Let's say we have developed our skills so well that we can bid game-making boards with 90% accuracy.  That is, if we bid game, there's a 90% chance it will make; if we don't bid game, there's a 10% chance it will make anyway.  Pretty good.

Now let's bid 10,000 boards that we previously examined and know that 90% will make.  When we bid game, we put that board in pile A, "Boards we feel will make game."  When we don't bid game we put them in a different pile B, "Boards we feel will not make game."

What percentage of the boards in pile B, "Boards we feel will not make game," actually will make game, on average? [This is an example of Bayes' rule, named after Rev. Thomas Bayes. Thomas Bayes, (c. 1702 – April 17, 1761) was a mathematician and Presbyterian minister.]

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