Risk of ruin
Compute the probability of losing enough that you cannot continue, and treat any non-trivial answer as disqualifying.
- Time cost
- 30 min
- Output
- A ruin threshold, a probability, and a compounded survival figure.
- Steps
- 5
Use when
- A decision has a branch you would not recover from.
- The same bet repeats, so a small per-round chance compounds.
- An expected value calculation looks good and you have not checked the tail.
Do not use when
- Nothing is at stake that you could not replace. Then this is a bad outcome, not ruin.
- You are using it to avoid every risk. Most downside is survivable and treating it as ruin is its own error.
Inputs required
- The definition of ruin, in specifics
- Per-round loss probability
- Number of rounds
Procedure
- 01
Define ruin concretely
Not “a bad year”. The state after which you cannot continue: the reserve is gone, the licence is lost, the relationship ends. Write the actual threshold.
- 02
Find the per-round probability
The chance of a loss large enough to reach that threshold in one round, or the chance of a sequence that compounds to it.
- 03
Compound over the horizon
Survival over n rounds is (1 − p) to the power n. A 2% per-round chance of ruin over 50 rounds leaves about a 36% chance of ruin overall. Small per-round numbers are not small.
- 04
Test against zero, not against expected value
A positive expected value with a 5% chance of ruin is not a good bet. The two quantities are not commensurable and cannot be traded against each other.
- 05
Remove the branch or do not take the bet
Cap the loss, buy the insurance, split the exposure, or decline. Reducing the probability is usually not enough — the branch has to stop being terminal.
Characteristic failure mode
Worked example
A small business considers a contract requiring an upfront outlay equal to eight months of reserve.
- 01Ruin defined: reserve below one month, at which point payroll fails.
- 02Probability the client pays late by more than 90 days: roughly 15%, from prior contracts.
- 03That single branch reaches the threshold.
Result
Expected value is strongly positive and the contract is declined in that form. It is taken with staged payments, which removes the terminal branch rather than reducing its probability.
Where this disagrees with another method
They will disagree, and when they do, risk of ruin wins. Expected value assumes you can play again; that assumption is exactly what ruin removes.
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