Five pirates splitting a hundred gold coins

Five pirates, ranked $1$ (most junior) to $5$ (most senior), must divide $100$ gold coins. The most senior surviving pirate proposes an allocation and everyone still aboard, the proposer included, votes. The plan is adopted if at least half the votes are in favour; if a strict majority votes against, the proposer is thrown overboard and the next most senior pirate proposes. If only one pirate is left he keeps all $100$. Each pirate values survival first and then coins, and all reason perfectly. How many coins does pirate $5$ keep under his best proposal? (Answer $0$ if he is always thrown overboard.)

$98$. Work backwards. With pirates $1,2$, pirate $2$ keeps all (his own vote is half). With three, pirate $3$ buys pirate $1$ for one coin. With four, pirate $4$ needs one more vote and buys pirate $2$ for one coin. With five, pirate $5$ needs two extra votes and buys pirates $3$ and $1$ (who get nothing otherwise) with one coin each, keeping $98$.