Dutch Book Theorem

The Dutch Book Theorem states that if a person's betting odds do not align with the true probabilities of events, a clever bettor can construct a series of bets that guarantees a profit regardless of the outcome. This means inconsistent or irrational odds expose you to a guaranteed loss—similar to being “tested” by a fair bookmaker. In essence, rational belief or probability assessments should be coherent; otherwise, they open you up to certain exploitation. The theorem highlights the importance of maintaining logically consistent expectations to avoid guaranteed losses in betting or decision-making scenarios.