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?




Comments
  1. Sign up to be emailed the solution to the bonus riddle: https://brilliant.org/tededpoisonapples/! Also, the first 833 of you who sign up for a PREMIUM subscription will get 20% off the annual fee. Riddle on, riddlers!

  2. As green apples bascket has 2 poisonous apples, the probability of being gone is 1/10 and red apples bascet has 3 poisonous apples, so the chances of being gone is 3/10… So Green bascket should be chosen

  3. I didn’t know about missing on purpose but i did pick the 60% wand and hoped to miss. But my logic was to win at round 2 so i was close

  4. for the apple riddle, if you pick the green one, there are three possibilities and only one kills you, making your chances of living 2/3, but if you pick the red one, there are also three possibilities, only one kills you, making your chances of living 2/3 again! It's not how many out of the apples are poisonous, it's about how many of you pick can be poisonous, with the exception of picking one poisonous apple because it takes two to kill you, not one, but the reason why it works like this is because it takes two to kill you, but no matter what, you pick none, one, or two poisonous apples, but two apples is always the most you can take, it doesn't matter because of this!

  5. basically what this I thought was: OH so if i chose: 1. the right wand, and 2. the right person, i will have a greater chance of success.

    but no, the correct answer was to MISS ON PURPOSE.
    that's like having three options, but hiding the fourth and correct answer so that the person wont know about it.

  6. 80% kill 90% wizard – lets see the answer 🤣

    Edit: wtf??? U didnt clarified you can miss on purpose !!!

    So yes, without that bending rules like in your answer 😳 the best chances are:
    Taking 80% wand and try to kill 90% wizard. If you kill her its 70% against your 80 % in yo7r way. If you don't succeed, 70% will attack her aswell. If he kills her, you have 80% chance of winning.
    There is ofcourse small chance neither of you or the other wizard kills her, but its still your best shot.

  7. I would pick the green apples because:
    If I eat a poison apple off the bat, there are three safe apples and one poison apple left. Thus, a 75% chance of survival. If I eat a safe one first, a 100% chance of survival. So, i have a 50% chance of either 75% or 100%. chance of survival. Leaving me with an 87.5% chance overall.
    I wouldn’t pick the red apples because:
    If I eat a poison apple off the bat, there are two safe apples and two poison apples left. Thus, a 50% chance of survival. If I eat a safe one first, a 100% chance of survival. So, I have a 50% chance of either 50% or 100% chance of survival. Leaving me with a 75% chance overall.

  8. My calculations at the apple riddle is that at the worst case scenario (meaning you eat at least one poisonous apple) is that the green apple gives you 66.6% chance of surviving while the red gives you 50% chance of surviving. Tell me what do you guys get?

  9. You didn't tell that we can miss the shot on purpose 😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤😤

  10. Reference to so many mathematicians and physicists. .. great job ted ed

    1. Sir Isaac Newton
    2. Gottfried Wilhelm Leibniz

    (Their names are in the names of the magic schools.. Newt-niz and Leib-ton)

    3. Carl Friedrich Gauss

    (The Gaussian)

    4. Amalie Noether

    (The Noether 9000)

    Can anyone tell me what the Bannekar refers to?

  11. Since we're making up rules as we go (like missing on purpose was never stated to be allowed), then obviously just wait a really long time until your opponents go to sleep, then cast your 100 % spell right between them to hit them both at the same time

  12. I know you guys are all saying the thing about how the riddle is kinda backwards…
    but can we talk about how the color is just put behind the picture wITHOUT BEING PROPERLY COLORED IN????????

  13. Like sam said (I thought this too) the only correct answer is to hit yourself with the 100% wand. It's guaranteed youll be teleported onto a mountain and be the last surviving wizard, or you can tell the other wizards (your two opponents to revolt against the judges and you take three wands they use there two and you kill the judges you will all be free

  14. Missing with Gaussian wand still lets you win about 56% of the time. You miscalculated it to be zero. You missed the 70% chance where the second wizard manages to knock out the third one, giving you a 80% chance to knock him out in the next hit 70*80/(100*100) is 0.56 as in 56%

  15. pick the gauciem and go for the sorceror and if i get him out then the 3rd person will go thus going out of order making me the winner

  16. I decided that it very important that you can't attack same person twice so i would grab 60% wand and shoot myself with it and hope for a miss(40%), then there's 90% chance that somebody will get eliminated in next turns and after that i'll try to hit with 60% remaining wizard, but probability of this is actually lower than just grabbin 100% wand and eliminating 90% wizard so i went to check the solution and god i wasted my time with this one

  17. the chance with noether 9000 and missing should be 0 % cuz the other 2 will focus you and if they miss you all die. if they do hit you, you die either way

  18. This is a TERRIBLE riddle. Rule 5 clearly states that you would be turned into a cat before you made your 2nd shot, at the end of the 1st round. Just because you chose to miss, that does not mean the 1st round did not start.

    11a: a unit of action in a contest or game which comprises a stated period, covers a prescribed distance, includes a specified number of plays, or gives each player one turn.

    https://www.merriam-webster.com/dictionary/round.

    You only get 1 turn before being turned into a cat, regardless of what you choose to do with the turn. downvoted.

  19. Also if you missed and the wizard turned the enchantress into a fish the first round would be over and you’d both be cats

  20. Why would the 70% guy ONLY miss on purpose when you have the 80% wand? Why wouldn't he still attack the 90% person knowing that he would be a target afterwards? 80% < 90% after all, so strategically it would make literally no sense for him to miss on purpose. The answer this video gives is wrong, you want the 80% and to miss on purpose. That would give you the greatest chance of victory

  21. I didnt think that you could miss on purpose, my idea was to:
    Get the bannekar, aim for the yellow mage and hope that i'll miss, then the red guy would target the yellow one as well since she's so dangerous and hopefully get her, then i'll aim for the red guy and hope that i get him

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