In this way, consider the case that there are only two pirates (the other pirates are thrown into the sea to feed the fish). Remember that they are P 1 and P2, where P2 is intense. Of course, P2' s best plan is that he will get 100 gold coins, while P 1 will get 0 gold coins. When voting, his own vote is enough for 50%.
Step forward. Now a more fierce pirate P3 has been added. P 1 knows-P3 knows he knows-if P3's scheme is rejected, the game will only be continued by P 1 and P2, and P 1 won't get a gold coin. So P3 knew that as long as P 1 was given a little sweetness, P 1 would agree to his plan (of course, if P 1 was not given a little sweetness, nothing would be gained anyway, and P 1 would rather feed P3 to the fish). So the best scheme for P3 is: P 1 get 1, P2 gets nothing, and P3 gets 99.
The situation at P4 is similar. He only needs two votes, and giving P2 a gold coin will make him vote for this scheme, because P2 will get nothing in the next P3 scheme. P5 used the same reasoning method, except that he had to convince his two companions, so he gave P 1 and P3 who got nothing in P4 plan one gold coin each, and kept 98 for himself.
By analogy, the best scheme of P 100 (that is, the boss of 100 pirates) is: he gets 5 1 piece himself, and gives one piece to P2, P4, P6 and P8 ... The person in P98 gets nothing in the P99 plan.
When you said that the boss would pay 50 yuan in the end, you might have counted yourself in all even-numbered calculations.
The gist of this problem is that, unlike many people's imagination, half of them get nothing in any distribution scheme. Because the issuer only needs to get half of the votes. Unnecessary neglect. Then the former distributor only needs to "buy" these people with each person 1 gold brick. You can get the rest of the gold bricks yourself.