Monday, March 26, 2012

Philosophizing About Probability

Over at Digital Orc he posted a video arguing about the distinction between "experimental" probability versus "theoretical" probability.  I disagree with his definitions.  Probability is always theoretical.  What he calls an "experimental" probability is better be described as an estimate of the probability subject to an experimental uncertainty.  From the rules of error propagation, it is actually possible to derive a formula for the uncertainty associated with one's estimation of a probability. 

Exactly how this distinction would be valuable to gamers is unclear to me, except maybe for assessing the fairness of one's dice.  Even then, though, to really do it properly you'd need to invoke Bayes theorem and calculate the probability that the dice are fair given that you rolled some number of successes.

What's valuable to gamers isn't a largely philosophical discussion of the nature of probability.  What's more useful is concrete tactical advice based on mathematical analysis.  That's more difficult, or at least more tedious.  Let's face it, multiplying all the little probabilities together to make the probability tree for a combat round is mind numbingly dull.  I still haven't filled out that darned transition matrix.  Maybe I should just give up and write the Monte Carlo.  Or maybe I should write a program for populating the matrix.  Huuuum...

7 comments:

  1. what is scientific notation
    Scientific Notation include in the mathematics course. In the world of science some time we deal with numbers which are very small and those which are very large. In some branches of science large numbers while in others very small numbers are used.

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  2. Probability Sampling
    Define Probability sampling, what is probability sampling? , types of Probability sampling,
    http://www.infoaw.com/article.php?articleId=946

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  3. Fairness of dice reminds me of http://deltasdnd.blogspot.com/2009/02/testing-balanced-die.html

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  4. My point was to distinguish the mathematical summation of many rolls versus few rolls.

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  5. Also, they aren't my definitions. I'm citing Holt Pre-Algebra Mathematics text.

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    Replies
    1. Fair enough. In truth, the definition of probability itself is a subject of considerable controversy in mathematics, made muddy by Bayesians.

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