# Ergodicity *You only get one run at it* --- The average outcome across many people is not the same as the average outcome for one person over time. A system is ergodic when the two match: what happens to a crowd at one moment tells you what happens to one member over many rounds. Most things in business, and most things that involve reinvesting your winnings, are not like that. The gap matters because expected value is a crowd number. It averages across all the ways things could go, including the ways where someone else prospers and you are ruined. You don't get to be the crowd. You get one sequence of outcomes, in order, and for anything multiplicative the order and the compounding decide what you actually end up with. A business can be profitable on average and still run out of cash on the way, because nobody gets to spend an average. [[One timeline]] walks the whole trap through a coin-flip game. Bet-sizing is where the idea earns its money. The Kelly criterion gives the fraction of your capital that maximises growth along one path - for a simple bet with win probability p and net odds b: $f^* = \frac{bp - q}{b} \quad \text{where } q = 1 - p$ You will never run it in a board meeting, and most practitioners deliberately sit below it anyway. What it changes is the question: not "is this attractive?" but "at this size?" A deal can be handsomely positive on expected value and still be wrong at the size proposed, because the losing branch ends the game, and nothing grows after that. Your investors will often read the same bet differently, and rationally so: a portfolio can afford a miss in a way that you just can't. [[Bolt-ons]] is the same judgment on a live acquisition, where the bet is management bandwidth as much as money. Two smaller corollaries travel with it. Paths compound, so an early shortfall changes what every later year has to deliver - [[Year one]] runs that arithmetic. And a good deal of what gets called conservatism is just this idea, felt: [[Halma]] does thousands of small deals precisely so that no single one is ever the company. ---