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The last of my troubleshooting rules is #5: What don’t you know?
This is shorthand for a process, or an internal conversation, that goes like this: read more...
Written February 24, 2014, as I walked to work. A goose was flying overhead. My uncle was dying, and I was thinking about my memories of him, and about how mysterious memory is, and how we create them for each other, and what going away really means. What’s the difference between a memory, a dream, a plan, and the present moment? Sounds like the beginning of a Buddhist joke. read more...
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...