It's always nagged me that statistical problems are scoped so small. Surely in saying there's 6 outcomes on a dice you'd obfuscated the billions of interactions between atoms and input possibilities in doing so. Thrower A and thrower B will undoubtedly throw slightly different which might actually constraint the outcomes and skew the 1 in 6 percentages?

It's similar to me to condensing 30 characters to 5 via an algorithm. You can go one direction but not the other and if your model was centered around the resulting 5 it doesn't really reflect what's actually happening which may skew the probabilities quite a bit. e.g. if the algorithm was "if first letter is not q, then first letter in output is q". If you were saying each has an equal percentage of occurring it'd be flat out wrong.

* I am not a statistician and have no idea what I'm talking about