Can you solve the wizard standoff riddle? - Dan Finkel

13,336,069 views ใƒป 2018-05-22

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Ido Dekkers ืขืจื™ื›ื”: Allon Sasson
00:07
Youโ€™ve been chosen as a champion to represent your wizarding house
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ื ื‘ื—ืจืชื ื›ืืœื•ืคื™ื ืœื™ื™ืฆื’ ืืช ื‘ื™ืช ื”ื›ื™ืฉื•ืฃ ืฉืœื›ื
00:11
in a deadly duel against two rival magic schools.
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ื‘ื“ื• ืงืจื‘ ืงื˜ืœื ื™ ืžื•ืœ ืฉื ื™ ื‘ืชื™ ืกืคืจ ืื—ืจื™ื ืœืงืกืžื™ื.
00:15
Your opponents are fearsome.
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ื”ื™ืจื™ื‘ื™ื ืฉืœื›ื ืœืœื ื—ืช.
00:17
From the Newt-niz school,
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ืžื‘ื™ืช ื”ืกืคืจ ื ื™ื•ื˜-ื ื™ื–,
00:18
a powerful sorcerer wields a wand that can turn people into fish,
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ืžื›ืฉืฃ ื—ื–ืง ื‘ืขืœ ืžื˜ื” ืงืกื ืฉื™ื›ื•ืœ ืœื”ืคื•ืš ืื ืฉื™ื ืœื“ื’ื™ื,
00:23
but his spell only works 70% of the time.
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ืื‘ืœ ื”ืœื—ืฉ ืฉืœื• ืขื•ื‘ื“ ืจืง 70% ืžื”ืคืขืžื™ื.
00:27
And from the Leib-ton school,
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ื•ืžื‘ื™ืช ื”ืกืคืจ ืœื™ื‘-ื˜ื•ืŸ,
00:29
an even more powerful enchantress wields a wand that turns people to statues,
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ืžื›ืฉืคื” ืืคื™ืœื• ื—ื–ืงื” ื™ื•ืชืจ ื‘ืขืœืช ืžื˜ื” ืงืกื ืฉื”ื•ืคืš ืื ืฉื™ื ืœืคืกืœื™ื,
00:34
and it works 90% of the time.
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ื•ื”ื•ื ืขื•ื‘ื“ 90% ืžื”ืคืขืžื™ื.
00:37
Lots are drawn, and youโ€™re chosen to cast the first spell in the duel.
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ื ืขืจื›ืช ื”ื’ืจืœื” ื•ืืชื ื ื‘ื—ืจื™ื ืœื”ื˜ื™ืœ ืืช ื”ืงืกื ื”ืจืืฉื•ืŸ ื‘ื“ื• ื”ืงืจื‘.
00:42
The Newt-niz magician will go second,
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ื”ืงื•ืกื ืžื ื™ื•ื˜-ื ื™ื– ื™ื”ื™ื” ืฉื ื™,
00:44
and the Leib-ton enchantress third,
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ื•ื”ืžื›ืฉืคื” ืžืœื™ื‘-ื˜ื•ืŸ ืฉืœื™ืฉื™ืช,
00:47
after which youโ€™ll repeat casting in that order until only one of you is left.
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ื•ืื—ืจื™ื” ืืชื ืชื—ื–ืจื• ืœื”ื˜ื™ืœ ื›ื™ืฉื•ืฃ ื‘ืกื“ืจ ื–ื” ืขื“ ืฉืจืง ืื—ื“ ื™ืฉืืจ.
00:53
The rules of magic duels are strict,
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ื”ื—ื•ืงื™ื ืฉืœ ื“ื• ืงืจื‘ ื”ืงืกื ืงืฉื•ื—ื™ื,
00:55
and anyone who casts out of order immediately forfeits the duel.
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ื•ื›ืœ ืžื™ ืฉืžื˜ื™ืœ ืงืกื ืœื ื‘ืชื•ืจื• ื™ื•ืฆื ืžื™ื™ื“ ืžื“ื• ื”ืงืจื‘.
01:00
Also, to prevent draws,
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ื›ืžื• ื›ืŸ, ื›ื“ื™ ืœืžื ื•ืข ืชื™ืงื•,
01:01
the rules stipulate that if everyoneโ€™s still standing
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ื”ื—ื•ืงื™ื ืงื•ื‘ืขื™ื ืฉืื ื›ื•ืœื ืขื“ื™ื™ืŸ ืขื•ืžื“ื™ื
01:04
at the end of the first round,
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ื‘ืกื•ืฃ ื”ืกื™ื‘ื•ื‘ ื”ืจืืฉื•ืŸ,
01:06
youโ€™ll all be turned into cats.
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ื›ื•ืœื›ื ืชื”ืคื›ื• ืœื—ืชื•ืœื™ื.
01:09
Now, you must choose a wand.
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ืขื›ืฉื™ื•, ืืชื ื—ื™ื™ื‘ื™ื ืœื‘ื—ื•ืจ ืžื˜ื” ืงืกื.
01:11
Your wizarding house presents you with three options:
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ื‘ื™ืช ื”ืงืกืžื™ื ืฉืœื›ื ืžืฆื™ื’ ืœื›ื ืฉืœื•ืฉ ืืคืฉืจื™ื•ื™ื•ืช:
01:14
the Bannekar, which binds one target with vines
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ื”ื‘ื ืงืจ, ืฉื›ื•ืจืš ืžื˜ืจื” ืื—ืช ื‘ื’ืคื ื™ื
01:18
and casts effectively 60% of the time,
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ื•ืื—ื•ื– ื”ื”ืฆืœื—ื” ืฉืœื• ื”ื•ื 60%,
01:21
the Gaussian, which turns one target into a tree
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ื”ื’ืื•ืกื™ื™ืŸ, ืฉื”ื•ืคืš ืžื˜ืจื” ืœืขืฅ
01:25
and works 80% of the time,
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ื•ืขื•ื‘ื“ 80% ืžื”ืคืขืžื™ื,
01:27
and the incredibly rare Noether 9000,
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ื•ื”ื ื•ืืช'ืจ 9000 ื”ื ื“ื™ืจ ื‘ื™ื•ืชืจ,
01:30
which banishes one target to a distant mountaintop
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ืฉืžื’ืจืฉ ืžื˜ืจื” ืื—ืช ืœืจืืฉ ื”ืจ ืžืจื•ื—ืง
01:33
and casts perfectly 100% of the time.
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ื•ืžื˜ื™ืœ ืืช ื”ืœื—ืฉ 100% ืžื”ื–ืžืŸ.
01:37
Your opponents are masters of strategy, as well as sorcery,
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ื”ื™ืจื™ื‘ื™ื ืฉืœื›ื ื”ื ืืฉืคื™ ื”ืืกื˜ืจื˜ื’ื™ื”, ื›ืžื• ื’ื ืงื•ืกืžื•ืช,
01:41
and you know theyโ€™ll make the choices that maximize their own chances of success.
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ื•ืืชื ื™ื•ื“ืขื™ื ืฉื”ื ื™ื‘ื—ืจื• ื‘ื—ื™ืจื” ืฉืชื’ื“ื™ืœ ืœืžืงืกื™ืžื•ื ืืช ื”ืกื™ื›ื•ื™ื™ื ืฉืœื”ื ืœื”ืฆืœื—ื”.
01:46
Which wand should you choose
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ืื™ื–ื” ืžื˜ื” ืงืกื ืชื‘ื—ืจื•
01:48
and what strategy should you employ
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ื•ืžื” ื”ืืกื˜ืจื˜ื’ื™ื” ืฉืœื›ื ืชื›ืœื•ืœ
01:50
to have the greatest chance of winning the duel?
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ื›ื“ื™ ืœื”ื’ื“ื™ืœ ืืช ื”ืกื™ื›ื•ื™ ืฉืœื›ื ืœืžืงืกื™ืžื•ื ืœื ืฆื— ื‘ืงืจื‘?
01:53
Pause the video now if you want to figure it out for yourself!
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ืขืฆืจื• ืคื” ืืช ื”ืกืจื˜ื•ืŸ ืื ืืชื ืจื•ืฆื™ื ืœื’ืœื•ืช ื‘ืขืฆืžื›ื!
01:56
Answer in: 3
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ืชืฉื•ื‘ื” ืขื•ื“: 3
01:57
Answer in: 2
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ืชืฉื•ื‘ื” ืขื•ื“: 2
01:59
Answer in: 1
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ืชืฉื•ื‘ื” ืขื•ื“: 1
02:00
You reach for the Noether 9000 first.
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ืืชื ืคื•ื ื™ื ืจืืฉื™ืช ืœื ื•ืืช'ืจ 9000.
02:03
After all, it makes sense to enter the duel with the most powerful wand.
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ืื—ืจื™ ื”ื›ืœ, ื–ื” ื”ื’ื™ื•ื ื™ ืœื”ื™ื›ื ืก ืœืงืจื‘ ืขื ื”ืžื˜ื” ื”ื›ื™ ื—ื–ืง.
02:07
But before you pick it up, you consider what would happen.
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ืื‘ืœ ืœืคื ื™ ืฉืืชื ื‘ื•ื—ืจื™ื ืื•ืชื•, ืืชื ืฉื•ืงืœื™ื ืžื” ื™ืงืจื”.
02:11
As the most dangerous wizard,
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ื›ืงื•ืกื ื”ื›ื™ ืžืกื•ื›ืŸ,
02:13
youโ€™d also be the target of the other two magicians,
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ืืชื ื’ื ืชื”ื™ื• ื”ืžื˜ืจื” ืฉืœ ืฉื ื™ ื”ืงื•ืกืžื™ื ื”ืื—ืจื™ื,
02:16
and youโ€™d need to take care of the most dangerous of them first.
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ื•ืืชื ืชืฆื˜ืจื›ื• ืœื“ืื•ื’ ืœื”ื›ื™ ืžืกื•ื›ืŸ ืžื”ื ืจืืฉื™ืช.
02:20
But afterward, thereโ€™s a 70% chance you'd be struck down by the remaining wizard.
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ืื‘ืœ ืื—ืจื™ ื–ื”, ื™ืฉ ืกื™ื›ื•ื™ ืฉืœ 70% ืฉืืชื ืชื™ืคื’ืขื• ืขืœ ื™ื“ื™ ื”ืงื•ืกื ืฉื ืฉืืจ.
02:25
Thatโ€™s trouble.
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ื–ื• ื‘ืขื™ื”.
02:27
Maybe itโ€™s better to take the Gaussian.
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ืื•ืœื™ ื™ื•ืชืจ ื˜ื•ื‘ ืœืงื—ืช ืืช ื”ื’ืื•ืกื™ื™ืŸ.
02:29
It works 80% of the time,
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ื”ื•ื ืขื•ื‘ื“ ื‘ 80% ืžื”ืžืงืจื™ื,
02:31
which means you wouldnโ€™t be a target until the enchantress was incapacitated.
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ืžื” ืฉืื•ืžืจ ืฉืœื ืชื”ื™ื• ื”ืžื˜ืจื” ืขื“ ืฉื”ืžื›ืฉืคื” ืชื ื•ื˜ืจืœ.
02:36
But if you succeeded in transforming her,
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ืื‘ืœ ืื ืชืฆืœื™ื—ื• ืœืฉื ื•ืช ืื•ืชื”,
02:39
youโ€™d probably be turned into a fish immediately after.
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ืืชื ื›ื ืจืื” ืชื”ืคื›ื• ืœื“ื’ ืžื™ื™ื“ ืœืื—ืจ ืžื›ืŸ.
02:42
If you transformed the sorcerer,
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ืื ืชืฉื ื• ืืช ื”ืžื›ืฉืฃ,
02:44
the enchantress would almost certainly turn you to stone.
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ื”ืžื›ืฉืคื” ื›ืžืขื˜ ื‘ื•ื•ื“ืื•ืช ืชื”ืคื•ืš ืืชื›ื ืœืื‘ืŸ.
02:48
It would really be better if you missed.
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ื–ื” ื™ื”ื™ื” ื‘ืืžืช ืขื“ื™ืฃ ืื ืชื—ื˜ื™ืื•.
02:51
And thatโ€™s when you have an idea:
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ื•ืื– ืขื•ืœื” ืœื›ื ืจืขื™ื•ืŸ:
02:53
what if you took the Gaussian, then missed on purpose?
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ืžื” ืื ืชืงื—ื• ืืช ื”ื’ืื•ืกื™ื™ืŸ, ื•ืื– ืชื—ื˜ื™ืื• ื‘ื›ื•ื•ื ื”?
02:57
Then, you would wait for the sorcerer to attack the enchantress,
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ืื–, ืืชื ืชื—ื›ื• ืฉื”ืงื•ืกืžืช ืชืชืงื™ืฃ ืืช ื”ืžื›ืฉืฃ,
03:00
and youโ€™d have an 80% chance of winning against the sorcerer.
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ื•ื™ื”ื™ื” ืœื›ื ืกื™ื›ื•ื™ ืฉืœ 80% ืœื–ื›ื•ืช ืžื•ืœ ื”ืžื›ืฉืฃ.
03:04
Itโ€™s a good idea, but thereโ€™s a problem;
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ื–ื” ืจืขื™ื•ืŸ ื˜ื•ื‘, ืื‘ืœ ื™ืฉ ื‘ืขื™ื”;
03:07
the sorcerer could also pass his turn
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ื”ืžื›ืฉืฃ ื™ื›ื•ืœ ื’ื ื›ืŸ ืœื•ื•ืชืจ ืขืœ ืชื•ืจื•
03:10
and the enchantress, knowing that she couldnโ€™t pass without becoming a cat,
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ื•ื”ืžื›ืฉืคื”, ืฉื™ื•ื“ืขืช ืฉื”ื™ื ืœื ืชื•ื›ืœ ืœืขื‘ื•ืจ ื‘ืœื™ ืœื”ืคื•ืš ืœื—ืชื•ืœื”,
03:14
would cast her spell on one of you.
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ืชื˜ื™ืœ ืืช ื”ื›ื™ืฉื•ืฃ ืฉืœื” ืขืœ ืื—ื“ ืžื›ื.
03:17
And since youโ€™re the most dangerous between you and the sorcerer,
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ื•ืžืื—ืจ ื•ืืชื ื”ื›ื™ ืžืกื•ื›ื ื™ื ื‘ื™ื ื™ื›ื ืœืžื›ืฉืฃ,
03:21
youโ€™d be the target.
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ืืชื ืชื”ื™ื• ื”ืžื˜ืจื”.
03:22
And thatโ€™s when you see what you really need to do:
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ื•ืื– ืืชื ืจื•ืื™ื ืžื” ืืชื ื‘ืืžืช ืฆืจื™ื›ื™ื ืœืขืฉื•ืช:
03:25
take the weakest wand, the Bannekar, and miss on purpose.
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ืœืงื—ืช ืืช ื”ืžื˜ื” ื”ื›ื™ ื—ืœืฉ, ื”ื‘ืื ืงืจ, ื•ืœืคืกืคืก ื‘ื›ื•ื•ื ื”.
03:29
Now the sorcerer knows that heโ€™ll be targeted by the enchantress
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ืขื›ืฉื™ื• ื”ืžื›ืฉืฃ ื™ื•ื“ืข ืฉื”ื•ื ื™ื”ื™ื” ื”ืžื˜ืจื” ืฉืœ ื”ืงื•ืกืžืช
03:32
and heโ€™ll have to try to turn her into a fish to avoid being turned into stone.
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ื•ื”ื•ื ื™ื”ื™ื” ื—ื™ื™ื‘ ืœื ืกื•ืช ืœื”ืคื•ืš ืื•ืชื” ืœื“ื’ ื›ื“ื™ ืœื”ืžื ืข ืžืœื”ืคื•ืš ืœืื‘ืŸ.
03:37
Seventy percent of the time heโ€™d succeed
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ืฉื‘ืขื™ื ืื—ื•ื– ืžื”ื–ืžืŸ ื”ื•ื ื™ืฆืœื™ื—
03:40
and youโ€™d have a 60% chance of winning the duel
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ื•ืœื›ื ื™ื”ื™ื” ืกื™ื›ื•ื™ ืฉืœ 60% ืœื–ื›ื•ืช ื‘ื“ื• ื”ืงืจื‘
03:43
at the beginning of the next round.
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ื‘ื”ืชื—ืœืช ื”ืกื™ื‘ื•ื‘ ื”ื‘ื.
03:45
If he fails, chances are heโ€™ll be turned to stone
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ืื ื”ื•ื ื™ื›ืฉืœ, ื”ืกื™ื›ื•ื™ื™ื ื”ื ืฉื”ื•ื ื™ื”ืคื•ืš ืœืื‘ืŸ
03:48
and youโ€™d still have a 60% chance of winning the duel against the enchantress.
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ื•ืขื“ื™ื™ืŸ ื™ื”ื™ื” ืœื›ื ืกื™ื›ื•ื™ ืฉืœ 60% ืœื–ื›ื•ืช ื‘ื“ื• ื”ืงืจื‘ ืžื•ืœ ื”ืงื•ืกืžืช.
03:53
Thereโ€™s a slim 3% chance youโ€™ll all be turned into cats,
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ื™ืฉ ืกื™ื›ื•ื™ ืงื˜ืŸ ืฉืœ 3% ืฉื›ื•ืœื›ื ืชื”ืคื›ื• ืœื—ืชื•ืœื™ื,
03:57
but when everythingโ€™s accounted for,
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ืื‘ืœ ื›ืฉืฉื•ืงืœื™ื ืืช ื”ื›ืœ,
03:59
you have better than even odds of winning with this strategy.
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ื™ืฉ ืœื›ื ืกื™ื›ื•ื™ ื˜ื•ื‘ ื™ื•ืชืจ ืœื–ื›ื•ืช ื‘ืืกื˜ืจื˜ื’ื™ื” ื”ื–ื•.
04:03
And thatโ€™s the best you can do.
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ื•ื–ื” ื”ื›ื™ ื˜ื•ื‘ ืฉืืชื ื™ื›ื•ืœื™ื ืœื”ื’ื™ืข ืืœื™ื•.
04:05
Hereโ€™s what the probability of winning for the different strategies looks like.
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ื”ื ื” ื”ื”ืกืชื‘ืจื•ืช ืฉืœ ื–ื›ื™ื” ืขื‘ื•ืจ ื›ืœ ืื—ืช ืžื”ืืกื˜ืจื˜ื’ื™ื•ืช ื”ืฉื•ื ื•ืช.
04:11
Who wouldโ€™ve thought that the best way to take your shot
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ืžื™ ื”ื™ื” ื—ื•ืฉื‘ ืฉื”ื“ืจืš ื”ื›ื™ ื˜ื•ื‘ื” ืœื”ืฆืœื™ื—
04:14
would be to throw away your shot?
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ืชื”ื™ื” ืœื•ื•ืชืจ ืขืœ ื”ืคื’ื™ืขื” ืฉืœื›ื?
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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