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My previous post on fair dice focused on some intuitive ideas about die fairness, and the beginnings of a mathematical approach. Now I’d like to describe the tests my die roller does. These are what I’ve settled on so far as a way to get some numbers to describe and compare the fairness of different dice.
First off, there’s the chi-squared goodness-of-fit test. This is a test that looks at the deviations in the histogram to get a total number (the chi-squared statistic) that characterizes how far the histogram deviates from ideal. You can also compare the result statistic to a mathematically-determined threshold that will give you a confidence value for the test; a 95% confidence is often chosen.
So hey, that’s great! We can reduce the whole set of results and its histogram to a single number for a given die, and then find out whether that die is fair or not with 95% confidence! Super! Right? read more...
If you like games, you’ve probably played games with dice, and you’ve probably thought about fair and unfair dice.
You might have seen “trick dice” advertised in the back of a comic book, for instance, or you might have flipped a string of heads on a coin and thought your way into the Gambler’s Fallacy or an instinctive Bayesian sense that the coin is biased towards heads.
If you have studied statistics, you’ve encountered more mathematical ways to treat these human observational instinct read more...
I read Scientific American religiously as a child. Sometime around 1980, in Martin Gardner’s “Mathematical Games” column, he reprinted a woodcut from an 1893 book called Puzzles Old And New by one Professor Hoffman. The illustration showed the pieces and assembled form of what Hoffman called the “Nut” puzzle, and Gardner explained that there were many variations of this puzzle.
I was fascinated, and wanted to see how it worked. So I made one out of balsa wood, and solved it. read more...
Clara and I wrote and recorded this for the Fall Creek Elementary School Talent Show, and she lip synced it with friends Ava, Clare, Grace, Nuala, and Tivona. It's a parody of "Dynamite" by Taio Cruz - see the (child-inappropriate) video on YouTube. I think it has to do with the similarities between the two most virulent parasites of childhood: pediculosis and Top 40 radio earworms.