You’ve been chosen as a championto 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 oforder 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 youwith three options:
the Bannekar, which bindsone 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 targetto 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 considerwhat would happen.
As the most dangerous wizard,
you’d also be the targetof the other two magicians,
and you ’ d need to take care of the most dangerous of them first.
there’s a 70% chance you’d be struck down by the remaining wizard.
Maybe it’s better to take the Gaussian.
It works 80% of the time,
就是说 在女巫被击倒前 你不会变成攻击的目标
which means you wouldn ’ t be a target until the enchantress was incapacitated.
But if you succeeded in transforming her,
you’d probably be turnedinto 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 sorcererto attack the enchantress,
and you’d have an 80% chanceof 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 dangerousbetween you and the sorcerer,
you’d be the target.
And that’s when you seewhat you really need to do:
take the weakest wand, the Bannekar,and miss on purpose.
Now the sorcerer knows thathe’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% chanceof winning the duel
at the beginning of the next round.
If he fails, chances are he’ll beturned to stone
and you ’ d still have a 60 % chance
of winning the duel against the enchantress.
There’s a slim 3% chanceyou’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 thoughtthat the best way to take your shot
would be to throw away your shot?
Hungry for more deadly duels?
Try this one now.
You and your oppoent have to choose between two bowls of five apples each.
In the green bowl, two of the apples are poisonous,
and in the red bowl, three are.
But if you choose the green bowl
you’ll have to eat three of the apples at random.
And if you choose the red bowl,
you’ll have to eat two at random.
Here is the catch, eat one poisonou apple and you’ll be fine,
but two will kill you.
Which bowl should you choose or does it not even matter.
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