Lake Wobegon Dice

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2021-08-16 20:00:08

Garrison Keillor’s fictional Lake Wobegon is a place “where all the children are above average.” Donald Knuth alluded to this in his exercise regarding “Lake Wobegon Dice,” a set of dice where the roll of each die is (probably) above average.

To see this, list out all the possible rolls where each die is above average. The triples show the value of A, B, and C in that order. We have A above average if the rolls are

It seems paradoxical for three different dice to each have a probability better than 1/2 of being above average. The resolution is that the three events

I ran across this in The Art of Computer Programming, Volume 4, Pre-fascicle 5A, Exercise 3. Fascicle 5 has since been published, but I don’t have a copy. I don’t know whether this exercise made it into the published version. If it did, the page number may have changed.

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