<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>