I have been tossing around this idea for some time now, but tonight seemed like the perfect time for something goofy after my last quasi-serious post about errata and how it affects the relationship between players of *Dungeons & Dragons 4th Edition* and the game itself. Below, I’m going to spend a good chunk of space tackling a “problem” that the majority of gamers, myself included, deal with on a consistent basis.

**Our dice suck.**

When I started playing D&D again a couple of years ago, I bought a set of dice that were black and orange. Those are the colors of my favorite ice hockey team, and orange is my favorite color. But then I wanted to diversify my dice collection, and since 4e has multiple points when multiple die are needed for a roll, I somehow justified buying four more sets. I play a Dragonborn Rogue and my green/copper dice seem to be a perfect fit for the character, and they have seemingly treated me well. I have another set of grey/orange dice that should be my favorite, but they are not.

Those grey/orange polyhedral pieces of plastic are forged from a source of unholy energy, and the d20 from that set was banished from any responsibilities long ago. I swear it was cursed, and the d20 from that set *loved* to roll numbers less than 5. I set it aside whenever I play, and hope the taint doesn’t rub off on my other dice.

But I’m a rational human being and realize that die rolls are random. I’m sure I’m just having a selective bias in my recall of good and bad rolls with the die. Any d20 will land on any given number 5% of the time. It’s simple math, but if you’re like me – you don’t believe the math. The math is **bullshit**. Certain dice are made to torment you mind, poison your soul and shatter your dreams. You and I know this to be *true*.

I would like the grey/orange die to “work” for me and since I’m an educated person, I decided to give the d20 from this set another a few weeks ago. Surely I’m acting like a fool and the die is just like any other d20 rolling around out there. We come to the first encounter against an Djinn on a mountain-side path, and I decide to spend a Daily Power and charge with a Handspring Assault. I push aside my self-doubt and grab the grey/orange die, and roll a . . .

2.

A f**king 2! Are you kidding me? As Wil Wheaton would say, “You can go right in the fuck off bag.”

I was pissed, and needless to say, I didn’t use the die again the rest of the night. I recently wrote an article about cheating in roleplaying games, and believe our relationship with our dice are likely one of the main contributing factors!

I realize the whole ordeal is in my head, but I decided to do something about it rather than stew on it any longer. I decided to run an experiment.

**Method**

I took my favorite d20 – a green/copper die – and the aforementioned d20 of scorn – a grey/orange die – and rolled them 200 times next to each other. If one or the other die fell off the table, then I picked up both dies and rolled again. (I’m perfectly aware that this is absurd.)

I recorded the die roll in an Excel Spreadsheet in two columns, one for the Grey die and one for the Green die. After the 200 rolls were entered into Excel, I ran some basic statistics to find out if the difference in the d20s was only in my head or a reality.

**Results**

The first 10 rolls showed exactly what I thought they would show. The green die crushed the grey die. The image to the right shows the rolls for both die. For example, on the first roll of the study both d20s resulted in a 9. The next roll resulted in a grey 9 and a green 20 (boo-yah!). The average value for the 10 rolls for the grey d20 was 7.4 but 12.0 for the green d20.

I thought to myself, Wow, I might not be crazy after all. Maybe the grey d20 really is a godforsaken chuck of soul-crushing darkness. I continued with the next 190 rolls.

The next graph shows the frequency of for the grey and green d20 with a given value out of the 200 rolls. For example, the grey d20 resulted in a value of “1” 12 times during the 200 rolls. The green d20 resulted in a value of “1” seven times during the 200 rolls.

A few things jump out from the graph. First, both dies seem to enjoy the number 13, as they both landed on 13 more often than any other number in the 200 rolls. That is simply creepy, and the less speculated about this result the better! The green d20 rolled double the amount of 20s compared to the grey die, while the grey die had almost double the amount of 1s compared to the green die. The natural 20s and 1s are the rolls that stand out the most to us, so this tiny piece of evidence suggests that maybe I’m not crazy.

Continuing forward, I wanted to isolate what I consider “good rolls,” rolls of 15 or greater. The chart below shows the same information but without the information for rolls of 1 through 14.

My hypothesis here gets shot to hell, as the grey die landed on a “good roll” 58 times out of 200 compared to 55 times for the green die. While the green die rolled more 20s, it rolled fewer 15s and 18s. Amazingly, the dice rolled the same number of 16s, 17s and 19s during the 200 rolls.

I went back to the data and examined the rolls as if they were opposing each other. On each roll, which die “won” or had the higher value. Since I rolled both die at the same time, I was able to go back and calculate this information. The results are below.

Of the 200 rolls, there were 7 (3%) ties. The grey die result was higher than the green die result 89 (45%) times, while the green die result was higher than the grey die result 104 (55%) times. The data here indicate that the green die performed better more often than the grey. But with only 200 opposed rolls, the difference is non-significant given the rest of the data.

Finally, I investigated the averages. I already discussed the first 10 rolls, but I examined the first 100 rolls, the second 100 rolls, and all 200 rolls together. The sum of the rolls and the overall average over the 200 rolls can be viewed the right. The green d20 resulted in a 0.80 greater average than the grey d20. The results show that – as any rational person would expect – the two d20s performed just about the same.

**Discussion**

What conclusions can be drawn from the results. First and foremost, I’m a bit “off” for spending time on studying something that is so obvious. Of course die rolls are random! If I were to roll the grey and green d20s 800 more times to reach an even 1,000, I’m sure the differences between the dice would be even smaller.

In addition to my penchant for wasting time on things like analyzing d20 rolls, the results prove something important. Our dice are not against us!

We all have bad rolls, and sometimes they happen at the worst time. We remember those rolls the most. I previously played poker for a few years, and I can still remember some of the worst beats I took because of “bad luck.” But I don’t remember hardly any of the hands I won because “I got lucky.” We tend to recall in brutal clarity the worst days of our lives, yet often remember the best days through a hazy fog.

My bias against the grey die is based on a very small sample set. During an average session of D&D as a player, we’ll likely get through two or possible three encounters, which each combat session going approximately 8 rounds (give or take). Taking into account Action Points, skill checks and other mechanics, I’m probably rolling a d20 – at the most – 30 times per session. And since our group plays twice per month, then I’m rolling a d20 up to 60 times per month. At that rate, it would take me over three months to roll as many d20s as I did tonight for the analysis. It’s tough to take the long view when the same twice “screws you” a few times in one night.

**Conclusion**

I learned that my grey d20 is not evil. It is not out to get me, and it doesn’t wish my rogue to die a horrible and quite violent death. Will I start using it again? Hah, I doubt it! But I think this post can be a service to your players who might complain (a bit too often) about “shitty/crappy” rolls. It’s all in the math. In the long run, even that terrible die that is out to get you will average out in the end.

But if you feel compelled to analyze your dice, then follow this method. If you come up with different results that show one die is performing poorly, then banish it from the table!

Unfortunately this was not a blind study. I don’t mean your bias, but of course the bias of the evil dice that knew they were being tested!

If the grey d20 is self-aware, then I’m *really* screwed!

In a current game, I’m playing a supposedly sneaky rogue. She has a +18 Stealth and to become hidden from the enemy I need better than a 25, so that means a 7 or greater.

My last six rolls on a d20: 1, 4, 2, 3, 5, 2

In and around all that, I roll 20s on stupid things like a saving throw vs deafness (honestly, who cares if the rogue is deaf?!?).

Now, normally I would take that die and melt it in to slag… but my “dice” are all VIRTUAL!

http://dice.brainclouds.net/

I have come to the conclusion that RANDOM.ORG is evil and wants me dead.

I played one game at the Virtual Table and they have the “dice” online. It’s not as rewarding to click on a button and get your result, even if it’s a good result.

Our Cleric once had to make a Heal check and could only fail on a roll of 1. So he had a 95% chance to successfully make the Heal check. When the 1 came up, the table erupted in fits of despair and disbelief.

Good times!

This post is made of win. Thanks for doing the analysis for us. :D

Maybe the grey die is just shy when it comes to being in the spotlight. Die have feelings too. :)

That made me laugh. I can still hang my hat on the results that my favorite green d20 resulted in more critical hits.

There have been more games than I care to think about where I try to keep telling myself “these rolls are random” as I watch my dice come up again and again with single digit numbers, and then I’ll hit a less significant roll like a saving throw and I’ll inevitably roll a natural 20; that’s when I want to take the die and destroy every atom of its existence as I scream “WHY COULDN’T YOU DO THAT ON AN ATTACK ROLL!”

Sometimes I almost think the dice get “attuned” to their player and it seems like as the player gets more upset or even despondant over bad rolls and such that the dice just reflect that and keep rolling worse and worse. It’s probably a good thing that’s not how it actually works though or every D&D player I know would be drugged out “happy pill” addicts trying to get better rolls.

After the first 10 rolls, I honestly thought, “Wow, I might not be crazy. Something *is* wrong with the die.” But no, everything even out in the long run. If the grey d20 consistently performed poorly, then THAT would have been an interesting article. I would have been advocating for everyone to test their dice.

Hah, probably for the best the results came out as expected.

really? that’s not how it works? because one table top session a friend was using the house dice and kept rolling low a ridicules number of time. and then when it reached -20F outside and we were gaming in a rather cold garage my dice wouldn’t roll higher then a five (for d20, d6 rolled 2s and 3s unless I kept them in my pocket. if I want to use a die for a game, I generally have to roll it about a hundred times before hand or it’s likely to crit fail me. yes a die has a even mathematical probability of rolling on a number, when we roll for games…. well there’s a reason why gamers have dice etiquette. cover your dice for the grappling rules.

Are you ready for the GUN SHOW?!?!?! BANG BANG!!! Red dice FTW!!!!

That die is close to being banned from the table. ;-)

200 rolls from the red d20 would have broken the capacity of Excel; it’s can’t handle firepower of that magnitude!

I had a player bring a caliper to the game table once, so he could test everyones dice for balance.. *sigh*…

I also had a player EAT any D20 that rolled a 1 on a saving throw!! Yes, he actually ATE IT!!

Sorta always wondered what it rolled when it returned to our World… But then again, it probably rolled like crap. (rimshot)

This is hilarious. The next project should be to do a chart of dice rolls as a player vs. as a DM. I’ve found, for some strange reason, the d20 I roll as a DM (that nearly kills the party) is most likely to suck when I use it as a player.

Then, I’m not sure how you’d chart it… but does anyone else find it creepy how often two d20’s rolled at the same time will come up with the same result? I swear, my girlfriend will roll the same result 3 out of 5 times with Twin Strike.

Great Post! Yes, I too was afflicted with Crapdice, but I sought help and believe I was cured. A company called “Game Science” explained it to me like this: most other dice out there are pulled off the plastic spru, painted completely and thrown in a giant rock polisher. That’s where they sit and rotate until all the paint comes off, then they are put in another and polished. All this rotation can elongate a die so that it becomes oblong and rolls consistently a certain way. I have 3 sets of Game Science dice that I use for my games and think I get pretty fair results.

I was going to note in principle that each dice will have a tendency because of manufacturing, materials aren’t perfect, etc. You, sir, have done one better. A word from a dice manufacturer (take with salt, since they want to sell you their dice).

Mr. Id, you may like second edition rules, where it was advantageous to roll UNDER your skill number and attribute number on skill and attribute checks. I.e. the lower the D20 roll the better!!!

This is one reason I have that Black D20 in my bag. If I need something to roll low, it has proven itself quite capable in that capacity. =)

Just to insert a little extra math nerd into the mix. The chance of rolling a d20 200 times and not getting a 20 is .00000035%

And now you know.

Jeff, although I’m *still* not ready to use the grey d20 at the table, going the Game Science route seems hardcore. I support and applaude the decision though!

AJ, I have used the grey dice when I’m dominated in your campaign to roll attacks. I think it performed well (rolled low) for me in those situations. Is that cheating??

Twixt, if I would have rolled 2 d20s 200 times each (total of 400 rolls) and NOT gotten a 20, then I think my article would have taken on another life entirely.

And I might have hung up my dice bag for good and retired.

I was gonna do 400 rolls, but my poor computer calculator can’t do the math, which means its lots and lots of zeros :P

Ok, broke down and found a better internet calculator. Not rolling a 20 in 400 rolls would put you at:

0.000000001228689%

Whew, I feel better now.

Oops, scratch that, missed a couple of zeros, should be:

0.00000000001228689%

Of course there is the popular self inflcited curse… when you say “I can only fail on a natural 1.” I think the odds shoot from 1 in 20 to a 50% chance yer gonna bone yerself.

I can’t even count how many times I’ve seen that happen, immediately after that uttered curse of destruction.

One of our staple gamers will throw away her entire set of dice every time she rolls a natural 20. It’s her thing, and she has her reasons.

It’s amazing, and crazy. She has plenty of money, goes through several sets every week, and makes our FLGS very happy.

We call her bat-shit crazy, but she digs it. We aren’t allowed to take ownership of her ‘used’ dice, but that’s okay because she always springs for the pizza, sushi, chips, and wine.

Wow, that is . . . interesting. What could her reasons be for that? How did that start?

Anyone who brings food and spirits to the game is of perfectly-sound mind in my opinion! ;-)

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If you have dice that have 2 colors in a blotchy or swirled pattern, it’s quite logical to assume they aren’t “random”. Each color is made of a different polymer with a slightly different density.

Given that the “1” and the “20” are on exact opposite sides, i would bet that your grey die is inappropriately weighted with the heavier polymer at the 20.

Sound crazy?

Look at a d20 and look at it with the 1 side up, now look at the numbers near it:

7, 13, 19 closest, and 3, 5, 9, 11, 15, 17, sharing a corner with it.

With the exception of the 5 all of these numbers show up as or more frequently on the grey die as the green one…

As for me… i only use solid color dice. :)

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A chi-square test will let you determine the probability that the die is fair. The math is a bit much to type out, but in excel, =chitest(A1:A20,B1:B20) will give you the “probability that [those rolls] could have happened by chance under the assumption of independence [i.e., not a a loaded die].”

Where each row corresponds to the value on the die (1-20), column A are your actual results after rolling X number of times, and column B is the result you would expect if the die were perfectly fair (i.e. 20/X, or 10 for each die face [every value in column B will be 10 if 200 rolls are performed]).

The result from the chitest is how likely your die is rolling fair. If the result is under 0.05 or 5% then good chance you have an unfair die.

Performing the test on your grey and green dice above, you’re evil nasty grey die has a higher probability of being fair (43% probability) compared to your green die (35% probability) (though really all this is saying is that most likely both dice are not loaded).

The best tests are done to something like 10,000+ rolls…just to be sure, but I find 500 rolls is my mental limit, heh.

Another thing that I find interesting is that between your two dice and three dice I have data on, all roll 13s a proportionately higher number of times (save one of my dice). Averaging the percentage of the time each number is rolled over the five dice; 13s have a 7.4% chance of being rolled (perfect die is 5% for any side), and the second highest rollers were 19s, 16s at 5.5% then 9s, and 6s at 5.4% and so on. The 13s are ~2% higher than the next highest dies which are only 0.5% higher than statistical average. The lowest average rollers were the 5s which were at 4.0% A low-roll equivalent to the 13s high would have had to have a 2.6% average chance.

The dice I used were all GameScience gem dice with mild flash on the 7s that I further filed down once I got the dice, before I rolled the tests. The 7s all share a corner with the 13s which in turn share a side with the 5s.

Both d20s are from Chessex sets. I went in thinking I would log 500 rolls but my eyes got blurry after 150 and I had to throw in the towel! Thanks for calculating the chi-square statistics as well. :)

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