from over-exploiting any given resource to extinction.
A weird flex Indian Rajas were said to have done is to release a horse and then follow it, offering to fight anyone they met upon the resulting (not so random) walk. https://en.wikipedia.org/wiki/Ashvamedha
I have read both ancient sword fighters and modern fencers advise to consciously plan an attack, but unconsciously trigger it: by letting noise from the environment decide the moment T=0, you're less likely to give your opponent any tells.
One might imagine that divination before battle would provide what the modern world calls a "mixed strategy" and could indeed by superior to pure strategies.
(compare the SSBN; see also https://www.atlanticcouncil.org/in-depth-research-reports/is... )
On a more peaceful note, if you wish to choose between popular dinner spots, it may be best to make the selection at hazard: http://www.eecs.harvard.edu/~michaelm/postscripts/handbook20...