The Kelly Model for gambling and investing

Kelly posited a scenario in which a horse-race better has an edge: a ‘private wire’ of somewhat reliable but not perfect tips from inside information. How should he bet? Wager too little, and the advantage is squandered. Too much, and ruin beckons. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate.