Pirate game facts for kids
The pirate game is a fun and simple math game that helps us understand how people make choices when they want to get the best outcome for themselves. It's a bit like a bigger version of another game called the ultimatum game.
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How the Game Works
Imagine five smart pirates, named A, B, C, D, and E, in order of who's in charge (A is the boss, then B, and so on). They've just found 100 shiny gold coins! Now they need to figure out how to share them.
The pirate rules for sharing are strict:
- The most senior pirate (Pirate A first) suggests how to split the coins.
- All pirates, including the one who made the offer, vote on the plan.
- If most pirates agree, the coins are shared, and the game is over.
- If there's a tie vote, the pirate who made the offer gets the final say.
- If most pirates say no to the plan, the pirate who made the offer is thrown overboard! Then, the next most senior pirate gets to make a new offer, and the game continues.
- This keeps happening until a plan is accepted, or until only one pirate is left.
Pirates make their decisions based on four main things:
- First, they want to stay alive!
- Second, if they survive, they want to get as many gold coins as possible.
- Third, if everything else is equal, they'd rather see another pirate thrown overboard. (This means they're very competitive!)
- Finally, pirates don't trust each other. They won't make secret deals or promises outside of the official coin-sharing plan.
You might think Pirate A would have to give away most of the gold to get everyone to agree. But that's not what happens! When pirates vote, they don't just think about the current offer. They also think about what would happen in future rounds if the current offer is rejected. Since everyone knows who's in charge, they can guess how others will vote.
Let's work backward to see how it plays out:
When Only Two Pirates Are Left
Imagine only Pirates D and E are left. D is the boss. D will offer to keep all 100 coins for himself and give 0 to E. Since D has the final say in a tie, his plan will pass.
When Three Pirates Are Left
Now, let's say C, D, and E are left. Pirate C knows that if his plan fails, D will be the next to propose and will give E nothing. So, to get E's vote, C needs to offer E at least one coin. C needs one other vote besides his own. If C offers E 1 coin, E will vote yes because 1 coin is better than 0. So, C proposes:
- C: 99 coins
- D: 0 coins
- E: 1 coin
When Four Pirates Are Left
What if B, C, D, and E are left? Pirate B needs two other votes to pass his plan (since he has the tie-breaking vote, he needs 2 votes out of 4, including his own, for a majority). B knows that if his plan fails, C will be the next to propose, and C will give D nothing. So, B can offer D just 1 coin to get D's vote. D will vote yes because 1 coin is better than 0. B proposes:
- B: 99 coins
- C: 0 coins
- D: 1 coin
- E: 0 coins
(You might think B could offer E 1 coin instead. But remember, pirates prefer to throw others overboard if they get the same amount of gold. So E would rather throw B overboard to get 1 coin from C later, if B offered E 1 coin. That's why B offers D the coin.)
The Final Solution for Five Pirates
Knowing all this, Pirate A can figure out the best plan. A needs two other votes to pass his plan (since he has the tie-breaking vote, he needs 2 votes out of 5, including his own, for a majority).
- A knows that if he's thrown overboard, B will offer C 0 coins. So, A can offer C 1 coin to get C's vote.
- A also knows that if B is thrown overboard, C will offer E 1 coin. So, A can offer E 1 coin to get E's vote.
So, the smartest plan for Pirate A is:
- A: 98 coins
- B: 0 coins
- C: 1 coin
- D: 0 coins
- E: 1 coin
This plan works because C and E will vote yes. They get 1 coin, which is better than the 0 coins they would get if A was thrown overboard and the game continued to the next round where B or C would be captain.
More Pirates, More Fun?
This game gets even more interesting when there are many more pirates than gold coins. For example, if there are 100 gold coins but hundreds of pirates, the game changes a lot!
When there are tons of pirates, some of them are "doomed" to be thrown overboard no matter what they propose, because they can't get enough votes. Other pirates might survive by giving away all the gold, or by giving small amounts to specific pirates who would otherwise get nothing.
For example, with 100 gold coins:
- If Pirate #201 is the captain, he can only survive by giving 1 coin to each of the lowest odd-numbered pirates (like #1, #3, #5, etc.), keeping none for himself.
- If Pirate #202 is the captain, he can survive by taking no gold and giving 1 coin to 100 pirates who wouldn't get gold from #201.
- Pirate #203, as captain, won't have enough gold to bribe enough pirates, so he will likely be thrown overboard.
- Pirate #204, however, can survive because Pirate #203 will vote for him (since #203 only survives if #204 does). This gives #204 a head start on votes, and he can bribe others.
The pattern of who survives and who doesn't becomes very complex with many pirates. It shows how tricky these kinds of strategic games can be!
See also
In Spanish: Juego de los piratas para niños
