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<blockquote data-quote="fuindordm" data-source="post: 1875824" data-attributes="member: 5435">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.&nbsp; On the theory that some of you will enjoy the discussion, here we go!&nbsp; I examined 3 methods:1. 4d6, drop the lowest2. shuffle deck of 24 cards numbered 1 to 6 into 6 piles, drop the lowest in each pile3. as #2, but replace one ace with a joker yielding 1d6.&nbsp; The standard, 4d6-drop-the-lowest method gave the following results.&nbsp; The +/- ranges given for the averages are one standard deviation, meaning that about 70% of the characters fell in that range.&nbsp;&nbsp; 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!&nbsp; A party generated this way will probably have a low roller and a high roller with a huge gulf in power between the two.&nbsp; IDL&gt; dicegen&nbsp;&nbsp; 10000 characters generatedaverage score:&nbsp; &nbsp; &nbsp;&nbsp; 12.26 +/- 2.84average point-buy value:&nbsp; &nbsp; &nbsp; 28.58 +/- 9.08average total modifier:&nbsp; &nbsp; &nbsp; 5.27 +/- 3.52Probability (%) that your high score is a...13:&nbsp; &nbsp; &nbsp;&nbsp; 4.9600014:&nbsp; &nbsp; &nbsp;&nbsp; 14.210015:&nbsp; &nbsp; &nbsp;&nbsp; 22.600016:&nbsp; &nbsp; &nbsp;&nbsp; 26.390017:&nbsp; &nbsp; &nbsp;&nbsp; 21.100018:&nbsp; &nbsp; &nbsp;&nbsp; 8.91000Probability that your low score is a...&nbsp;5:&nbsp; &nbsp; &nbsp;&nbsp; 4.27000&nbsp;6:&nbsp; &nbsp; &nbsp;&nbsp; 9.21000&nbsp;7:&nbsp; &nbsp; &nbsp;&nbsp; 13.9400&nbsp;8:&nbsp; &nbsp; &nbsp;&nbsp; 18.8700&nbsp;9:&nbsp; &nbsp; &nbsp;&nbsp; 19.650010:&nbsp; &nbsp; &nbsp;&nbsp; 16.1300Here's an alternative that I heard about on these boards and tried once as a player, that I quite liked.&nbsp; Take a deck of cards with only the aces through sixes (24 cards), and distribute them into 4 piles.&nbsp; 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.&nbsp; 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.&nbsp;&nbsp; IDL&gt; cardgen&nbsp;&nbsp; 10000 characters generatedaverage score:&nbsp; &nbsp; &nbsp;&nbsp; 12.3189+/-&nbsp; &nbsp; &nbsp; 2.64898average point-buy value:&nbsp; &nbsp; &nbsp; 28.6032+/-&nbsp; &nbsp; &nbsp; 1.97667average total modifier:&nbsp; &nbsp; &nbsp; 5.43670+/-&nbsp; &nbsp;&nbsp; 0.919316Probability (%) that your high score is a...13:&nbsp; &nbsp; &nbsp; 0.51000014:&nbsp; &nbsp; &nbsp;&nbsp; 8.8900015:&nbsp; &nbsp; &nbsp;&nbsp; 29.380016:&nbsp; &nbsp; &nbsp;&nbsp; 33.380017:&nbsp; &nbsp; &nbsp;&nbsp; 23.510018:&nbsp; &nbsp; &nbsp;&nbsp; 4.33000Probability that your low score is a...&nbsp;5:&nbsp; &nbsp; &nbsp;&nbsp; 2.80000&nbsp;6:&nbsp; &nbsp; &nbsp;&nbsp; 7.36000&nbsp;7:&nbsp; &nbsp; &nbsp;&nbsp; 13.3900&nbsp;8:&nbsp; &nbsp; &nbsp;&nbsp; 21.7500&nbsp;9:&nbsp; &nbsp; &nbsp;&nbsp; 26.560010:&nbsp; &nbsp; &nbsp;&nbsp; 19.8200Finally, 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.&nbsp;&nbsp; I replaced one of the aces with a 'Joker' that rolls a d6 for its value when it comes up.&nbsp; 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&gt; cardgen_mod(Replaced one '1' with a joker that generates 1d6)&nbsp;&nbsp; 10000 characters generatedaverage score:&nbsp; &nbsp; &nbsp;&nbsp; 12.5985+/-&nbsp; &nbsp; &nbsp; 2.56889average point-buy value:&nbsp; &nbsp; &nbsp; 30.6249+/-&nbsp; &nbsp; &nbsp; 3.34127average total modifier:&nbsp; &nbsp; &nbsp; 6.27540+/-&nbsp; &nbsp; &nbsp; 1.40328Probability (%) that your high score is a...13:&nbsp; &nbsp; &nbsp; 0.19000014:&nbsp; &nbsp; &nbsp;&nbsp; 6.8800015:&nbsp; &nbsp; &nbsp;&nbsp; 26.580016:&nbsp; &nbsp; &nbsp;&nbsp; 34.950017:&nbsp; &nbsp; &nbsp;&nbsp; 25.940018:&nbsp; &nbsp; &nbsp;&nbsp; 5.46000Probability that your low score is a...&nbsp;5:&nbsp; &nbsp; &nbsp;&nbsp; 1.45000&nbsp;6:&nbsp; &nbsp; &nbsp;&nbsp; 4.39000&nbsp;7:&nbsp; &nbsp; &nbsp;&nbsp; 10.4600&nbsp;8:&nbsp; &nbsp; &nbsp;&nbsp; 19.1300&nbsp;9:&nbsp; &nbsp; &nbsp;&nbsp; 26.380010:&nbsp; &nbsp; &nbsp;&nbsp; 24.1300Ben</blockquote>

[QUOTE="fuindordm, post: 1875824, member: 5435"] 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 [/QUOTE]

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