Canada Math Contest #2 - Problem 5

A game starts with $1 in the bank and starts at stage 1. At stage n, the player rolls a die. If a 1 or 2 is rolled, the game ends and they win nothing. If a 3, 4, or 5 is rolled, the game ends and they win all the money currently in the bank. If 6 is rolled, they advance to stage n+1, and the amount of money in the bank doubles. If E is the game’s expected value, find 1000E.