Post/Author/DateTime	Post
oma 09-29-06, 09:42 AM	Comparing 4d6 drop the lowest and a 28pt buy. What are the differences between them and which will result in higher attributes? I just know that there is someone out there who has done the math on this correctly. If you would enlighten me I would appreciate it. I want to offer my Players the option of a point buy that gives them probably lower attributes but with more control OR the option to roll dice with the idea that it could be better, but they must keep what they roll. As I am trying to get real data, please do not respond with wild theories or groundless facts. Straight answers for a straight question please. Thanks
dokesa 09-29-06, 10:59 AM	I have a 24 mb Excel file with die rolls, even after I strip out just about all of the equations and just keep the values. 3d6: 16, 14, 12, 10, 9, 7 (22 points) 4d6: 16, 15, 13, 12, 10, 8 (29 points) 5d6: 17, 16, 14, 13, 11, 9 (38 points) First, I listed all the combinations of die rolls in this manner (using 3d3 for simplicity): 111, 112, 113, 122, 123, 133, 222, 223, 233, 333 Then, I figured out the permutations (as above): 1, 3, 3, 3, 6, 3, 1, 3, 3, 1 I then ordered the ability scores in a similar manner as above. Eliminate all invalid scores based upon the minimum of the highest score and the total modifiers. Combine the permutations for the die rolls within each ability score and the permutations of the ability scores. Add up all the possible combinations and you wind up with the following tables: 3d6 highest lowest 3 0 0 0 500 121955 2333597 4 0 0 0 48420 1624995 7066701 5 0 0 0 356040 5495850 11628342 6 0 0 12150 2582350 15033700 16150720 7 0 0 129375 7782675 25561050 17195280 8 0 1638 2145213 24082233 38211558 16078650 9 0 36450 7123575 38561075 38441450 11693750 10 0 1322244 23672169 51243489 31704264 7269318 11 0 4973724 36605439 47869839 21861144 3901338 12 900675 16676775 47585025 37081525 12800275 1774825 13 2790249 24195381 41256411 23116191 6118161 651651 14 7061790 27880590 27301890 10881990 2160765 172935 15 9434380 21953260 14246260 4057660 581410 33670 16 11336532 14004636 5534556 1051356 101586 3990 17 8942022 5673618 1253538 138978 7983 189 18 4700206 820126 70966 3466 91 1 4d6 3 0 0 0 0 33615 1226985 4 0 0 0 3920 765860 5700380 5 0 0 0 48200 3519350 12607850 6 0 0 0 953820 15559425 25829055 7 0 0 0 4243080 36177330 36198990 8 0 0 346890 25284530 81691820 44285360 9 0 0 2657655 63043435 115550890 41270320 10 0 274500 28095990 155673830 135992180 32443460 11 0 2792760 76774260 209074420 117670360 21286840 12 0 29408700 195753225 233916065 85216760 11845310 13 0 79433040 251867340 186053260 50100160 5337160 14 28161760 182961760 261609760 116038560 23048160 1844640 15 59952543 205643931 175630521 53153381 7616471 441077 16 113332980 184597764 85429644 16471244 1591514 62510 17 114948828 90650124 22393044 2501604 143694 3402 18 80273634 16289826 1489866 72786 1911 21 5d6 3 0 0 0 0 19335 929259 4 0 0 0 1000 607450 5645020 5 0 0 0 17400 3433350 15309660 6 0 0 0 794580 21675060 42999324 7 0 0 0 4768200 63552600 75391560 8 0 0 216750 41162950 182601250 112204930 9 0 0 2677320 132650920 322603000 127427704 10 0 236880 54578280 457537480 484835080 121150960 11 0 4005960 203545860 775366060 505562260 93850120 12 0 77513904 746589354 1127886154 440626864 61958968 13 0 277659120 1230988770 1092699370 305342320 32671240 14 0 949091220 1711010070 833556570 166301520 13314840 15 366133383 1455877731 1412115441 450589381 64594651 3740737 16 913560450 1658546010 833707710 163836310 15830485 621775 17 1107078020 952494260 250103660 28258860 1623210 38430 18 952253544 206046696 19547976 956616 25116 276 I took the median for each score to get the arrays at the top.
metalmorphosis 09-29-06, 12:11 PM	I just made this pretty little bell curve in excel before I realized I couldn't even show it to you. Oh well... here's the data for 4d6 (drop lowest): 3 0.08% 4 0.31% 5 0.77% 6 1.62% 7 2.93% 8 4.78% 9 7.02% 10 9.41% 11 11.42% 12 12.89% 13 13.27% 14 12.35% 15 10.11% 16 7.25% 17 4.17% 18 1.62% (for all you extra sick people out there who want to do this in excel, make 4 columns (1 for every d6) and insert numbers to represent all possible combinations (1296 rows). In column 'E', insert this formula - =IF(AND(D1<=C1,D1<=B1,D1<=A1),A1+B1+C1,IF(AND(C1<=D1,C1<=B1,C1<=A1),A1+B1+D1,IF(AND(B1<=A1,B1<=D1,B1<=C1),A1+C1+D1,B1+C1+D1))) ) anyway... 4d6, on average, will probably give you more ability points than point buy would allow, but I like the point buy system the best if you have a specific character in mind. Die rolls will always be random... point buy allows you to adjust ability scores to your liking. Plus, you can push your key ability up to 16, 17 or even 18, and the chances of rolling one of those scores on your primary ability using 4d6 is pretty slim...
oma 09-29-06, 12:48 PM	1st off. thank you very much for your response. 2nd--I think I understood about 15% of all that, (which is to say not much). Can I rely on your understanding of math to determine that over the long haul 4d6 drop the lowest will result in average 29 point buy characters?
metalmorphosis 09-29-06, 01:08 PM	1st off. thank you very much for your response. 2nd--I think I understood about 15% of all that, (which is to say not much). Can I rely on your understanding of math to determine that over the long haul 4d6 drop the lowest will result in average 29 point buy characters? Yes, but the point buy system gives you control in how you build your character. My DM has gone old school on us and we're now rolling straight 3d6 for abilities.
dokesa 09-29-06, 01:51 PM	Can I rely on your understanding of math to determine that over the long haul 4d6 drop the lowest will result in average 29 point buy characters?Mine is correct in that I haven't been able to find any errors in my thinking yet; it hasn't been verified by anyone else. I have a math major, but haven't used it in a long time. My DM has gone old school on us and we're now rolling straight 3d6 for abilities.Ouch!
frasmage 09-29-06, 02:09 PM	well, I guess my current character certainly got MEGALUCK with his stats, rolling 4d6 I got an 18,16,16,16,16,11! My best stats ever (that is equivalent to 59 point buy)
Krusk 09-29-06, 04:17 PM	anyway... 4d6, on average, will probably give you more ability points than point buy would allow, but I like the point buy system the best if you have a specific character in mind. Die rolls will always be random... point buy allows you to adjust ability scores to your liking. Plus, you can push your key ability up to 16, 17 or even 18, and the chances of rolling one of those scores on your primary ability using 4d6 is pretty slim... Usually when we are rolling characters, if you talk to the dm they will allow you to take a -1.5 to a stat to raise another stat by 1. the -1.5 varies from you get a free stat point to a -2 depending on who is dm and how nice they are that day. *-edit we also dont allow half stats IE 17.5. so youd have to take a -2 if the the dm said it was a 1.5 trade and you already had a 17 you were making an 18. we also allow for taking the penalty to more than one stat, IE lowering your dex and con by one each instead of just your dex 2. And we also make sure the dm approves all stat changes, usually nothing lower than a 7 and never anything higher than an 18.
Bulletproof_Condom 09-29-06, 04:30 PM	Usually when we are rolling characters, if you talk to the dm they will allow you to take a -1.5 to a stat to raise another stat by 1.I've never encountered a DM that does that.
metalmorphosis 09-29-06, 04:56 PM	I can't say that I know of any DMs that do that either... If my rolls don't meet the minimum required to play the class I want, I can re-roll the whole thing, but swapping points has always been a no-no... Of course, our DM is known as 'NastyDM'.. maybe there are actually nice DMs out there. :P
2y1y1z2 09-29-06, 05:08 PM	In all honesty, I don't really like rolling stats. Just because you, as a player, have terrible luck, doesn't mean that your character should. Point buy eliminates player fluctuation. I do this mainly because I have a player who consistently rolls 14-18 for stats and one that consistently rolls 10-14. Oh, and I've had some pretty nasty DM's too. One of them would look at your rolled stats and if they qualified for "crib death" (Our term for an unplayable character, stat-wise) He'd just say "Okay, you're undead." Sure, a d12 every level is nice, but when you've got a 3 Strength...
Androlphas 09-29-06, 05:25 PM	In all honesty, I don't really like rolling stats. Just because you, as a player, have terrible luck, doesn't mean that your character should. Point buy eliminates player fluctuation. I do this mainly because I have a player who consistently rolls 14-18 for stats and one that consistently rolls 10-14. Oh, and I've had some pretty nasty DM's too. One of them would look at your rolled stats and if they qualified for "crib death" (Our term for an unplayable character, stat-wise) He'd just say "Okay, you're undead." Sure, a d12 every level is nice, but when you've got a 3 Strength... Yikes! :eek: I like the point buy system, it keeps things fair across the board, plus the big selling point for me is not what you get with it, but what you avoid - a stat lower than 8.
makeshiftwings 09-29-06, 05:46 PM	1st off. thank you very much for your response. 2nd--I think I understood about 15% of all that, (which is to say not much). Can I rely on your understanding of math to determine that over the long haul 4d6 drop the lowest will result in average 29 point buy characters? Look at it this way, if you rolled completely average each time on a 4d6 drop the lowest, your scores would be 13/13/13/13/13/13, which is a 30 point buy. But most people would say 28 point buy is better than straight 13's, because you can min/max your scores and give yourself some 16's in exchange for some 8's, which is almost always better for any type of character.
Solaris 09-29-06, 07:14 PM	I just did a simple brute-force search (computing the sum, over all possible arrays of scores, of the product of the cost of the array and the probability of rolling it) and got 29 for the mean point-cost of the 4d6 method. Incidentally, although this agrees with the results of the earlier poster with the spreadsheet, my result of 18 for the mean cost of the 3d6 method does not. I think my way is the more accurate, since it computes the actual mean while the previous poster was reading a median value from a table (not to disparage his hard work, of course!) So the upshot is that 4d6 will roll slightly higher on average than 28 points, has less control than point-buy, and the possibility of rolling scores from 3 to 7 is balanced by the possibility of having multiple high scores out of range of the point-buy. It's probably a fair choce to give your players.
Nom 09-30-06, 01:29 AM	Also note that (1) the mean bonus of (3 from 4d6) rolling is less than its equivalent point-buy value, due to the inability to avoid odd scores (which are approximately 50% of the total). (2) (3 from 4d6) rolling converted to point buy has a long tail on the high side, especially when the "hopeless character" rules are included. The median is less than the mean. The net effect is that more characters will be "below average" than "above average", but the "above average" characters might be way above average. (3) All of the above assumes that when you say (3 from 4d6) you actually mean that. Even a little fudging can easily slide the power scale way up.
dokesa 10-01-06, 08:32 AM	I just did a simple brute-force search (computing the sum, over all possible arrays of scores, of the product of the cost of the array and the probability of rolling it) and got 29 for the mean point-cost of the 4d6 method. Did you do (18-2)^6 possibilities or (6^4)^6 possibilities?
metalmorphosis 10-01-06, 12:41 PM	Did you do (18-2)^6 possibilities or (6^4)^6 possibilities? Why wouldn't it just be 6^4 possibilities? I just did a simple brute-force search (computing the sum, over all possible arrays of scores, of the product of the cost of the array and the probability of rolling it) and got 29 for the mean point-cost of the 4d6 method. How did you consider rolls of 3-7 for point cost? The mean value for 4d6 (drop lowest) would be 12, which would be a 24 point buy across all 6 ability scores. That's kinda close to the 25 point buy standard.
Solaris 10-01-06, 02:13 PM	Since the point-buy method doesn't allow you to spend negative points for low scores (though presumably you could opt to lower a score below 8 if you really wanted to), and since the rolling method doesn't allow you to discard any set of scores having one or more score less than 8, the only way to do it "by the book" is to consider all sets of six 3-18 scores, with scores of 8 or less costing 0 points. If you want a score of 3-7 with point-buy, it's free. So it was 16^6. If you're thinking I've missed out some combinations... As I mentioned, during my summation, I multiplied each set's cost by the probability of obtaining that set with 4d6; this does the combinatorics implicitly.
Krusk 10-01-06, 03:26 PM	Reason you've never met a dm who does that, 1-my friend decided to start doing it because one guy kept whineing about using point buy 2-The rest of our regular group decided it was a good idea. 3-You have not met us, and most other dm's dont do that.