Seeing the Pirate's game posted (thanks magicalcheese!) reminded me of my classes in polysci/game theory, so I thought I'd take a shot at making Pirates 3. So here's my spin:
So after some more looting and plundering and general pirating, the pirates have picked up an additional member (making for 7 pirates total) and now they each have 100 gold coins.
Somehow (I highly suspect there was rum involved ), they agreed to allow the captain to levy a "pirate tax". The captain can choose tax each crew member a different amount, but the proposed tax scheme (like all proposed tax schemes) must be voted upon in the usual pirate format.
(For those of you who missed the previous pirates strings created by magicalcheese, here are the rules: The captain must obtain approval (yes votes) from at least half his crew (including himself) or else there will be a mutiny, the current captain will be forced to walk the plank, and the next highest ranked member of the crew will become the new captain, and the process will repeat until a proposal passes.
However there is one extra catch in this case: for the pirates who vote "no" on a proposal that passes, the amount of tax they have to pay is the proposed amount divided by (the number of pirates who vote no+1), rounded to the nearest whole coin. For example, if out of 7 pirates, if three of them are taxed 100 gold coins and vote no, then they each have to pay 100/(3+1)=25 gold coins to the captain.
As before, assuming they are all really smart (and relatively sober during the voting...), and really greedy, what is the maximum amount the captain can get out of taxes without risking his life?
I just tried working this out myself, but maybe someone will find a better answer than I did...