Originally posted by wolfgang59
A man offers you this bet;
He will flip a coin and you call. The coin is fair.
If you win he gives you £2.
If you lose you give him £1.
If you win you can play on. Same odds.
(ie If you win he gives you £6 if you lose you give him the £3.)
You can only continue playing after a win.
You must invest all your money if you continue.
What is you ...[text shortened]... his strategy?
(ie if you played the game each day what would you expect to be up after a year?)
If you keep winning, no problems.
Once you lose you can't continue and you will have a total loss of 1 pound.
In one game you'd expect to win 0.5 * 2 + 0.5 * -1 = 1/2 pounds.
After two games you'd expect to win
0.5 * -1 + 0.25 * -3 +0.25 * (6+2) = 3/4
After three games
0.5*-1 + 0.25*-3 + 0.125*-9 + 0.125*(18+6+2) = 7/8
After N games: (2^N - 1)/2^N.
Still working on optimal strategy.