Your second ducat, like your second million, is never quite as sweet.
At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.
Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.
The ultimate compound return rate is acutely sensitive to fat tails.
The assumption that anything true is knowable is the grandfather of paradoxes.
There is a deep connection between Bernoulli's dictum and John Kelly's 1956 publication. It turns out that Kelly's prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric means of outcomes.