A newbie D&D player will usually generate their first character and be disappointed. They roll the dice, add them up, and realize they have a perfectly run-of-the-mill character. They were hoping to get a few lucky rolls and come up with someone really special. Then they get an idea: Maybe I’ll just toss this character and roll up a new one. Maybe this time I’ll get lucky.
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There are six attributes that define a character: Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. You start by rolling four six-sided dice. Discard the lowest die. Add the other three together for a number from 3 (feeble) to 18 (magnificent). Do this once for each of your six attributes, and then you have your character. An attribute of ten is “average” for a human being. However, your character is (hopefully) better than the average human, which is one of the reasons they are a hero in the game world and not milking cows and shoveling dung like everyone else. The rulebooks claim that 12 is the average value of an attribute for a player character, although below I’ll show that it’s actually slightly higher than this.
An attribute of eighteen is hard to come by, since three of the four dice have to come up sixes. But it’s even harder to throw a three, since all four dice would need to come up as ones. (Note that you have to roll up all six stats one after another. Rolling one stat over and over until you get a number you like is cheating. This is important.)
But back to our newbie. They look at the attributes they rolled:
| The Newbie | |
|---|---|
| STR | 13 |
| DEX | 17 |
| CON | 9 |
| INT | 14 |
| WIS | 12 |
| CHA | 13 |
| (Average 13) | |
They see that their character has an average attribute of 13. With a score of 13, they are going to actually be a point stronger than the typical character. But still. That 9 is disappointing. If only they had thrown something higher there! They note that only one number is over 16, which is where the really “good” values are. The newbie looks at the score and starts wondering how much better they could do. How hard could it be, anyway?
I wrote a little program to demonstrate exactly this. I had it roll up 100 million characters and tally the results. It keeps track of how common the various scores are, and how likely it is that you can score at or above a given number. It will also record the best and worst characters. Note that I doubt there have been 100 million characters in the history of Dungeons & Dragons. That’s a third of the population of the U.S. Well under 10% of the population plays D&D, and many that do use prefab stats or point-buy instead of rolling the dice. So even in it’s 30 year history, and even allowing for that fact that some players have several characters, I think the number of legitimate (rolled) characters falls well short of 100 million.
I’m sure most of what I’m doing here is probably available online if I were to google around for it, but it’s far more interesting to go through the steps and see the results myself.
100,000,000 Characters
It turns out that rolling the dice this way produces a bell curve with astoundingly steep sides. An average score of 3 is possible, but to get it, you would need a six-sided die come up with a 1, over and over again, for a total of 24 times times in a row. Over the course of 100 million characters this never happened, which shouldn’t be a surprise. The odds of 24 consecutive 1’s is 1 in 624. More exactly: 1 in 4,738,381,338,321,616,896. I’m sure it’s never been done.
So at least we don’t have to worry about that happening.
All 18’s is a little more likely (1 in 101,559,956,668,416) but that never happened either.
From the list below, we see that 12.3 is the most common score. If our newbie hopes to re-roll his character and get an average score of 14, the odds are against him. 29% of the characters created have a score of 13 or better, but only 7% have 14 or better. If he’s shooting for 15, his chances drop all the way to 0.7%. He’ll probably roll over a hundred characters before he sees one with a score of 15. The odds of throwing a character with a score of 16 or better are an astounding 1 in 4,065. If 16 still isn’t good enough and he wants to hold out for a 16.3, his odds shoot up to 1 in 18,867. Assuming he rolls up a character every minute, he will be at it for over 13 days non-stop to generate 18,867 characters.
Ten might be the normal score for Stableboys and Milk Maids, but only 3.5% of the characters he rolls will be that weak. Note that the rules suggest that you should discard anything with a score of eleven or less, which will happen 16% of the time.
To get these stats the program had to roll the dice 2.4 billion times. Read on to see all the stats and charts in detail…
Continue reading 〉〉 “One Hundred Million Characters, Part 1”
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