Am I the only one not seeing the point or relevance of “Thomas Lumley”'s graph ?
Well, given that I posted exactly such thing in this thread, yes, I do. But, I have no idea if that pattern I see is statistical pareidolia. I know that humans are very bad about intuitively estimating what randomness looks like.
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Just how much juice are you putting through the electromagnet under that table?
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To check if dice are properly balanced you need a Dice Balancing Caliper
This is what all casino’s used to use along with those serious about their dice in a Crap game.
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It improves the table! (a pallet table I made myself)
I figure it’s like the kind of table you’d “find” such dice on. Soft wood, rough, varnished, medievaley.
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People pay extra for weathered tables… Hmm…these metal dice could be a way to trick gamers into doing your Artisanal Weathered Table business’s peening for you. 
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The sign of a true aficionado. I hope you posted the making-of-the-table video
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I didn’t, but should have!
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Fair enough. Distressing, but in a good way.
You also need a lot more statisticians doing the analysis. There’s a sufficiently high chance that any individual statistician will make mistakes either in choosing a statistical test and its parameters, or in applying it. To control for this, you need a sufficiently large sample size. I’d recommend getting at least 1000 statisticians to do the analysis independently.
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You’ll need to specify the p value in advance. Can’t have you P-Hacking the P-Hackers…
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So, who’s going to start the GoFundMe for a dice rolling bot?
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Someone who does stats professionally? what are the odds of that??!?
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And a locksmith, for when Rob locks the bot’s results in a safe…
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Each face has different amount of material removed to create a unique number. There is a weight positive bias on #1 face etc…
I had a look at this paper. It’s predicting that a realistic dice has two asymmetry parameters, α and β. The weight imbalance caused by cutting out material to make the pips is modelled by α, and the tendency for the dice to be manufactured as imperfect cubes, either oblate or prolate along a particular axis (In Rob’s case, both the dice are asymmetric on the 1-6 axis as compared to the 3-4 and 5-2 axes) is modelled by β.
The probability P(j) for the die rolling a value j is then:
So for Rob’s dice, I find that α1 and β1 for die 1, and α2 and β2 for die 2 are:
It’s quite surprising how the asymmetry is visible: If you assume the 1-6 axis is the asymmetry, the χ2 = 0.546, whereas if you put the asymmetry axis in δj along 2-5 or 3-4, I find χ2 > 4.
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“Rough metal dice, fresh off the forge!”
Sure, they WERE forged, but you threw them.
Now they’re cast.
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As someone who actually remembers statistics lectures, I’m glad that statistical significance has already been brought up.
For those who aren’t following, the theoretical distribution of the results over many observations (rolls) of two unbiased six-sided dice should approximate a Normal distribution (the bell curve), with the mean around 7.
In the case that our experimental results give us something that doesn’t quite look like a perfect Normal distribution, the p-value is a measure of the probability that this difference is actually still consistent with the expected behaviour we would see from dice following a Normal distribution.
e.g. we roll a die twice. We get two sixes. Our distribution is not a curve. It is just 100% sixes. Does that mean that our die is biased? No. We have not rolled enough times to tell.
What’s the p-value of these two observations - i.e. the probability that we could get two sixes in a row when rolling a FAIR die? You intuitively know the answer: pretty high. Therefore this is not a statistically significant result, and we can’t say that the results indicate the die is unfair.
The reason I’m trying to explain this is that I believe many people are scared off statistics by the math (chi-squared? That’s a great name for a concept), but I really enjoy the logic and basic principles behind it, and it is useful to apply a statistical mindset when examining data.
This helps, particularly when statistics is often applied improperly to interpret data to help further agendas.
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Incidentally, in my circle of board-gaming friends, I am known for consistently making extremely poor dice rolls, compared to the other players.
Probability calculations assume that there are no other factors affecting the theoretically perfect die and that each roll is not affected by any previous rolls. This is not necessarily the case, depending on how the dice are handled.
There was a study which showed that dropped toast is more likely to end up buttered-side down on the floor, not because of the butter, but purely due to the typical height that it is dropped from, and the mean number of rotations it makes on the way to the floor.
I suspect some repeatable factor is similarly influencing my dice rolls. You would have to take care that it isn’t influencing your data as well.
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