5 Pirates Assign 100 gems question reprint Mathematics

5 pirates have grabbed 100 gems, each one of the same size and priceless. &NBSP
They decided to be so divided:  
1. Draw lots to determine your own number (1,2,3,4,5)  
2. First, the distribution scheme is proposed by number 1th and then all 5 people vote, and when and only if more than half of the people agree,
     will be assigned to the sea to feed the sharks. &NBSP,
3. If 1th is dead, then a distribution plan is proposed by 2nd, and then 4 people vote,
     when and only if more than half of the people agree, distribute according to his proposal, otherwise they will be thrown into the sea to feed the sharks. &NBSP,
4. And so on  
 
Condition:  
every pirate is a very intelligent person who can judge the pros and cons rationally and make a choice. &NBSP
Question:  
The final allocation results. &NBSP
Hint:  
The principle of the Pirate's judgment:  
1. Save your  
2. Get as much gem   as possible;

The distribution of the 
 1th number is: 1th 97, 2nd 1 Gems are not, 3rd 1, 4th 1 stones are also not, 5th 2. 
 
 forward from the back, if the number 1-3 bandits are fed sharks, only 4th and 5th, then 5th must vote against the number 4th feed the sharks, 
 to take all the gold coins. So, number 4th only supports number 3rd to survive. The number 3rd knows this, will mention (100,0,0) the distribution scheme, 
 to 4th, 5th Skinflint and all the gold coins have been, 
 because he knew that 4th had nothing but will vote in favour of the vote, plus his own vote, his plan can be passed. 
 However, the scheme of 2nd, deduced to 3rd, would propose a (98,0,1,1) scheme that would give up 3rd and give a gold coin of 4th and 5th. 
 Since the scheme is more advantageous for numbers 4th and 5th than for distribution 3rd, they will support him rather than expect him to be out and be allocated by 3rd. 
 This way, number 2nd will take 98 gold coins. 
 However, the 2nd plan will be understood by number 1th, and 1th will propose (97,0,1,2,0) or (97,0,1,0,2) the option of giving up 2nd, 
 and giving 3rd a gold coin, while giving 4th (or 5th) 2 gold coins. As a result of this programme for number 1th, for 3rd and 4th (or 5th), the 
 is better than the 2nd distribution, they will vote 1th for the vote, 
 plus 1th of their own tickets, 1th of the program can be passed, 97 gold coins can easily fall into the bag. This is no doubt that number 1th can get the maximum benefit