Or, how you can create positive returns out of a random walk simply by rebalancing a portfolio.
Let's say you have $100 that you want to distribute 50% in stocks and 50% in cash. $200 in stocks, $200 in cash.
On the first day, the stock halves in price, so you now only have $100 in stock. You rebalance your portfolio by buying another $50 in stock, bringing your assets to $150 in stock, $150 in cash (total $300).
The next day, the stock doubles in price. Your stock is now worth $300. You sell some stock ($75 worth to bring your portfolio back to 50%/50%). Now you have $225 of stock, $225 of cash.
An investor who didn't rebalance their portfolio would have broken even, but you've profited $50.
The rebalanced portfolio is actually less volatile than the underlying assets. So not only is the return greater, but the risk-adjusted return is greater. You can run a Monte Carlo simulation to show that Shannon's demon is true. In some cases, you can even use it to turn two "losing investments" into a winner!
When does Shannon's Demon work? The underlying assets have to be volatile enough and uncorrelated (or negatively correlated). Rebalancing costs have to be zero (or small enough).
Shannon's Demon goes by a few different names: rebalancing premium, volatility pumping, or a short gamma.
The Kelly Criterion is another rebalancing mechanism that's highly linked to Shannon's Demon. Kelly worked with Shannon at Bell Labs.