Ruin and absorbing barriers
Some risks aren't worth any expected return because they end the game.
An absorbing barrier in probability is a state you can enter but not leave. Russian roulette has an absorbing barrier (death). Bankruptcy is often an absorbing barrier (you can't easily come back from it). Loss of professional reputation can be one.
Once you cross an absorbing barrier, the future stops. No more bets. No more returns. The expected value of any bet with non-trivial probability of an absorbing barrier is misleading; you can't optimise across paths that include zero.
For operators, the discipline is to never take bets that include ruin, regardless of how attractive the math looks. Survival first. Optimisation second. Most catastrophic business failures are companies that took one too many bets with absorbing-barrier downside.
Examples in the wild
Companies that bet the business on a single technology, customer, or supplier eventually hit the bad case. The survival should come from the structure, not from luck.
Investors using extreme leverage during a normal year can be wiped out in a single bad week. The absorbing barrier (forced liquidation) ends the game even though their thesis would have worked given more time.
Health choices that include catastrophic downside (extreme sports without safety gear, drug experimentation) have absorbing barriers. The expected value math is irrelevant; the time-path is what counts.
Ruin and absorbing barriers is one of the mental models we apply through real cases inside the Pareto MBA — a part-time program for professionals who want to think clearly about business.