Completely overwhelmed by the response to my last post – I didn't take into account that a lot of you guys are as much geeks as I am :), – let me explain the solution strategy. It uses what is called 'backward induction':
If the oldest pirate (pirate 1) is the only survivor of the big massacre, he will keep all 100 pieces of gold.
Thus, whatever pirate 2 suggest, he is gonna be killed (even if he offers all the gold to the oldest, that one will still want to kill him).
Hence, pirate 2 will accept whatever offer pirate 3 makes, for the benefit of mere survival. So pirate 3 can keep all the gold to himself, and still get his own vote and that of pirate 2.
In order to survive, pirate 4 needs to get 3 votes: His own plus two of his fellows'. He knows that pirate 2 and 1 are easy to convince: He merely needs to offer them one single piece of gold. Then the remaining 98 pieces are all his. So: If pirate 5 dies, this is gonna be the outcome of the game: 98 pieces of gold for pirate 4, no gold for pirate 3, 1 piece of gold for pirates 2 and 1, no further deaths.
So what does the youngest pirate know?
- Pirate 4's vote is his if and only if he offers him 99 pieces of gold.
- Pirate 3's vote is his if and only if he offers him 1 piece of gold.
- Pirate 2's vote is his if and only if he offers him 2 pieces of gold.
- Pirate 1's vote is his if and only if he offers him 2 pieces of gold.
Since, in addition to his own, the youngest pirate needs two more votes, the highest amount of gold he can keep for himself is 97 pieces, give one to pirate 3 and two to either the oldest or the second oldest pirate.
However, in real life, most people don't think as far... so rest assured, with such bloodthirsty pirates, a few people will die because we fail to teach game theory to poor mortals around the world! :) :)
If the oldest pirate (pirate 1) is the only survivor of the big massacre, he will keep all 100 pieces of gold.
Thus, whatever pirate 2 suggest, he is gonna be killed (even if he offers all the gold to the oldest, that one will still want to kill him).
Hence, pirate 2 will accept whatever offer pirate 3 makes, for the benefit of mere survival. So pirate 3 can keep all the gold to himself, and still get his own vote and that of pirate 2.
In order to survive, pirate 4 needs to get 3 votes: His own plus two of his fellows'. He knows that pirate 2 and 1 are easy to convince: He merely needs to offer them one single piece of gold. Then the remaining 98 pieces are all his. So: If pirate 5 dies, this is gonna be the outcome of the game: 98 pieces of gold for pirate 4, no gold for pirate 3, 1 piece of gold for pirates 2 and 1, no further deaths.
So what does the youngest pirate know?
- Pirate 4's vote is his if and only if he offers him 99 pieces of gold.
- Pirate 3's vote is his if and only if he offers him 1 piece of gold.
- Pirate 2's vote is his if and only if he offers him 2 pieces of gold.
- Pirate 1's vote is his if and only if he offers him 2 pieces of gold.
Since, in addition to his own, the youngest pirate needs two more votes, the highest amount of gold he can keep for himself is 97 pieces, give one to pirate 3 and two to either the oldest or the second oldest pirate.
However, in real life, most people don't think as far... so rest assured, with such bloodthirsty pirates, a few people will die because we fail to teach game theory to poor mortals around the world! :) :)
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