The Pirate Game

A brutal logic puzzle beloved by quant and tech interviewers — it looks like chaos but has one exact answer.

5 pirates (ranked most-senior to least: P5, P4, P3, P2, P1) have looted 100 gold coins. They divide them by strict pirate law:

1. The most senior pirate proposes how to split all 100 coins.
2. All pirates (including the proposer) vote. If half or more approve, the split happens. Otherwise the proposer is thrown overboard, and the next-most-senior pirate proposes — and so on.

Every pirate is perfectly logical and prioritizes, in order:

1. Survival (staying alive above all),
2. then maximizing their own gold,
3. then (as a tiebreaker) they'd prefer to throw someone overboard if it doesn't cost them coins.

You are P5, proposing first.

How many coins can you propose to keep for yourself and still survive?

(Answer with a single number.)