If you want to decide whether you should take a bet, the first step is to calculate expected value. Flipping a coin where you win or lose the same amount (win $1 for heads, lose $1 for tails) has an expected value of zero.
It’s not a bet you should make.
Very few bets are that straightforward… and it turns out that you can have games where the arithmetic mean of a game (its EV) is positive but the geometric mean is negative.
There’s some light math in this post but it’s good reading:
the jackpot age [scimitar capital] – “The discrepancy between arithmetic and geometric means forms what I call the Jackpot Paradox. Physicists call it the ergodicity problem and traders call it volatility drag. You can’t always eat the expected value when it’s squirreled away in rare jackpots. Risk too much hunting jackpots and the volatility will turn positive expected value into a straight line to zero. In the world of compounded returns, the dose makes the poison.
[…]
That taste for outsized risk has seeped into everyday culture. Wage growth has severely lagged compounded capital, causing ordinary people to increasingly see their best shot at real upward mobility in negative EV jackpots. Online gambling, 0DTE options, retail meme stocks, sports betting, and crypto memecoins all testify to the phenomena of exponential wealth preference. Technology makes speculating effortless, while social media spreads the story of each new overnight millionaire, luring the broader population into one giant losing bet like moths to a light.
We’re becoming a culture that worships the jackpot and increasingly prices survival at zero.“