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Try a de Finetti game on your law firm that estimates odds of success for a lawsuit

When embroiled in a law suit, many times inside lawyers ask their litigation counsel: “What are our chances?” Define successful outcome as you will, they want the partner to give the odds. The experienced and wise litigation partner replies, reluctantly, “Seventy percent.” That estimate is a subjective probability, according to mathematicians. It estimates an outcome of a single event, as compared to an outcome from a series of similar events that could be simulated like coin tosses.

A neat idea follow-up question comes from Keith Devlin, The Unfinished Game: Pascal, Fermat, and the Seventeenth Century Letter that Made the World Modern (Basic Books 2008) at 162, as originally proposed by an Italian mathematician, Bruno de Finetti.

Offer the partner a deal based on a thought experiment. Imagine a jar containing 100 balls, 70 of them red (since the estimate was 70% likelihood of a successful resolution), 30 black. Give her a choice. Draw one ball from the jar and if it’s red, the law department will pay the firm $250,000 (or some substantial amount). If the resolution of the case is not a success – as defined in advance and represented by a black ball – the firm rebates $250,000. The estimate was legitimate and confident if the partner agrees to the game; she will modify her estimate if not. A de Finetti test ultimately establishes a correspondence between subjective possibility and frequentist possibility.