<p>Wait but wou;dn’t three and four figure out that if they got it to the third person they could get a 50-50 split? They would both agree because otherwise they would die.</p>
<p>Each pirate wants the absolute maximum he can get. Each only cares about how much he himself gets. </p>
<p>If you get to the third person, pirate 3 would still split 99-1-0 because pirate 4 will agree to anything >0 because his alternative would be to give everything up to pirate 5 in fear of being killed.</p>
<p>Scenario 1:
You’re a wimpy pirate. The others gang up and kill you. No gold for you.</p>
<p>Scenario 2:
You’re an awesome pirate. You gang up on the others and kill them like 4 little Indians. You now have all of the gold and some pretty nice skulls.</p>
<p>^^ But pirate 3 also knows that if pirate four doesn’t agree he’ll die. So either they both die or neither of them die. Pirate 3 won’t take the chance of not giving him enough gold and dying.</p>
<p>Pirates are too stupid to think all of this through, and as such the 97 gold proposal would be voted down as ridiculous (at first glance). Remember, not all pirates are CCers.</p>
<p>^^ And actually pirate 4 isn’t going to die if he decides to give 100% to pirate 5 they would both be alive. So pirate 4 probably isn’t worried about being killed its pirate 3 that’s in trouble.</p>
<p>^^ I agree real pirates would just fight each other for the gold.</p>
<p>Answer: While the pirates are coming up with the plan, a Ninja comes and silently steals the gold.</p>
<p>
</p>
<p>Condition 1: The pirates are logical and mathematically inclined.
Condition 2: Each pirate wants the most possible gold for himself. Everyone else be damned, if only it wasn’t for the fact that he needs a…
Condition 3: >50% agreement among pirates still left alive.</p>
<p>If it’s down to 2 pirates, pirate 5 will ALWAYS vote down whatever pirate 4 says unless pirate 4 offers 100 coins for him (and even then, pirate 5 could still decide to have him killed just out of spite). For example, if pirate 4 offers a 50-50 split, pirate 5 votes him down (so pirate 4 doesn’t get the >50% agreement), to be left with 100 coins. And because he knows that 100>50, and he cares only for the maximum amount of gold he can get, this is what he’ll do. When it gets down to the last two pirates, pirate 5 will always come out with all 100 coins.</p>
<p>
</p>
<p>Pirate 4 is fine with only 1 coin because he knows that this is the absolute greatest amount he can get (if he downvotes Pirate 3’s plan, he ends up having to give everything up to pirate 5). Therefore, pirate 4 will logically always agree to this 99-1-0 plan.</p>
<p>
almost there is giving the philosophy majors a bad rep. </p>
<p>I agree with messiah and aero. ;)</p>
<p>^^ But why would pirate 3 risk dying by giving him just one coin. It’s such a dick move that it would probably make pirate 4 more likely to choose the fifth pirate even if he would get one less coin. At that point its not his life that is on the line. Would he rather get one coin and let someone live that was being an a-hole and giving him one coin or would he rather lose that coin and keep his dignity.</p>
<p>^Which is why
</p>
<p>Harry’s dead on about the conditions. Also, the plan maker (you) get to vote. I’m seeing a lot of close-to-correct answers, but some of you are still a little bit off.</p>
<p>^That was Aero, I was just quoting him.</p>
<p>^^^ But the alternative is that pirate 3 and 4 both get one coin. If they make an agreement to split it (it doesn’t have to be 50 -50 but they each get more than pirate 1 was offering them) they would be benefiting. So pirate 3 is safe as long as he goes along with their their agreement and obviously he would want to because he would be getting more than one coin. If they could do this and receive more than one coin why would they go along with pirate 1’s idea?</p>
<p>Aero, if the 3rd pirate split it 99-1-0, wouldn’t he still not get as much as he possibly could? Why not 100-0-0? The 4th guy knows that if he doesn’t agree with the 3rd pirate, he’s dead.</p>
<p>Also, I think this thread’s digressed from the main question: how should the FIRST pirate distribute the gold so that he gets the most possible?</p>
<p>I saw one or two 97-0-1-0-2 answer(s). Why would you give the 5th pirate more than 1 gold?</p>
<p>So the answer is either 98-0-1-1-0 or 98-0-1-0-1.</p>
<p>But pirate 3 is never going to vote for pirate 1’s plan because he knows that if he can eliminate the first two and he gives pirate 4 more money than he would have gotten they outnumber pirate 5. If he makes this agreement beforehand and they stick to the no trickery clause pirate 4 will vote with him.</p>
<p>Condition 1: The pirates are logical and mathematically inclined.
Condition 2: Each pirate wants the most possible gold for himself. Everyone else be damned, if only it wasn’t for the fact that he needs a…
Condition 3: >50% agreement among pirates still left alive.
Condition 4: No planning beforehand. OP will have to check this, but based on my knowledge of other game theory problems, this is usually another condition to simplify things. Otherwise, we’re left with networks of potential agreements and backstabbers.</p>
<p>New answer! Given one more condition:</p>
<p>
</p>
<p>I figured pirate 1 would want to offer pirate 5 more than what pirate 2 would offer him to absolutely ensure that pirate 5 votes for him, even though pirate 5 would be equally well-off with just 1 coin. Otherwise, there’s a chance that pirate 5 downvotes pirate 1 just for the hell of it. However, if we add a 5th condition stating that the pirates are not capricious and will take the largest sum offered on its first time, then a 98-0-1-0-1 would be the actual best answer.</p>
<p>Pirate 5 would not downvote this because he wouldn’t reach a scenario in which he could earn >1 coin (if he keeps downvoting with the intent of getting to scenario 1, he’d get to scenario 2, and be outvoted by pirates 3 and 4).</p>
<p>Pirate 4 downvotes this.</p>
<p>Pirate 3 does not downvote because he’ll only get to scenario 3 before being outvoted (he does not assume that pirate 5 wants to keep downvoting, because pirate 3’s best case scenario is pirate 5s worst case, and pirate 3 gets to establish the optimal route first).</p>
<p>Pirate 2 downvotes.</p>
<p>Pirate 1 doesn’t downvote.</p>
<p>^If we accept that new condition, could it be 100-0-0-0-0? Pirate 4 has to accept 0 coins regardless because of what would happen if he and 5 were alone, and pirate 5 must do the same regardless because of what would happen at the 3-4-5 stage.</p>
<p>In bold are the “yes” votes.</p>
<p>Pirate 3 – 100
Pirate 4 – 0
Pirate 5 – 0</p>
<p>Pirate 2 – 100
Pirate 3 – 0
Pirate 4 – 0
Pirate 5 – 0</p>
<p>Pirate 1 – 100
Pirate 2 – 0
Pirate 3 – 0
Pirate 4 – 0
Pirate 5 – 0</p>