“Sort” of! 
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The 1 is usually opposite the 6, a 6 bias is also to a lesser extent a 1 bias.
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Word!
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Now Rob can say, “No, let’s use my Forged Steel Game Breaker Dice. Sure, they will tear up your game board, but they are Genuine Renaissance Faire Quality™ and I’ve run a Chi-Square test on them, so we know they are (possibly) fair!”
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I shall take this opportunity to plug Sublime Text (https://www.sublimetext.com/) as my text editor of choice, that let me pull apart, sort, and put back together that list.
Hardly an amazing task, but it’s a wonderful editor.
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Cool, though I wish it would let me search and replace special characters, such as tabs and CRs in formatted text, handy for fixing malformed PDF text to quote in BBS. I suppose I could do so in an HTML editor that lets me paste formatted text and then search and replace in HTML view or something…
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If you can describe them in regex (I can’t think how to do CRs off the top of my head, but I’m very rusty), you should be able to search for them. There’s a toggle when searching.
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Cool, thanks. My Regex skilz are at level “I know Regex exists” 
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There’s no way to know how fair they are based on the data provided.
Rolling them and tallying the results gives you a probability estimate of how fair they are, but to actually know you need to call in the high-precision measuring gear and some physicists.
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Not really. Rolling them is the true measure of whether they roll fair. In the end, the only thing that matters is the results, not whether they are perfectly square. Testing the actual results might seem more tedious than trying to use metrology to measure the shape of the dice to to the nano-meter, but measuring the dice is just a proxy for whether they should roll fair, not that they actually do.
To test fairness Rob just needs more trials. 
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Rolling them tells you if they were apparently fair in the past. It doesn’t say anything definitive about the future.
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The same would be equally true for physical measurements. The only variable is whether the dice are deforming from use.
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Physical measurements will give you a solid future prediction of the probability distribution rather than an estimate of the most likely distribution.
Get your measurements good enough, and all physical dice are biased to some degree. Measurement and physics allows you to establish the degree and direction of bias (within the limitation of your measurement resolution).
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I suppose since I’m not an engineer I tend to give experimental results a higher degree of reliance because the results are the results, not the prediction based off of measurements entered into a model which may be imperfect. With something as simple a die, I suppose the model may be near perfect, and yet if there is a bubble in the casting and your measurements only measure dimensions, you’ll miss it. Or if you don’t measure the squareness of the edges. Or if you don’t check that the elasticity is the same on all 6 sides. Or measure the stickiness of the sides. Or the smoothness. The statistical results show the actual results, not the the results of a model.
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Because I’m not an engineer (neuroscientist/psychopharmacologist), I know that you should never put too much faith in prior results.
Rats are sneaky fuckers [1].
[1] And inferential statistics, as they are currently used in the biological sciences, are dodgy as all hell.
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Or models
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@beschizza If you lump the results from both sets of dice together (which is reasonable if you assume they’re manufactured in the same way, and so share the same bias) and run the chi-squared test on all 600 numbers, it’s claiming that the chance that a pair of fair dice would randomly generate biased results at least as extreme as you found is only 1.8%
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You probably need more rolls to be sure.
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The dice have been hacked by Russians!
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Hmm…can you just sum the data from different trials like that for a Chi-square test? I have no idea. I would say that hand forged dice cannot be assumed to share the same bias, though. Yet, the numbers do seem to suggest that for both dies the sides with fewer hollow divots (die spots) are a lot more likely land on the bottom as one might expect if un-equal weight distribution from the die spots were to have a significant effect on the outcome, so the chi-square tests for the individual dies surprised me when they came up as within probability. Dunno.
I know statistics can be non-intuitive. So, I’m not sure what to think.
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