The bog-standard D&D approach of rolling 3d6 results in the following (infamous) normal distribution:
3: 46448 ## 0.46%
4: 138958 ##### 1.4%
5: 277199 ######### 2.8%
6: 462721 ############## 4.6%
7: 693847 ##################### 6.9%
8: 972031 ############################## 9.7%
9: 1156618 ################################### 12%
10: 1252304 ###################################### 13%
11: 1252510 ###################################### 13%
12: 1156952 ################################### 12%
13: 970769 ############################## 9.7%
14: 694804 ##################### 6.9%
15: 462733 ############## 4.6%
16: 277365 ######### 2.8%
17: 138397 ##### 1.4%
18: 46344 ## 0.46%
Real pretty-like, but apparently also real boring as far as Kevin Siembieda was concerned. The Palladium approach (in most of their games anyway) is to add another d6 on top if your inital roll was >15; for obvious reasons, that distribution has a hole at 16:
3: 46734 ## 0.47%
4: 139454 ##### 1.4%
5: 278080 ######### 2.8%
6: 463234 ############## 4.6%
7: 693088 ##################### 6.9%
8: 970752 ############################## 9.7%
9: 1159394 ################################### 12%
10: 1248913 ###################################### 12%
11: 1248609 ###################################### 12%
12: 1159218 ################################### 12%
13: 970938 ############################## 9.7%
14: 694658 ##################### 6.9%
15: 462903 ############## 4.6%
16: 0
17: 46270 ## 0.46%
18: 69841 ### 0.7%
19: 77344 ### 0.77%
20: 77271 ### 0.77%
21: 77180 ### 0.77%
22: 77518 ### 0.78%
23: 30861 # 0.31%
24: 7740 # 0.077%
Needless to say I find that hole at 16 disturbing. "Get over it!" I hear you say. "We've been doing it this way since the early eighties!" I hear you say. Well you've been doing it wrong I say. The distribution has another bothersome property, namely that it basically says that there are many more people in the Palladium megaverse with strength 18, 19, 20, 21, and 22 than there are with strength 17; that makes absolutely no sense to me. So we'll need to find another way to roll those attributes.
Note that you can only roll a 16 initially if you roll at least one 6; in other words the numbers 16, 17, and 18 which "gate" that extra d6 basically encode whether you rolled one, two, or three sixes initially.
If one wanted to avoid the "ugly" gap at 16, an alternate approach could be to allow for an extra d6 if any of the initial three rolls was a 6. Yes, that means that a roll of (1, 1, 6) which adds up to 8 will get the extra d6, but a roll of (5, 5, 5) which adds up to 15 will not. So what? Spread out the love I say! And the resulting distribution is ... interesting?
3: 46298 ## 0.46%
4: 139114 ##### 1.4%
5: 278211 ######### 2.8%
6: 462385 ############## 4.6%
7: 694291 ##################### 6.9%
8: 833002 ######################### 8.3%
9: 902567 ############################ 9%
10: 904789 ############################ 9%
11: 832740 ######################### 8.3%
12: 694061 ##################### 6.9%
13: 625586 ################### 6.3%
14: 600869 ################### 6%
15: 578239 ################## 5.8%
16: 556044 ################# 5.6%
17: 532851 ################ 5.3%
18: 463221 ############## 4.6%
19: 355143 ########### 3.6%
20: 238305 ######## 2.4%
21: 146683 ##### 1.5%
22: 77040 ### 0.77%
23: 30760 # 0.31%
24: 7801 # 0.078%
Nothing much changes at the tails (so <8 or >21), but we can see that starting at 8 some of the results get "pushed up" because of the extra d6 that goes into the mix. I like how you suddenly get a decent chance for an 18 and chances go down gradually for 19, 20, and 21. So this is my preferred way for rolling Palladium attributes. Your mileage may of course vary.
Some Palladium games say that if the extra d6 comes up 6, you roll another extra d6 on top. That ends up looking like this:
3: 45741 ## 0.46%
4: 139011 ##### 1.4%
5: 278691 ######### 2.8%
6: 462725 ############## 4.6%
7: 695501 ##################### 7%
8: 971532 ############################## 9.7%
9: 1156869 ################################### 12%
10: 1249592 ###################################### 12%
11: 1249207 ###################################### 12%
12: 1157252 ################################### 12%
13: 972894 ############################## 9.7%
14: 695661 ##################### 7%
15: 462137 ############## 4.6%
16: 0
17: 46350 ## 0.46%
18: 69346 ### 0.69%
19: 76583 ### 0.77%
20: 77664 ### 0.78%
21: 76965 ### 0.77%
22: 31123 # 0.31%
23: 15762 # 0.16%
24: 11717 # 0.12%
25: 12724 # 0.13%
26: 12759 # 0.13%
27: 12978 # 0.13%
28: 12940 # 0.13%
29: 5092 # 0.051%
30: 1184 # 0.012%
Let's ignore the hole at 16 and just look at the distribution between 17 and 30. There are three obvious chunks here: 17 to 22, 23 to 28, 29 to 30. This once again seems strange to me, ideally we should see a smooth tail, not one that comes in chunks. And again the "any 6 in the initial roll" trigger does better as far as I am concerned:
3: 46492 ## 0.46%
4: 138795 ##### 1.4%
5: 277586 ######### 2.8%
6: 463410 ############## 4.6%
7: 694735 ##################### 6.9%
8: 833280 ######################### 8.3%
9: 902447 ############################ 9%
10: 903006 ############################ 9%
11: 832890 ######################### 8.3%
12: 694124 ##################### 6.9%
13: 625307 ################### 6.3%
14: 578780 ################## 5.8%
15: 536343 ################# 5.4%
16: 497294 ############### 5%
17: 463368 ############## 4.6%
18: 386683 ############ 3.9%
19: 297007 ######### 3%
20: 223587 ####### 2.2%
21: 165806 ##### 1.7%
22: 123385 #### 1.2%
23: 96515 ### 0.97%
24: 76511 ### 0.77%
25: 58900 ## 0.59%
26: 40022 ## 0.4%
27: 24301 # 0.24%
28: 13141 # 0.13%
29: 4991 # 0.05%
30: 1294 # 0.013%
Note that the tails are once again roughly the same (so <8 and >27 this time) but chances for extremly high attributes seem "more natural" this way. At least to me.
First published: 2026-05-09 Last updated: 2026-05-09