Character Generation - What Are The Chances

There are a large number of methods to generating characters in roles playing games. A goal of these systems is to create a character that is random and therefore somewhat unique. Once this aim is satisfied, peoples ideas seem to vary about what features a good character generation system has and what kind of characters it produces. Some players wonder which method will give the best chance at a great character especially if a Dungeon Master gives a choice of methods for character generation. This page simply analyzes each method showing what the average score will be using that method and shows the chance of getting the highest and lowest score for that particular ability score.

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3 d6 Done Six Times

Average Score	Is 10.5. AD&D rates a score of 10 as an average human.
High Scores	The chance of getting an 18 in a given ability is about 0.5%. The chance of getting one 18 in any of your six abilities is 3.5%
Low Scores	The chance of getting a 3 in a given ability is about 0.5%. The chance of getting one 3 in any of your six abilities is 3.5%
Bell Curve
Analysis	This is certainly the most hard core way of producing characters. Characters are extremely average with very few extreme ability scores, 55% of all characters made this way will not have a single score of 3, 4, 5, 6 and the same percentage wont have a 15, 16, 17 or 18. Some would say that this is a good thing as real world people with 18 wisdom are as rare as Ghandi and this should be reflected in the gaming world too. There is a counter argument that if your character were to motivated enough to become an adventurer they must be from a pool of people who are above average anyway and so this method doesn't reflect the natural selection that occurs for would be adventurers.

3 d6 re-roll all 1's Done Six Times

Average Score	Is a 12.
High Scores	The chance of getting an 18 in a given ability is about 0.8%. The chance of getting one 18 in any of your six abilities is 4.7%
Low Scores	The lowest score achievable with this system is a 6. This is simply because any score lower requires one of the dice to be a one which is therefore re-rolled. The chance of getting a 6 in a given ability is about 0.8%. The chance of getting one 6 in any of your six abilities is 4.7%
Bell Curve
Analysis	Susan form Germany wrote in with this method asking for an analysis. She described this method as meaning a roll of 3d5+3. The bell curve is symmetric, looking just like the 3d6 curve but squashed up towards the high end.

4d6 Take The best 3 Done 6 Times

Average Score	Is 12.25. AD&D rates a score of 10 as an average human.
High Scores	The chance of getting an 18 in a given ability is about 1.6%. The chance of getting one 18 in any of your six abilities is about 10%
Low Scores	The chance of getting a 3 in a given ability is about 0.1%. The chance of getting one 3 in any of your six abilities is .6%
Bell Curve
Analysis	This is the current method of creating characters in AD&D. This method pretty much eliminates multiple low scores in any character. Half of all characters made with this method will not have a single score of 3, 4, 5, 6, 7 or 8. With and average of just over 12, the average ability of a character is in the bonus modifier range which starts at 12. Some analysis of the high end of the spectrum shows that, although generous, the system still only averages 60% of characters with at least one ability score of 16,17 or 18.

4d6 re-roll all 1's Take The best 3 Done 6 Times

Average Score	Is 13.44.
High Scores	The chance of getting an 18 in a given ability is about 2.7%. The chance of getting one 18 in any of your six abilities is about 15%
Low Scores	The chance of getting a 6 in a given ability is about 0.15%. The chance of getting one 6 in any of your six abilities is 8.5%
Bell Curve
Analysis	This is another method that Susan form Germany emailed me about. It produces a very high average score and eliminates very lows scores but doesn't seem to produce an extremely excessive amount of 18's. This method will give a high powered character with very few weaknesses nearly every time though and might not be the best choice if you're looking for some balance.

3d6 done Twelve Times, Take The Best 6

Average Score	12.7
High Scores	The chance of getting an 18 in a given ability score is 0.9% The chance of getting an 18 in any of a character's scores is about 5.5%
Low Scores	This is the method to use if you never want a character with an ability score of three. You will get a character with a single score of 3 in every 20 billion characters generated this way. Actually, it occurs less often than that. In fact only 20% of characters will have a score 9 or less, the rest have 10 or higher in everything. For those 20%, the score will be a 9 or an 8 and the ratio of 9's to 8's is about 10 to 1. The scores 3, 4,5 ,6 and 7 simply almost never happen and are not worth mentioning.
Bell Curve
Analysis	This method certainly produces an interesting bell curve. In AD&D, modifiers start at a score of 12. Using this method, 72% of all scores are 12 or above, making for characters that, for the most part, will be adding bonus modifiers for their dice rolls. This method still doesn't produce lots of supper characters as the curve falls away quickly at the high end. If you are a player and are offered the option of these last two methods, you should chose this one if you are looking for all round good scores and no bad ones and you should chose the other method if you are prepared to risk low scores in the change that you will get more higher ones like 17 or 18s.

3d6 Rolled Six Times For Each Ability

Average Score	14.25
High Scores	The chance of getting an 18 in a given ability score is 2.75% The chance of getting an 18 in any of a character's scores is about 15%
Low Scores	Only 10% of characters will have a score of 10 or 9. Scores of 8 or less virtually never occur.
Bell Curve
Analysis	This is a method for producing super characters. If Ghandi and Einstein are super humans then there will be one in every adventuring party. Sometimes, a single character will be both Ghandi and Einstein. Few parties will ever have an individual that is below average at anything at all. Some 95% of all abilities will produce a bonus modifier.

Role up 12 Characters And Chose The Best

Average Score	Combined is 74.75 each ability averages 12.45
High Scores	You have about 1 in a million chance of rolling up character whose combined scores total 100 points. Thats an average score of 16.66. A more realistically reachable combined score is about 5% for a score between 82 and 86. Average score for 84 this is 14.
Low Scores	You have a bout a 1% change of getting a score of between 66 and 60. Anything less is improbable. You have a 7.5% chance of getting a score of 67, 68 or 69.
Bell Curve
Analysis	All of my stats are computer generated and this method creates problems in doing statistical analysis because choosing the “best” character can be difficult using a simple program. An example may be 4 scores of 10 and two of 18 compared with all six scores of 13. If you simply add all the scores and choose the highest you end up with the “plain” character whereas I would chose the character with the two 18's allowing specialization in a particular character class. Having said that, the method for producing the stats above is simply chose by the character with the highest combined scores. Susan from Germany mailed me about a great method for selecting the better character character in the above example and I will be posting some results using this method very shortly. The average character using the 3d6 6 times method has a combined score of 63. The chance of getting a character worse than that with this method is 1 in 5000. I'm a big fan of this method because it virtually eliminates the chance of getting a very below average character without producing lots of super characters. With 72 rolls of 3d6 you are fairly sure to get scores of 16 and 17 to select from which allows you to excel in your chosen character class.

5d4 Subtract 2

Average Score	10.5
High Scores	The chance of getting an 18 in a given ability is about 0.1% The chance of getting one 18 in any of your six abilities is about 0.6%
Low Scores	The chance of getting a 3 in a given ability is about 0.1%. The chance of getting one 3 in any of your six abilities is 0.6%
Bell Curve
Analysis	This one was suggested by `GETB`. This method was suggested as an alternative to 3 d6. It tends to produce results that are a bit closer to average with very few extreme results. You will almost never get an 18 with this system. Only 12% of characters made with this system will have 16 or better. 70% of all characters made with this system wont have better than a 14 in any attribute.

6 d4 Take the best 5Subtract 2

Average Score	11.8
High Scores	The chance of getting an 18 in a given ability is about 0.5% The chance of getting one 18 in any of your six abilities is about 2.7%
Low Scores	The chance of getting a 6 in a given ability is about 0.02%. The chance of getting one 6 in any of your six abilities is 0.12%
Bell Curve
Analysis	This is the second one suggested by `GETB`. It produces a slight improvement in results compared to the 5 d4. This system really eliminates the low scores with only 25% of characters getting a 3,4,5,6 or 7 on any ability score with the 7 being far more common than all the others combined. High scores are a little more common but no ridiculously so with 60% of all characters getting a 15 or better in at least one ability.

4d6 Take the Best 3 then, of those 3, re roll 1's till there are no 1's

Average Score	12.69
High Scores	The chance of getting an 18 in a given ability score is 1.73% The chance of getting an 18 in any of a character's scores is about 10%
Low Scores	The chance of getting a 6 in a given ability is about 0.5%. The chance of getting one 6 in any of your six abilities is 2.96%
Bell Curve
Analysis	This one was suggested by Thomas who was looking for something with a little more power than 6d4 pick the best 3 but less that 4d6, re-roll 1's and pick the best 3. This system picks up the average by just under half a point. It does give a modest kick to the scores without being excessive.