Why optimize expected compound return (ECR) rather than expected net worth?
First ECR also optimizes median expected wealth. If you follow the strategy of betting 100% of your money on every bet the median return after more than 1 bet is -100%. After 6 bets or so the 99th percentile is even -100%. There is a very small chance of a huge return and a large chance of losing all your money. This does not seem sensible. ECR also optimizes utility if utility is a logarithmic function of net worth. [Utility is way of measuring how happy you are, given your wealth]. Betting everything optimizes utility only if happiness is proportional to wealth. But is someone with $1bn really a thousand times as happy as someone with $1m? This seems unlikely. Optimizing expected compound return optimizes utility if utility is a logarithmic function of wealth. A logarithmic utility is more realistic than a linear utility. With logarithmic utility, a given amount of extra money becomes less valuable as you get wealthier. For example, a person with $1b is unlikely to get very excited b
