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  • You've been chosen as a champion to represent your wizarding house

  • in a deadly duel against two rival magic schools.

  • Your opponents are fearsome.

  • From the Newt-niz school,

  • a powerful sorcerer wields a wand that can turn people into fish,

  • but his spell only works 70% of the time.

  • And from the Leib-ton school,

  • an even more powerful enchantress wields a wand that turns people to statues,

  • and it works 90% of the time.

  • Lots are drawn, and you're chosen to cast the first spell in the duel.

  • The Newt-niz magician will go second,

  • and the Leib-ton enchantress third,

  • after which you'll repeat casting in that order until only one of you is left.

  • The rules of magic duels are strict,

  • and anyone who casts out of order immediately forfeits the duel.

  • Also, to prevent draws,

  • the rules stipulate that if everyone's still standing

  • at the end of the first round,

  • you'll all be turned into cats.

  • Now, you must choose a wand.

  • Your wizarding house presents you with three options:

  • the Bannekar, which binds one target with vines

  • and casts effectively 60% of the time,

  • the Gaussian, which turns one target into a tree

  • and works 80% of the time,

  • and the incredibly rare Noether 9000,

  • which banishes one target to a distant mountaintop

  • and casts perfectly 100% of the time.

  • Your opponents are masters of strategy, as well as sorcery,

  • and you know they'll make the choices that maximize their own chances of success.

  • Which wand should you choose

  • and what strategy should you employ

  • to have the greatest chance of winning the duel?

  • Pause the video now if you want to figure it out for yourself!

  • Answer in: 3

  • Answer in: 2

  • Answer in: 1

  • You reach for the Noether 9000 first.

  • After all, it makes sense to enter the duel with the most powerful wand.

  • But before you pick it up, you consider what would happen.

  • As the most dangerous wizard,

  • you'd also be the target of the other two magicians,

  • and you'd need to take care of the most dangerous of them first.

  • But afterward, there's a 70% chance you'd be struck down by the remaining wizard.

  • That's trouble.

  • Maybe it's better to take the Gaussian.

  • It works 80% of the time,

  • which means you wouldn't be a target until the enchantress was incapacitated.

  • But if you succeeded in transforming her,

  • you'd probably be turned into a fish immediately after.

  • If you transformed the sorcerer,

  • the enchantress would almost certainly turn you to stone.

  • It would really be better if you missed.

  • And that's when you have an idea:

  • what if you took the Gaussian, then missed on purpose?

  • Then, you would wait for the sorcerer to attack the enchantress,

  • and you'd have an 80% chance of winning against the sorcerer.

  • It's a good idea, but there's a problem;

  • the sorcerer could also pass his turn

  • and the enchantress, knowing that she couldn't pass without becoming a cat,

  • would cast her spell on one of you.

  • And since you're the most dangerous between you and the sorcerer,

  • you'd be the target.

  • And that's when you see what you really need to do:

  • take the weakest wand, the Bannekar, and miss on purpose.

  • Now the sorcerer knows that he'll be targeted by the enchantress

  • and he'll have to try to turn her into a fish to avoid being turned into stone.

  • Seventy percent of the time he'd succeed

  • and you'd have a 60% chance of winning the duel

  • at the beginning of the next round.

  • If he fails, chances are he'll be turned to stone

  • and you'd still have a 60% chance of winning the duel against the enchantress.

  • There's a slim 3% chance you'll all be turned into cats,

  • but when everything's accounted for,

  • you have better than even odds of winning with this strategy.

  • And that's the best you can do.

  • Here's what the probability of winning for the different strategies looks like.

  • Who would've thought that the best way to take your shot

  • would be to throw away your shot?

You've been chosen as a champion to represent your wizarding house

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    Evangeline posted on 2018/05/23
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