LYRICFLUENT
LYRICFLUENTCan You Solve The Pirate Riddle? Lyrics by Alex Gendler, Addison Anderson
Below, you will find the lyrics for Can You Solve The Pirate Riddle? by Alex Gendler.
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?
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
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