An island, a boat, and a roulette

You are on an island where a volcano is going to erupt anytime soon, wiping out everything with it. The only way to leave the island is via boat, but the captain of the boat asks for £80 for the ride. You have only £70. On the island there's a casino with roulette. What do you do to maximize your chances of survival?

(riddle taken from a Colin Bruce book)

• That boat captain is an a'hole. He'd let you DIE for the lack of a tenner? Nov 21, 2017 at 18:48
• Stay along with the captain, sure it saves your life. ;-) Nov 22, 2017 at 18:22

Place your bet where you have a 50% chance of winning (Red, Black, Odd, Even, etc.)

1. Gamble £10. If you win £10, you're safe. If you lose, you still have £60 left.

2. Gamble £20. If you win £20, you're safe. If you lose, you still have £40 left.

3. Gamble £40. If you win £40, you're safe. If you lose, you're screwed.

So you have only a 1-in-8 chance of not making it off the island. Pretty good, given the circumstances.

• @dr01 Thanks for the edit. I'm not really familiar with how a roulette works :-) Nov 21, 2017 at 18:59
• Relevant (and certainly long familiar to Rand, even if he doesn't know much about roulette specifically, since he's a mathematician): en.wikipedia.org/wiki/St._Petersburg_paradox Nov 21, 2017 at 21:10
• Incidentally, on actual roulette wheels you have slightly less than a 50% chance of winning when you make such bets, because the wheel has an extra space (or sometimes multiple extra spaces) that don't count as red or black, as odd or even, etc. This doesn't change the choice of strategy, but it makes it slightly less likely to succeed. Nov 21, 2017 at 21:11
• @GarethMcCaughan Perhaps even more relevant: en.wikipedia.org/wiki/Martingale_(betting_system) Nov 21, 2017 at 21:58
• @Gareth and GPR Yep, I've long heard about that "keep doubling the stakes, must eventually win" paradox. (It was also used to great and dramatic effect by Mat Cauthon - my namesake's gambling friend - in The Gathering Storm.) In this case, though, you've got nothing to lose in terms of money - if you don't get that extra cash, you're dead. Dovie'andi se tovya sagain, as Mat would say. Nov 22, 2017 at 12:13