How much to bet on a coin that lands heads 60 per cent of the time

Question

You have a bankroll and can make as many bets as you like on a coin that lands heads with probability 0.6. Each bet pays even money: bet x, and you win x on heads or lose x on tails. You may bet any fraction of your current bankroll each time. 1. Betting everything every time has the highest expected value. Why is it a terrible idea? 2. What fixed fraction of your bankroll should you bet on each flip to make your wealth grow as fast as possible in the long run? 3. What happens if you bet twice that fraction?

Accepted Answer

Bet 20 per cent of your bankroll each time. Betting 40 per cent grows your wealth no faster than not betting at all, and anything above that loses money in the long run. Why "bet everything" fails. Betting your whole bankroll has expected value 1.2 times your stake per flip, the best possible. But after n flips you are bankrupt unless every flip was heads, which has probability 0.6 to the n, essentially zero. The expected value is carried entirely by that vanishing chance of an astronomical win. Almost surely you end with nothing. The growth rate. Bet a fixed fraction f. After many flips, abo…

How much to bet on a coin that lands heads 60 per cent of the time

Your answer

Discussion

Learn the concepts

Related questions