Dice Rolling Machine

  

D20 Dice Roller. Rolls a D20 die. Lets you roll multiple dice like 2 D20s, or 3 D20s. Add, remove or set numbers of dice to roll. Combine with other types of dice (like D18 and D22) to throw and make a custom dice roll. Roll the dice multiple times. You can choose to see only the last roll of dice. Display sum/total of the dice thrown.

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The new D&D set includes cards that have players roll 20-sided dice. The only 20-sided dice that Magic players frequently carry with them are spindown dice, where the numbers count up sequentially on adjacent sides. (Although notably the dice for this prerelease in particular are not spindowns.) So the age-old debate around whether it's ok to roll those for a random result has finally become relevant to Magic. There are four angles from which I've seen people claim this is a problem, which I'll go though one at a time.

'Spindowns aren't designed for rolling, so their manufacturing process doesn't try to make them fair.'

Dice Rolling Machine

This does not seem to be true. Most dice designed for casual gaming use a pretty lazy manufacturing process and aren't completely fair. (The dice being marketed in that video aren't much better.) You'll notice if you look at casino dice that they don't have physical holes in the sides that could lead to weighting differences, don't have rounded edges that reduce bouncing, aren't made out of multiple colors of plastic that could be different densities, and are transparent to ensure that there are no air bubbles. The dice you buy in your LGS aren't like that, and they're already slightly unfair even if they're not spindowns.

'All the high numbers are at one end and all the low numbers are at the other, so any accidental imperfections are more likely to result in a consistent bias towards one end of the scale.'

This is true, but there are some mitigating factors.

The first is that any bias in the results is very small; just fractions of a percent. While in theory this is still a problem, in practice it's significantly less impactful than the biases you get from improper shuffling, which is far more common.

Virtual dice roller for kids

Secondly, this bias is going to be random for each die. One die might be more likely to land on high numbers, and one die might be more likely to land on low numbers. As long as you're just picking a random die and using it, these biases will cancel out and you won't be at any advantage or disadvantage. The only way this is problematic is if a player is rolling a die thousands of times to determine what it's biased towards, and then choosing to use dice that are biased towards a specific number.

'Players can cheat by melting it.'

This seems to be mostly an urban legend. Plenty of people online claim that putting a die in the microwave oven or normal oven will affect its center of balance, but those who actually try it seem to meet with limited success. It'll likely depend on the type of die, since different kinds of plastic have different melting profiles. If someone did manage to use this method to make a die that's both significantly weighted while still looking indistinguishable from a regular one I wouldn't be that surprised, but I don't think it'll be trivial to get it right.

This is largely irrelevant, because people can just buy loaded or trick dice online. The distribution of numbers on a spindown will make a loaded one a bit more consistent, but you can't really trust non-spindown D20s either.

'Players can cheat more easily by rolling it in a specific way.'

'Trick shots' with dice where they roll in a predetermined way are possible, and spindowns make them easier since you only need to end in a specific region rather than one exact face. This can be mitigated by making sure that the die bounces around enough that enough chaos is introduced and the thrower can't control for a certain outcome. Casinos do this with a pointy backboard that the dice have to bounce off of in order for the roll to be valid. As long as a spindown is not thrown from a specific orientation and rolls/bounces a significant distance on the table, they're not going to succeed in achieving a non-random result.

Here is an example of me rolling a spindown in an advantageous manner. And here's someone else doing it a bit better. Could this fool someone who isn't paying attention? Definitely. But anyone doing this consistently with different people is going to get noticed pretty fast, and it'll to be nearly impossible to argue that they didn't know what they were doing.

Testing

Gamers are very prone to superstitions around dice (and to a lesser extent, randomness in general), and will sometimes roll a die many times in order to see if it's fair. Unfortunately even a few hundred rolls is generally insufficient to find small biases; some numbers will come up more often than others in any finite sample. (Here's an example of someone erroneously concluding that spindowns are actually more fair because they did far too few tests; their results were effectively just random noise.) Floating a die in salt water is another test people do, which is good at detecting density imbalances, but useless for anything else like shape asymmetries.

In order to really tell if a die is fair, it needs to be rolled several thousand or more times, like with an automated dice-rolling machine. That said, some amount of useful data can be gotten with a smaller number of trials, as described here. Keep in mind that most imperfections are per die, not per manufacturing run or per company, so just because one die from a box is fair or seems to have a bias doesn't mean the others will be the same.

Dice

(Testing a bunch of dice, finding one that rolls higher numbers more often, and choosing to use that one is obviously cheating, regardless of whether it's a spindown or not.)

Conclusion

Non-malicious differences between spindowns and regular D20s are irrelevant; if you're confident no one is cheating, there's effectively no difference. It is easier to cheat with spindowns, either by rolling them in a careful way or using one that's more likely to roll higher. The first cheat is somewhat easy to catch, but could fool a decent number of players. The second cheat takes a fair amount of effort to set up and can be done with regular D20s almost as easily.

It is in general better to use systems that make cheating harder. However, regular D20s are less accessible for most Magic players, and I'm not sure if forcing everyone to go and buy non-spindown dice is worth it just to offset such low-value potential cheats. If you're really concerned about cheating you shouldn't be using dice at all; use something like this instead. (Most phone apps like MTG Familiar also have a dice roller.) I'd encourage people to default to non-spindowns when they have one on hand, but personally I wouldn't have any problem with someone rolling a spindown die in my games for now.

Do note that in sanctioned tournaments, spindown dice are prohibited by the Magic Tournament Rules. With regards to casual play, I'd like to to quote an 8 year old Reddit post:

Friends, do everything in your power to avoid playing with anyone that has a passionate opinion about whether or not to roll a spindown die in your fantasy card game. Your life will be so much more enjoyable if you don't seek out conflict over something this trivial.

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We've all been there: you're at a pick-up roleplaying group at your local game shop, and that noisy munchkin to your right—who is playing some kind of half-dragon triple-multiclassed character from an out-of-print rulebook that he found a PDF of online—seems to roll more than his fair share of natural 20s. Okay, maybe we haven't all been there, but let me tell you: it's annoying when someone appears to be awfully lucky with their rolls.

The issue is slightly less pronounced with board games, where everyone tends to use the same pool of dice, but having dice regularly come up high or low can obviously affect how the game plays out.

Putting aside cases of intentional cheating, did you know that dice—particularly polyhedral dice like d20 or d8—are almost universally unbalanced? Some are more balanced than others, but as you would expect from mass-produced objects, small flaws in manufacturing and materials nearly always push each individual die either above or below the expected average roll.

Rolling Dice App

The question is, if we accept that no die will be completely fair, how do we at least make sure that the dice we're rolling aren't so unbalanced as to be unfair?

The ol' golf ball test

Dice Rolling Machine

The simplest though not most accurate method of testing the balance of your dice is to float them in a glass of salted water. Depending on the die, you may have to add a lot of salt to achieve flotation. Place the die in the water, note which side of the die faces upwards, and then give it a flick.

For reasonably balanced dice, you should see a good variety of numbers facing upwards. For badly balanced dice, you'll probably see the same one or two faces regularly. Throw those bad dice out.

The, er, automatic roller and computer vision method

And then, of course, if you're the rare breed of roleplayer-cum-DIY-maker supernerd, you could create an automated rolling system that rolls your dice thousands of times, and then from those results work out the standard deviation for the perfect average roll.

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That's what Mark Fickett did, and you should read his superb (and very long) write-up of what he found out. I will summarise his setup and results here.

The die rolling machine is essentially a servo attached to a small ice cream tub, hooked up to an Arduino. The servo fires, the die is rolled, and then the Arduino triggers a camera overhead that takes a photo. Some computer vision software locates the die in the photo and extracts the number on the face of the die. The number is recorded, and then the process begins again, rolling the die hundreds or thousands of times until an adequate sample size has been reached.

Fickett used his machine to analyse a bunch of d20 made by popular brands—Chessex, Wiz, Game Science, etc.—and reported on his findings.

For the most part, the results were a mixed bag. The Chessex dice were all reasonably fair in that the rolls averaged about 10.5 (the perfect average roll on a d20), but the results were highly variable between each die (i.e. each die favoured different numbers, but the averaged total was close to 10.5). Wiz dice were similar: mostly fair, but with variable results.

In both cases, the Wiz and Chessex dice tended towards symmetrical distributions: so, if 20 came up a lot, 1 was also quite common on that same die, keeping the average at around 10.5. This is most likely down to the construction of the die (two halves stuck together) and the arrangement of the numbers (opposite sides always add up to 21).

Game Science dice, which have very sharp edges, are promoted by the company as being especially fair. In testing, one die had a very fair standard deviation of 0.07, but another had a not-especially-fair deviation of 0.12 (in fact, that die turned in an average roll value of 10.67, making it one of the 'luckiest' of the bunch).

Crystal Caste, which sells some rather unusually shaped dice (but no one in the UK seems to import them), had the worst fairness, with high deviations and low averages. (One die averaged just 10.18 and '1' was the most likely roll. If you get a lot of critical failures while roleplaying, maybe you've been using a Crystal Caste die?)

Here's a graph tallying up the fairness of all the dice tested. The red line shows how close the dice got to the ideal average (10.5); the blue bars show the deviation from perfectly fair roll frequency distribution (i.e. each face turns up roughly the same number of times).

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Dice Rolling Machine Cheat

Correlation between geometry and roll frequency

Fickett also attempted to correlate the geometry of the die (specifically the distance between opposite sides of the die) and the observed frequency of rolled numbers. In some cases there was a correlation, with a longer distance resulting in a higher frequency for those two sides; in other cases, there was no correlation at all. This is likely because there can be other factors at play that aren't so easily measurable, such as any imperfections of the material inside the die.

One weakness of Fickett's analysis is that he only rolled plastic dice, because the automated rolling system probably wouldn't be strong enough to withstand thousands of metal die rolls. He also admits that the dice might behave differently when rolled in a different context (in a larger/smaller bucket, across a table top, etc).

Similar dice-fairness analyses have been performed by other people, too. The Awesome Dice Blog compared Chessex and Game Science d20s and found that, while Game Science dice were indeed quite fair, they rolled significantly fewer 14s (a finding that is somewhat backed up by Fickett's numbers). 1000d4 performed a huge analysis (by hand!) that found Game Science dice to be the most consistent, and Crystal Caste dice came out rather better than in Fickett's tests.

Ultimately, while some brands seem to be fairer (i.e. closer to an average of 10.5) than others, there is still lots of intra-brand variability (i.e. two dice from the same maker can roll a very different set of numbers).

One solution, if you really want to make sure that your dice rolls are fair, would be to analyse the characteristics of the dice you actually own. A more realistic solution, though, would be to buy a big bag of same-brand dice and force everyone to use dice from the same pool. And if anyone wants to bring their own dice to the gaming table, throw them into a glass of salt water first.

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