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 . . .
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.
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.
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.
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.
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!