Thursday, May 7, 2015

Roll dem dice

I found an article today that described some people testing dice to figure out how random they actually are.  The people writing the article rolled two different d20s made by different manufacturers to see if one manufacturers claims of better randomness were actually warranted.  Unlike many gamers I know they did not use a sample size of four to decide if a die is fair or not - they rolled the dice 10,000 times and recorded the results.  It turns out that the d20s they tested were quite biased, with many numbers showing up 20% too often or too little, which is extraordinarily unlikely in a sample set that large if the die was indeed truly random.  The die with the more grandoise claims to true randomness was generally better distributed except that the number 14 was extremely underrepresented due to a bump on the opposite side of the die.  One would assume that if that bump were shaved off expertly then it would in fact be the better randomization engine.

The simple thing we can take away from this is that cheaply made dice with numbers carved into them are not as random as we would like when rolled by humans.  They *are* loaded.  But they *aren't* loaded in the way people tend to complain about.  The results were scattered about without any particular tendency to high rolling or low rolling.  Neither of the dice were especially good or bad, and they definitely weren't good or bad enough that anyone could have been sure about it without hundreds or thousands of carefully recorded rolls.

Thing is though, we don't actually care very much how good the randomization quality actually is.  People buy dice because they are pretty, feel good, and are easy to read.  I am a numbers geek and still if you offered me the die with bigger claims to true randomness I would turn it down.  It has sharp corners, numbers that are hard to read, and doesn't look as nice.  I am rolling dice in part because I want a random number generator, and in part because I like the experience.  I could use an app to generate much better random numbers and I do not do that - in fact I don't even consider it.

I want to roll dem dice!

There would certainly be a point where a die was simply too unfair for me to be willing to use it.  A die that generated 10% 20s, 0% 1s, and was otherwise fair would be far too loaded for me to be willing to use it, even though it would be to my advantage to do so.  That said, if a die isn't actually really loaded towards being good or bad then I don't much care if all the results are equally likely.

If I wanted perfection I would use an algorithm.  I want to toss sparkly, colourful bits of plastic around and use that to decide my results, and so that is what I do.

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