# Can you solve the wizard standoff riddle? – Dan Finkel

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?

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Gandalf has entered chat

I wasn't really paying attention but then I heard "throwing away my shot" then a Hamilton Logo, I was like It's my time to shiinnnee

Me:

avada kedavr-What they found funny that no one in the comment section even mentioned is that who's to say that they know what percentage your wand and the treat level it stands for. I would rather schools give away their advantage like that?