Can you solve the wizard standoff riddle? - Dan Finkel

譯者: Lilian Chiu 審譯者: Helen Chang

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

你被選為你的巫術學院的代表

in a deadly duel against two rival magic schools.

與兩間魔法學校的對手致命決鬥。

Your opponents are fearsome.

你的對手讓人望而生畏。

From the Newt-niz school,

來自 Newt-niz 學校，

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

是一個強大的法師， 他揮動魔杖就能把人變成魚，

but his spell only works 70% of the time.

但他的咒語只有 70% 的成功率。

And from the Leib-ton school,

另外還有來自 Leib-ton 學校，

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

是位更強大的女巫， 揮動魔杖就能把人變成雕像，

and it works 90% of the time.

且成功率有 90%。

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

抽籤的結果是，你被抽中 在決鬥中可以先施魔咒。

The Newt-niz magician will go second,

Newt-niz 的魔法師排在第二，

and the Leib-ton enchantress third,

Leib-ton 的女巫則是第三，

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

之後，就用這個順序輪流施魔咒， 直到只剩下一人為止。

The rules of magic duels are strict,

魔法決鬥的規則很嚴格，

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

不照順序施魔咒的人 就馬上喪失決鬥資格。

Also, to prevent draws,

此外，為了避免平手，

the rules stipulate that if everyone’s still standing

規則規定，只要在第一回合的最後

at the end of the first round,

所有人都沒倒下，

you’ll all be turned into cats.

所有人都會被變為貓。

Now, you must choose a wand.

現在，你必須選擇一枝魔杖。

Your wizarding house presents you with three options:

你的巫術學院提供你三個選擇：

the Bannekar, which binds one target with vines

Bannekar，能將一個目標 用藤蔓綁住，

and casts effectively 60% of the time,

成功率為 60%，

the Gaussian, which turns one target into a tree

Gaussian，能將一個目標 變成一棵樹，

and works 80% of the time,

成功率為 80%，

and the incredibly rare Noether 9000,

還有非常稀有的 Noether 9000，

which banishes one target to a distant mountaintop

能將一個目標流放到 遙遠的山頂上，

and casts perfectly 100% of the time.

成功率是完美的 100%。

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

你的對手精通策略以及法術，

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

你知道他們做選擇的考量是要 讓他們自己的成功率能達到最高。

Which wand should you choose

你該選擇哪一枝魔杖

and what strategy should you employ

且要採取哪一種策略

to have the greatest chance of winning the duel?

才最有可能贏得決鬥？

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

如果你想要自己解解看， 在這裡將影片暫停！

Answer in: 3

公佈答案倒數：三。

Answer in: 2

公佈答案倒數：二。

Answer in: 1

公佈答案倒數：一。

You reach for the Noether 9000 first.

你一開始想要拿 Noether 9000。

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

畢竟，帶著最強大的魔杖 參加決鬥是合理的選擇。

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

但，在你把它拿起來之前， 你想了一下會發生的狀況。

As the most dangerous wizard,

若你是決鬥中最危險的巫師，

you’d also be the target of the other two magicians,

你就會成為另外 兩位魔法師的目標，

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

而你得要先把他們兩人當中 最危險的那一位解決掉。

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

但，之後，就有 70% 的可能， 你會被剩下的那位巫師擊倒。

That’s trouble.

那就是問題所在。

Maybe it’s better to take the Gaussian.

也許選 Gaussian 會比較好。

It works 80% of the time,

它的成功率有 80%，

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

那就表示，在女巫被打倒之前， 你都不會成為目標。

But if you succeeded in transforming her,

但如果你成功將她變身，

you’d probably be turned into a fish immediately after.

你可能接著馬上就會被變成魚。

If you transformed the sorcerer,

如果你把法師變身，

the enchantress would almost certainly turn you to stone.

幾乎可肯定女巫會把你變成石頭。

It would really be better if you missed.

如果你失誤反而會更好。

And that’s when you have an idea:

此時，你就有了個點子：

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

如果你選擇 Gaussian， 然後故意失誤呢？

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

那麼，你就可以等法師攻擊女巫，

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

且你會有 80% 的機會打贏法師。

It’s a good idea, but there’s a problem;

這是個好點子，但有個問題：

the sorcerer could also pass his turn

法師也有可能故意失誤，

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

那麼女巫知道她不能在不被 變成貓的情況下通過第一回合，

would cast her spell on one of you.

她就會對你或法師 其中一人施魔咒。

And since you’re the most dangerous between you and the sorcerer,

因為和法師相比，你比較危險，

you’d be the target.

你就會成為目標。

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

此時，你就知道 你真正該做什麼選擇了：

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

拿最弱的魔杖 Bannekar， 並且故意失誤。

Now the sorcerer knows that he’ll be targeted by the enchantress

現在，法師知道 他會成為女巫的目標，

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

他就會試著將女巫變成魚， 來避免自己被變成石頭。

Seventy percent of the time he’d succeed

他的成功機會有 70%，

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

而在下一回點開始時，

at the beginning of the next round.

你有 60% 的機會贏得決鬥。

If he fails, chances are he’ll be turned to stone

如果他失敗了， 他很可能會被變成石頭，

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

而你要和女巫決鬥， 會有 60% 的機會獲勝。

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

只有 3% 非常低的可能性， 所有人會被變成貓。

but when everything’s accounted for,

但把一切都考量進去後，

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

用這個策略你會有最高的勝算。

And that’s the best you can do.

這是你能做到最好的狀況。

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

表中列出的是 不同策略的獲勝機率。

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

誰想得到，最好的攻擊方式，

would be to throw away your shot?

就是放棄自己的攻擊機會？