In Nature Magazine this month, and then republished by Scientific American, David Spiegelhalter argues that probability probably doesn’t exist.
I’m no maths wiz, but I found it a fascinating paper. It does get into the quantum world, but one argument is that probability is subjective. Here’s an example,
If someone tosses a coin, what’s the chance of it landing head-up? It’s 50/50, right? If someone asks you before the coin toss, and you say 50/50, the coin is tossed and covered up – is it still 50/50?
If the person tossing the coin had a ready supply of coins with heads on both sides is the probability still 50/50?
If the person tossing the coin had a ready supply of coins with heads on both sides and was trying to rip you off, is the probability still 50/50?
As we can see, many factors affect probability, and we’ll get back to those for dice.
The article also cites British Intelligence. The Ministry of Defense has official rules for word use. If an MI5 agent says something is “Probable,” there’s a 55% to 75% chance of it being so. “Highly Unlikely” means a 10% to 20% chance.
Are dice random?
The probability of rolling 7 on 2d6 is 16.67%. It’s the most likely outcome. Our MI5 agent would classify that as “Highly Unlikely”. In fact, no one total on 2d6 is probable at all… and we’re back into the dangers of probability and the language around it.
However, dice don’t even get that far. In a 2012 paper called The three-dimensional dynamics of the die throw, it’s shown that how the dice are thrown and what they are thrown against determine the outcome.
Professor Persi Diaconis at Stanford University explained this to Numberphile on YouTube years ago.
The 2012 paper by M. Kapitaniak, J. Strzalko, J. Grabski and T. Kapitaniak says;
The die throw is neither random nor chaotic. From the point of view of dynamical system theory, the result of the die throw is predictable.”
In practice, it just takes a tiny change such as the position of your hand or the face-up value of the dice and a repeated throw of the die will get a different result. This is an academic predictability and not a practical one.
It does mean that the quality of your dice makes a difference. Also, back in 2012, Geek Native dug into this and asked Are RPG dice good enough quality to be truly random?.
Supporting the blog was an old video of Colonel Louis Zocchi, the founder of GameScience, getting into the topic.
Our 2012 post also had the results of 10,000d20 by Awesome Dice, who noticed that both Chessex d20 and GameScience Precision d20 were less likely to roll 14 than any other number.
Conclusion
Dice aren’t random. If you were perfect at being able to recreate the conditions of one die throw to another, then you would be able to recreate the throw.
On top of it all, using terms like ‘probably’ to get into this is a rabbit hole of danger and dead ends.
Join (or start) the healthy debate. Share your observations below.
