Actuarially fair odds are odds or premiums set equal to the expected loss or expected payout, with no extra margin for expenses, capital, or profit.
The expected-value benchmark
If an event occurs with probability (p) and pays (X) when it occurs, the actuarially fair price is:
$$ \text{Fair price} = pX $$
In insurance language, if a loss of size (L) occurs with probability (p), the actuarially fair premium is (pL).
Why real-world prices differ
Actual insurance premiums and betting odds usually include:
- administrative expenses,
- capital costs and solvency buffers,
- compensation for risk,
- pricing effects from market power and asymmetric information.
That is why actuarially fair odds are mainly a benchmark for analysis rather than the final market quote.
Why economists care
This benchmark separates the pure expected-loss component from the markup created by risk aversion, adverse selection, and institutions. It is useful in insurance economics, gambling markets, and any setting where probabilities must be converted into prices.