TedTest

From the Ted Talk by Alex Gendler: Can you solve the pirate riddle?

Unscramble the Blue Letters

It's a good day to be a pirate. Amaro and his four meatys, Bart, Charlotte, Daniel, and Eliza have struck gold: a chest with 100 cions. But now, they must divvy up the btooy according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pratie, including aarmo himself, gets to vote either yarr or nay. If the vote pessas, or if there's a tie, the coins are divided according to plan. But if the majority veots nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to psrpooe a new distribution and all remaining pirates vote again. If his plan is rejected, he walks the plank, too, and Charlotte takes his plcae. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a proposal is accepted or there's only one pirate left. Naturally, each pirate wants to stay alvie while getting as much gold as possible. But being pirates, none of them trsut each other, so they can't collaborate in adcavne. And being blood-thirsty ptireas, if anyone thinks they'll end up with the same aomunt of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at loicgal deduction and knows that the others are, too. What distribution should Amaro propose to make sure he lives? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 aewsnr in: 1 If we follow our intuition, it seems like Amaro should try to bbrie the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be thinking about the current proposal, but about all possible outcomes down the line. And because the rank order is known in advance, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought pesocrs. She'd reason this out by wnikrog backwards from the last possible scenario with only her and Daniel remaining. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to override him, so Eliza wants to avoid this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to offer her slightly more than nothing, one coin. Since this ensures her support, Charlotte doesn't need to offer dnaiel anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the diieocsn to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for clratothe or Eliza. Now we're back at the initial vote with all five pirates standing. Having considered all the other scenarios, Amaro knows that if he goes overboard, the decision comes down to Bart, which would be bad news for Charlotte and eilza. So he offers them one coin each, kieepng 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of common knowledge where each person is aware of what the others know and uses this to predict their rioeansng. And the fnial distribution is an example of a Nash equilibrium where each player knows every other players' sgaettry and coohses theirs accordingly. Even though it may lead to a wsroe outcome for everyone than cooperating would, no individual player can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other pirates might need to find better ways to use those impressive logic skills, like rnviseig this asurbd pirate code.

Open Cloze

It's a good day to be a pirate. Amaro and his four ______, Bart, Charlotte, Daniel, and Eliza have struck gold: a chest with 100 _____. But now, they must divvy up the _____ according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each ______, including _____ himself, gets to vote either yarr or nay. If the vote ______, or if there's a tie, the coins are divided according to plan. But if the majority _____ nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to _______ a new distribution and all remaining pirates vote again. If his plan is rejected, he walks the plank, too, and Charlotte takes his _____. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a proposal is accepted or there's only one pirate left. Naturally, each pirate wants to stay _____ while getting as much gold as possible. But being pirates, none of them _____ each other, so they can't collaborate in _______. And being blood-thirsty _______, if anyone thinks they'll end up with the same ______ of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at _______ deduction and knows that the others are, too. What distribution should Amaro propose to make sure he lives? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 ______ in: 1 If we follow our intuition, it seems like Amaro should try to _____ the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be thinking about the current proposal, but about all possible outcomes down the line. And because the rank order is known in advance, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought _______. She'd reason this out by _______ backwards from the last possible scenario with only her and Daniel remaining. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to override him, so Eliza wants to avoid this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to offer her slightly more than nothing, one coin. Since this ensures her support, Charlotte doesn't need to offer ______ anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the ________ to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for _________ or Eliza. Now we're back at the initial vote with all five pirates standing. Having considered all the other scenarios, Amaro knows that if he goes overboard, the decision comes down to Bart, which would be bad news for Charlotte and _____. So he offers them one coin each, _______ 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of common knowledge where each person is aware of what the others know and uses this to predict their _________. And the _____ distribution is an example of a Nash equilibrium where each player knows every other players' ________ and _______ theirs accordingly. Even though it may lead to a _____ outcome for everyone than cooperating would, no individual player can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other pirates might need to find better ways to use those impressive logic skills, like ________ this ______ pirate code.

Solution

pirates
amaro
chooses
votes
absurd
coins
amount
revising
logical
decision
worse
pirate
eliza
daniel
propose
place
trust
keeping
charlotte
booty
passes
reasoning
strategy
answer
process
advance
bribe
alive
working
final
mateys

Original Text

It's a good day to be a pirate. Amaro and his four mateys, Bart, Charlotte, Daniel, and Eliza have struck gold: a chest with 100 coins. But now, they must divvy up the booty according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pirate, including Amaro himself, gets to vote either yarr or nay. If the vote passes, or if there's a tie, the coins are divided according to plan. But if the majority votes nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to propose a new distribution and all remaining pirates vote again. If his plan is rejected, he walks the plank, too, and Charlotte takes his place. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a proposal is accepted or there's only one pirate left. Naturally, each pirate wants to stay alive while getting as much gold as possible. But being pirates, none of them trust each other, so they can't collaborate in advance. And being blood-thirsty pirates, if anyone thinks they'll end up with the same amount of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at logical deduction and knows that the others are, too. What distribution should Amaro propose to make sure he lives? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our intuition, it seems like Amaro should try to bribe the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be thinking about the current proposal, but about all possible outcomes down the line. And because the rank order is known in advance, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought process. She'd reason this out by working backwards from the last possible scenario with only her and Daniel remaining. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to override him, so Eliza wants to avoid this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to offer her slightly more than nothing, one coin. Since this ensures her support, Charlotte doesn't need to offer Daniel anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the decision to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for Charlotte or Eliza. Now we're back at the initial vote with all five pirates standing. Having considered all the other scenarios, Amaro knows that if he goes overboard, the decision comes down to Bart, which would be bad news for Charlotte and Eliza. So he offers them one coin each, keeping 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of common knowledge where each person is aware of what the others know and uses this to predict their reasoning. And the final distribution is an example of a Nash equilibrium where each player knows every other players' strategy and chooses theirs accordingly. Even though it may lead to a worse outcome for everyone than cooperating would, no individual player can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other pirates might need to find better ways to use those impressive logic skills, like revising this absurd pirate code.

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
pirate code	2
offer daniel	2

Important Words

absurd
accepted
accurately
adjust
advance
alive
alternative
amaro
amount
answer
avoid
aware
bad
bart
benefit
booty
bribe
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changing
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code
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considered
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day
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deduction
distribute
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divided
divvy
eliza
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excellent
figure
final
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follow
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gold
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impressive
including
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individual
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keeping
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lead
left
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logic
logical
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making
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move
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moving
nash
naturally
nay
news
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override
pass
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person
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player
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predict
previous
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proposal
propose
rank
reason
reasoning
rejected
remaining
repeats
revising
scenario
scenarios
secure
situation
skills
slightly
standing
start
stay
strategy
struck
support
takes
theory
thinking
thinks
thought
tie
trust
turns
vote
votes
walk
walks
ways
working
worse
yarr