"Precision Dice and How to Test if a Dice is Fair!" Topic

I recently bought some dice, which looked really cool and as it happens they kept rolling sixes, with an alarming frequency. Now, that would be OK, but as I happen to be playtesting my own rules, this really made me skeptical!

So, I looked into the whole thing and it appears the way common dice are manufactured they can be inherently unfair, due to uneven weight and size presented by each face, plus, the non-precise cube shape, plus the presence of air bubbles. But, how unfair?

Long story short, I got my stats books out, and I run a Chi-test on my usual dice and the new ones. The new ones are really unfair dice – certified – with only 300 rolls per dice! My usual dice have a very low probability of being fair (about 20%), which I would expect to go to 'unfair' if I kept rolling to increase my sample size. They all go to the trash bin!

Then, I bought some dice sold as 'precision' dice. Yes, they are more likely to be fair, probability jumping to 60-90%, but as it happens three out of four tested dice appeared to be rolling high on the same number…So, not so good either, and I am not prepared to repeat rolling till the end of time to find out, or test each single dice (I need 12-24 dice for my new game).

I finally decided to buy some real precision dice, used in professional backgammon. Very expensive too…but precise to 3/10,000 of an inch – they say! I expect them to arrive soon for their turn on the test 'wheel'. Will they be true to their name?

By the way, I used a spreadsheet to generate 1000 numbers simulating a D6 roll. VERY variable results ranging from highly unfair to moderately fair…It appears, as I found out, that these random numbers are actually pseudo-random. Go figure!

There is quite a bit of skepticism on the internet about the issue of being sure of rolling a random number and I just wanted to add my experiences!

PS…I found a very nice spreadsheet that does all the statistics for you in case you want to test your own dice…You can find it here: link

PPS…I also have some certified D6 that constantly roll high sixes!

PPPS…Yes, I know it's a 'die' but I prefer the modern usage of the word.

I bought a load of casino dice and our gaming has reached a higher standard of excitement.

Before rolls were getting silly with constant high numbers but now they are so random you've really no idea what to expect. The only downside is the size of the dice and expense. Wargaming is worth it!

I'd say you have put more work into this than every gamer I have collectively known. I get my D6 dice at the dollar store.

What 79th said: I've used "used" casino dice before and saw NO difference compared to board game dice.

Rocky Russo once referred me to an FBI study that concluded there is no way to obtain consistency in controlling how dice will roll. But I can't point you to the study, as it was not on the Net at the time and I haven't any recollection of how to obtain the study.

The point made is that the variable factors are always too random and numerous to allow for consistent "cheating" dice. If you insist on a single rolling "venue", e.g. "my dice tower, my dice, and only here", then I am confident in saying that your opportunities for gaming comrades will steadily diminish: until you find yourself reduced to solo gaming; even then, you will find ways to "cheat" yourself….

Check this out.
YouTube link

Sorry, but your size sample is too small. This is a case of the Gambler's Fallacy arising again, based on the assumption that dice "can't" roll the same number multiple times in a row. Of course they can; that's entirely how dice work. On a d6, the chance of any given number appearing on a roll is 1 in 6. But guess what; on the next roll, the chance of that number appearing again is 1 in 6, and it keeps being 1 in 6 no matter how many times you roll. And yes, that can produce multiple identical results in repetition. And if you limit your comparison to "rolling high," that is, generating numbers of 4, 5 or 6, then the odds become 1 in 2. Given those odds, three hundred rolls is not enough to determine that dice are "unfair"

OP mentions a percent chance dice are "fair", but how fair is fair? Are we talking about a die that rolls a six 54 times out of 300 instead of 50? 55 times? I'm not sure I'm interested in that degree of "unfair".

You might just want to use a spinner. Or perhaps a d20 numbered 1-6 three times, with a green 0 and 00.

On the other hand, if all this helps you enjoy gaming more, who cares about math?

I highly recommend the book "The Drunkard's Walk: How Randomness Rules Our Lives"

So how much do you want for that Die that roll all 6's?

Here's a write up of a solid mathematical study.

Actually it's 1's that are statistically more common in certain types of cheap dice (Chessex, GW, etc.). Small dice with rounded corners can have a typical high of 29% for rolling a 1. 33% for a very few.

For cheap fairness, big square Yahtzee dice are the way to go.

I don't mind splurging and go for small precision backgammon dice.

link

Can you get me a d20 that does that?

I got some Dwarven Metal dice link and they always seem to roll low. But I still use them, as I love those dice!

Friends, thanks for sharing your thoughts!

I did a normal test, it that all six outcomes were checked, not only the highs and lows. The sample size was more than enough, but certainly it is never enough with statistics!

I was not looking for ways to control the dice or identify how to roll high scores etc…I was looking to see if my dice are fair – and most likely they were not. It does not make much of a difference if you roll one or two dice now and then in a game, but if you roll 12 dice and need sixes, then a load of sixes will certainly not be normal.

Dice can be unfair not only because of the different weight of the material removed to make the pips, but also due to air bubbles in the plastic, the differences in how rounded are the edges, and in the case of D12-D20, how small becomes each face by the rubbing process during polishing.

Anyway, my D6 that roll constantly high are free to anyone who wants to pay postage for them…PM if interested.

John, yes, I tried these too…rather variable results. I got the opaque ones, so it might have been air bubbles in some of them. Too bad because they look really nice!

test them with the water test?

link

link

Casino dice are best.

The dimples in the dice lighten them on one side, causing sixes to be rolled disproportionately, which could either be a good, or a bad thing, depending upon your rules.

Wrt random number generators on a computer:
Of course they're pseudo-random. What do you think the computer does?

BTW, working with random number generators in most of my research (Monte Carlo integration …), I would put more trust in pseudo-random generators for large sample sizes than throwing dice. These RNGs are designed to come up with even distributions …

300 is a relatively low sample size, BTW.
If you only count the sixes, then you have a binomial distribution with probabilities 1/6 and 5/6. Variation on the number of 'successes' (rolling a 6) for 300 tries = sqrt(300*1/6*5/6) ~ 6.5.
How many sixes did you score in your experiment?

Also regarding pseudo-random computer numbers: Not all are equally good/bad. The ones in a spreadsheet are probably the simplest/worst kind. For a die roller at least try to find one that gathers randomness from the system (mouse movements, data written to disk, current time in nanoseconds… combine lots of non-random information and you get quite random results, like /dev/random in Linux; not sure what it is called on Windows). There is also truly random hardware, and I'm told this is becoming standard even in normal CPUs these days.

Also, something scary about computer randomness: I read an article some years ago about game AI describing how to make pseudo-random generators that looks more random. Because if you generate numbers like 1111 or 1212 or 1234 gamers will think the random number generator is broken. So you implement a filter that makes sure the numbers _look_ more random (discard anything that looks too regular). Which of course means they are in fact less random, but players are happier.

Something to think about when looking at a any digital game or die-roller. If it looks random to you, never any recognizable patterns etc, maybe it is because it is deliberately not random. Real randomness typically do produce lots of results that a human brain will think is not random.

I have counted all results (1 to 6) and not only sixes!

If the dice randomness of die rolling bothers people, pick a different system: I've experimented with tokens (in my case Dominos) bulled from a bag by players generating random numbers of one to six.

With Dominos you have to have a mechanism of determining how you achieve a single dice roll (each domino has two numbers on it, of course). But that's quite easy. (I am working on a set of rules called "The Domino Effect"…)

Dominos can also be had with bigger number variations than 1 to 6 (for example a 1 – 9 link )

And there is always the blank in there as well for a laugh!

Actually, I'm not bothered much by the random stuff. I figure it all evens out in the end.

But it was just a suggestion. :)

John T

test them with the water test

Those which float, are witch dice: burn them!
Those which are drowned, were innocent.

I've always wanted to get into using cancelled casino dice, but as was mentioned they generally have a small circle stamped into one side when they are retired from a casino. To me this always seems like it'd unbalance them?

I also have seen some sharper edged dice (as compared to the unreasonable round edged Chessex stuff) but the numbers aren't painted, so that's a turn off.

Play rules where not all roll tests are high = good