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 mateys, Bart, cothlatre, Daniel, and Eliza have struck gold: a chest with 100 cnois. 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, iclinndug 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 martijoy votes nay, aamro must walk the plank and Bart becomes captain. Then, Bart gets to propose a new droititiubsn 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 ezila until either a proposal is aetpcecd or there's only one pritae left. Naturally, each pirate wants to stay alvie 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 eenelcxlt at logical deduction and knows that the others are, too. What distribution should Amaro propose to make sure he lievs? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our iiuionttn, 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 priedct 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 wonirkg backwards from the last possible sairneco with only her and deanil remniniag. 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 cstos. Now we move to the povuires doeicisn pnoit with three pirates left and Charlotte making the posarpol. Everyone knows that if she's ototveud, 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 slgltihy more than nothing, one coin. Since this ensures her sproput, Charlotte doesn't need to offer Daniel anything at all. What if there are four pretias? 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 sindntag. 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 oreffs them one coin each, keeping 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the aetilarvnte would be wosre 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 omtocue 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 rviinseg this absurd pirate code.

Open Cloze

It's a good day to be a pirate. Amaro and his four mateys, Bart, _________, Daniel, and Eliza have struck gold: a chest with 100 _____. 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, _________ 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 ________ votes nay, _____ must walk the plank and Bart becomes captain. Then, Bart gets to propose a new ____________ 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 _____ until either a proposal is ________ or there's only one ______ left. Naturally, each pirate wants to stay _____ 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 _________ at logical deduction and knows that the others are, too. What distribution should Amaro propose to make sure he _____? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our _________, 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 _______ 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 _______ backwards from the last possible ________ with only her and ______ _________. 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 _____. Now we move to the ________ ________ _____ with three pirates left and Charlotte making the ________. Everyone knows that if she's ________, 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 ________ more than nothing, one coin. Since this ensures her _______, Charlotte doesn't need to offer Daniel anything at all. What if there are four _______? 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 ________. 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 ______ them one coin each, keeping 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the ___________ would be _____ 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 _______ 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 absurd pirate code.

Solution

majority
standing
outcome
working
daniel
slightly
coins
support
costs
alternative
lives
eliza
worse
pirate
proposal
charlotte
previous
distribution
including
offers
remaining
pirates
amaro
alive
scenario
excellent
accepted
outvoted
decision
intuition
revising
point
predict

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
captain
chances
changing
charlotte
chest
chooses
code
coin
coins
collaborate
common
concept
concepts
considered
cooperating
costs
current
daniel
day
decision
deduction
distribute
distribution
divided
divvy
eliza
ensures
equilibrium
excellent
figure
final
finally
find
follow
fun
game
gold
good
grudgingly
hat
impressive
including
increase
individual
initial
interesting
intuition
involves
keeping
knowing
knowledge
lead
left
line
lives
logic
logical
logicians
majority
making
mateys
move
moves
moving
nash
naturally
nay
news
offer
offers
order
outcome
outcomes
outvoted
overboard
override
pass
passes
pause
person
pirate
pirates
place
plan
plank
player
point
predict
previous
process
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