All pirates assume tat the other players will play optimally.
Consider the case where there r just two pirates B and A in the order of seniority.. So B will decide how to split the gold. All the pirates are very greedy and only 50% votes are required for approval. So B will choose to keep all the gold and vote for himself.. Thus A will get zero..
If there are three pirates C,B and A then C must get 2 votes 2 win. A knows tat he will get nothing if C is killed. So if C agrees to give him atleast 1 gold coin, voting for C is a better option for A. So C will keep 99 coins and give 1 coin to A. So the coin distribution is 99, 0, 1
If there r 4 pirates, D,C,B and A then the same reasoning can be applied and D will provide the loser in the 3 people scenario above with a gold coin. Since B is the loser. He will get a gold coin. B knows tat if he does not vote for D, C will take over and he wont get any gold as shown above.
So the distribution becomes 99,0,1,0
If there r 5 pirates, E,D,C,B and A we need 3 votes for E to win.. So E will give 1 coin each to losers in the 4 person scenario. So C and A will get a coin each
So the distribution decided by the most senior pirate to ensure his survival and maximize his gold is 98,0,1,0,1.
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2 comments:
98, 0, 1, 0, 1 will not work because the 4th and 3rd pirate will not vote for the 5th guy. You didnt give any to the 2nd guy so he will not vote for you either. Therefore, the 5th guy loses 2 to 3.
You dont consider the scenario that each pirate is capable of simulating the scenario upto the end in his mind. When you consider this, at some point in the game, the 4th and 3rd pirate stand a chance to win 99 gold. Why would they agree to take 1 or none then?
yes it will work?? y wudnt it work?? if the 3rd and 5th guy dont vote for the first guy.. he will get killed.. thn the second guy will play optimally and giv nothin to the 3rd and 5th guy..
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