Question

5 Three Pirates Sharing 100 Gold Coins

Three pirates of different ages have a treasure of 100 gold coins. They decide to split the coins using this scheme:

• The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

  • – If more than 50% (exclusive) of the pirates vote for it, then the coins will be shared that way and the game ends. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. Note that if exactly 50% of the pirates vote for it, then the pirate proposing the scheme will be thrown overboard.

  • – As pirates tend to be a bloodthirsty bunch. If a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

• Assuming that all 3 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates).

1. What will happen?

2. Assume now Captain Hook spots the scene and wants to share the gold as well. That is, now we have four pirates sharing the coins. Captain Hook will be the first to propose a scheme to share the coins. Assume the same rule applies. What will happen?

Answer 1

In the situation when the gold coins are to be distributed among 3 pirates and all of them are intelligent, rational, greedy and do not wish to die, Pirate 3 knows that if his proposal gets rejected , Pirate 2 also won't get anything as his proposal will be rejected too ( by exactly 50% votes ). In this case, Pirate 1 will get all the coins.
So, Pirate 3 will bribe the Pirate 2 for 1 coin. Pirate 2 will agree as something is better than nothing.
Now, when pirate 3 will propose, pirate 2 will vote for him and pirate 1 will vote against him.
Therefore, the final distribution of the coins will be this way :
{ Pirate 1, Pirate 2 , Pirate 3} { 0, 1, 99 }

Now, Captain Hook also joins. He will propose the scheme and he needs votes from at least 2 other pirates for his proposal to get accepted. Pirate 4 knows that if he dies, Pirate 3 will propose the scheme and Pirate 1 won't get anything and Pirate 2 will get just 1 coin ( according to the previous case - proposal with 3 pirates )
So, Pirate 4 will bribe Pirate 2 with 2 coins and Pirate 1 with 1 coin. They both will agree as they are getting more coins than in the other case.
So, the final distribution of the coins will be this way:
{ Pirate 1, Pirate 2 , Pirate 3 , Pirate 4 } { 1 , 2 , 0 , 97 }