fuindordm
Adventurer
So, I'm starting a new campaign soon and whipped up a program to test a couple of character generation methods and see what the differences are. On the theory that some of you will enjoy the discussion, here we go! I examined 3 methods:
1. 4d6, drop the lowest
2. shuffle deck of 24 cards numbered 1 to 6 into 6 piles, drop the lowest in each pile
3. as #2, but replace one ace with a joker yielding 1d6.
The standard, 4d6-drop-the-lowest method gave the following results. The +/- ranges given for the averages are one standard deviation, meaning that about 70% of the characters fell in that range. The main thing I notice about this method is the huge variance in characters: it commonly generates stats with an equivalent point-buy value between 20 and 37! A party generated this way will probably have a low roller and a high roller with a huge gulf in power between the two.
IDL> dicegen
10000 characters generated
average score: 12.26 +/- 2.84
average point-buy value: 28.58 +/- 9.08
average total modifier: 5.27 +/- 3.52
Probability (%) that your high score is a...
13: 4.96000
14: 14.2100
15: 22.6000
16: 26.3900
17: 21.1000
18: 8.91000
Probability that your low score is a...
5: 4.27000
6: 9.21000
7: 13.9400
8: 18.8700
9: 19.6500
10: 16.1300
Here's an alternative that I heard about on these boards and tried once as a player, that I quite liked. Take a deck of cards with only the aces through sixes (24 cards), and distribute them into 4 piles. Treat each pile as 4d6, dropping the lowest. This method has very similar average stat values and average equivalent point-buy, but the common range of point-buy values is 26 to 30--much narrower, and a party generated this way will be much more balanced. Also, the chance of seeing someone with an 18 is somewhat lower, but 16's and 17's are about as common as they were before.
IDL> cardgen
10000 characters generated
average score: 12.3189+/- 2.64898
average point-buy value: 28.6032+/- 1.97667
average total modifier: 5.43670+/- 0.919316
Probability (%) that your high score is a...
13: 0.510000
14: 8.89000
15: 29.3800
16: 33.3800
17: 23.5100
18: 4.33000
Probability that your low score is a...
5: 2.80000
6: 7.36000
7: 13.3900
8: 21.7500
9: 26.5600
10: 19.8200
Finally, here's a variation on the card generation method that I'm adopting for my campaign to bring the players in line with a character generated using 4d6 who rolled a point-buy of 34. I replaced one of the aces with a 'Joker' that rolls a d6 for its value when it comes up. As you might imagine, this lifts the average point-buy by a couple of points, but does more to wipe out the very low scores than to enhance the high ones.
IDL> cardgen_mod
(Replaced one '1' with a joker that generates 1d6)
10000 characters generated
average score: 12.5985+/- 2.56889
average point-buy value: 30.6249+/- 3.34127
average total modifier: 6.27540+/- 1.40328
Probability (%) that your high score is a...
13: 0.190000
14: 6.88000
15: 26.5800
16: 34.9500
17: 25.9400
18: 5.46000
Probability that your low score is a...
5: 1.45000
6: 4.39000
7: 10.4600
8: 19.1300
9: 26.3800
10: 24.1300
Ben
1. 4d6, drop the lowest
2. shuffle deck of 24 cards numbered 1 to 6 into 6 piles, drop the lowest in each pile
3. as #2, but replace one ace with a joker yielding 1d6.
The standard, 4d6-drop-the-lowest method gave the following results. The +/- ranges given for the averages are one standard deviation, meaning that about 70% of the characters fell in that range. The main thing I notice about this method is the huge variance in characters: it commonly generates stats with an equivalent point-buy value between 20 and 37! A party generated this way will probably have a low roller and a high roller with a huge gulf in power between the two.
IDL> dicegen
10000 characters generated
average score: 12.26 +/- 2.84
average point-buy value: 28.58 +/- 9.08
average total modifier: 5.27 +/- 3.52
Probability (%) that your high score is a...
13: 4.96000
14: 14.2100
15: 22.6000
16: 26.3900
17: 21.1000
18: 8.91000
Probability that your low score is a...
5: 4.27000
6: 9.21000
7: 13.9400
8: 18.8700
9: 19.6500
10: 16.1300
Here's an alternative that I heard about on these boards and tried once as a player, that I quite liked. Take a deck of cards with only the aces through sixes (24 cards), and distribute them into 4 piles. Treat each pile as 4d6, dropping the lowest. This method has very similar average stat values and average equivalent point-buy, but the common range of point-buy values is 26 to 30--much narrower, and a party generated this way will be much more balanced. Also, the chance of seeing someone with an 18 is somewhat lower, but 16's and 17's are about as common as they were before.
IDL> cardgen
10000 characters generated
average score: 12.3189+/- 2.64898
average point-buy value: 28.6032+/- 1.97667
average total modifier: 5.43670+/- 0.919316
Probability (%) that your high score is a...
13: 0.510000
14: 8.89000
15: 29.3800
16: 33.3800
17: 23.5100
18: 4.33000
Probability that your low score is a...
5: 2.80000
6: 7.36000
7: 13.3900
8: 21.7500
9: 26.5600
10: 19.8200
Finally, here's a variation on the card generation method that I'm adopting for my campaign to bring the players in line with a character generated using 4d6 who rolled a point-buy of 34. I replaced one of the aces with a 'Joker' that rolls a d6 for its value when it comes up. As you might imagine, this lifts the average point-buy by a couple of points, but does more to wipe out the very low scores than to enhance the high ones.
IDL> cardgen_mod
(Replaced one '1' with a joker that generates 1d6)
10000 characters generated
average score: 12.5985+/- 2.56889
average point-buy value: 30.6249+/- 3.34127
average total modifier: 6.27540+/- 1.40328
Probability (%) that your high score is a...
13: 0.190000
14: 6.88000
15: 26.5800
16: 34.9500
17: 25.9400
18: 5.46000
Probability that your low score is a...
5: 1.45000
6: 4.39000
7: 10.4600
8: 19.1300
9: 26.3800
10: 24.1300
Ben
