Other Software > Developer's Corner
Dice analyzer machine project
mouser:
So, this die is possibly fair?
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I'm writing a little paper on this project and i will discuss the nature of these statistics a little bit. These probabilistic things can be tricky to wrap your head around.
No matter what experiment you do, its ALWAYS going to be possible that the results came from a fair (or unfair) die. The best you can do is say how unlikely it would be to get results like these if the die was fair.
mouser:
So one aspect of the statistics im very wobbly on is the relation between the chisquared statistic and the confidence intervals for the histogram bars.
The chi-squared is evaluating how likely the complete set of results came from a fair die. For a fair die, the frequency counts from all bins (die faces) should be roughly equal.
The histogram confidence intervals are evaluating each bin independently according to how likely the counts would be in that range.
Im not sure how to talk about how these statistics differ in their estimates..
The chi-squared suggests that this distribution wouldn't be surprising to see from a fair die, while the histogram confidence intervals seem to suggest that it would be.. I don't know if that means I'm calculating something wrong or misusing some statistic..
mouser:
Another kind of statistic you might want to look at when analyzing a die is whether there are patterns between two successive rolls (e.g. do 6's always follow 1s?).
For that we can use the same statistics as shown above when counting frequencies, but looking at a separate histogram for each die face, counting the subsequent die face frequencies.
And for pure visuals, a heatmap can help show unusually high/low frequencies of certain previous-subsequent die roll pairings:
Note: This chart has too little data to be truly informative-- it's just meant for illustrative purposes.
mouser:
Just a note that after some playing with raspberry pi i decided also to experiment with Arduino, and wired up the die roller to a relay and an arduino and now have the pc talking with the arduino and automatically engaging the die roller. :up:
I try to stay away from hardware because i get too frustrated too quickly, but i must admit it's fun to manipulate physical mechanisms through code.
mouser:
After 2000+ rolls looks like we can be pretty confident that this D6 die i've been testing with has a real bias, and shouldn't be used in any tournaments*:
* Technically speaking, the bias could be caused either by an unfair die or an insufficiently randomizing rolling machine.
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