No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember. Regardless, there's no way it's 1 in 100,000 to roll 93 or higher. Not with any class is it THAT high.
Anyway, absolutely take the 18/00 roll. Obviously there's a 1 in 100 chance of getting that strength. But you've got that strength AND an amazing roll of 90. That's as good as you're likely to get for a long, long time. Like another poster said, 18/00 with 15 CHA is better than 18/99 with 18 CHA. The way I roll is, I work out what stats I'd like before I start, and if it'd take more than like 150-200 rolls to get, I consider it too difficult and instead aim lower. Your roll statisticallly takes a lot longer than 150-200 times.
No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
The probability is different (way higher) because you're not rolling numbers belonging to the 1-18 set but rather: - in some cases 3-18 - in others 9-18 - and in some even 15-18
No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
The probability is different (way higher) because you're not rolling numbers belonging to the 1-18 set but rather: - in some cases 3-18 - in others 9-18 - and in some even 15-18
If any roll below, say, a 10 and it gets rounded up it doesn't change the odds of getting an 11, just so ya know. Stat redistribution makes it a little easier to switch around but you can't really afford to be short-stacked for 93 as if you score the minimum (3) on one roll you've got to score 18 on everything else. (Probability approx 1 in two trillion). Nevertheless the simple fact you've been going for four days should demonstrate that the odds are massively against you.
Like another poster said, 18/00 with 15 CHA is better than 18/99 with 18 CHA.
I know that but I keep thinking I'll just take any Str with 18s across the board (except for Wis score), play through the game, grab the Str tome and in the end my char will be better by 3 points.
Of course, at the same time, I realise that not taking this 18/00 and going for a lousy 18/23 might just as well turn out to be the decision that will kill me along the process :P
Like another poster said, 18/00 with 15 CHA is better than 18/99 with 18 CHA.
I know that but I keep thinking I'll just take any Str with 18s across the board (except for Wis score), play through the game, grab the Str tome and in the end my char will be better by 3 points.
Of course, at the same time, I realise that not taking this 18/00 and going for a lousy 18/23 might just as well turn out to be the decision that will kill me along the process :P
If you're taking the character through to BG2, I'd possibly agree. But I don't think end-game power BG1 matters. It's power throughout the duration of the game that does. The STR tome comes in Candlekeep I think? I'm normally there after Durlag's Tower and all BG sidequests.
No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
The probability is different (way higher) because you're not rolling numbers belonging to the 1-18 set but rather: - in some cases 3-18 - in others 9-18 - and in some even 15-18
If any roll below, say, a 10 and it gets rounded up it doesn't change the odds of getting an 11, just so ya know. Stat redistribution makes it a little easier to switch around but you can't really afford to be short-stacked for 93 as if you score the minimum (3) on one roll you've got to score 18 on everything else. (Probability approx 1 in two trillion). Nevertheless the simple fact you've been going for four days should demonstrate that the odds are massively against you.
I don't know for sure but I don't think it gets rounded up. It's not like you roll a given stat (which has min req, say, 9) and all the rolls of 1 to 8 get rounded up to 9. I think that if you're rolling a Str for an Elf Fighter (min req 9) the probability of rolling 18 is not 1/18 - it's 1/10.
No, this takes all things in to account. This is the probability of scoring these across 18 dice. It's completely accurate. Besides, minimum requirements don't change probability. These are your odds with any creature that has as many penalties as they do bonuses, though you can correct for discrepancies by adding and subtracting the difference from your total to find your new probability. That is to say if you gain 2 in racial bonuses in one area and only lose 1 in penalties you'd subtract 1 from your total to find your probability.
Just as a demonstration you can do this sum yourself - your odds of getting straight 18s is 1/6^18 or 1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6.
Any roll that's less than 75 gets rerolled. And there's other reroll minimums for each stat that I don't remember
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
The probability is different (way higher) because you're not rolling numbers belonging to the 1-18 set but rather: - in some cases 3-18 - in others 9-18 - and in some even 15-18
If any roll below, say, a 10 and it gets rounded up it doesn't change the odds of getting an 11, just so ya know. Stat redistribution makes it a little easier to switch around but you can't really afford to be short-stacked for 93 as if you score the minimum (3) on one roll you've got to score 18 on everything else. (Probability approx 1 in two trillion). Nevertheless the simple fact you've been going for four days should demonstrate that the odds are massively against you.
I don't know for sure but I don't think it gets rounded up. It's not like you roll a given stat (which has min req, say, 9) and all the rolls of 1 to 8 get rounded up to 9. I think that if you're rolling a Str for an Elf Fighter (min req 9) the probability of rolling 18 is not 1/18 - it's 1/10.
The probability was never 1 in 18, for three D6 the probability of scoring an 18 is 1 in 216... this might explain the basis of your misunderstanding. Also, according to our previous poster that's exactly what happens. I couldn't say I know for certain but it'd make sense if they were trying to stick partially to the p&p rules.
I looked into the stats of rolling a while back but I don't remember everything. I saved some test rolls to get an idea of the chances at opposite ends of the spectrum. Small sample sizes of 100. Human Fighter gets low rolls and Human Ranger gets high rolls:
I looked into the stats of rolling a while back but I don't remember everything. I saved some test rolls to get an idea of the chances at opposite ends of the spectrum. Small sample sizes of 100. Human Fighter gets low rolls and Human Ranger gets high rolls:
I remember a good test was looking into how often a Paladin rolled a 17 vs an 18 for charisma. Again, don't remember results.
Realistically it's way too small of a sample to be conclusive but it definitely suggests that there's a minimum stat round-up involved. Thanks, interesting stuff.
Yesterday I generated an elf assassin for solo run (not HC solo). During that process once I threw 14,14,14,14,14,14 - of course without redistribution. It was the first time I saw 6 identical abilites. It was really funny.
Friend spell was already mentioned You also get the bracers of Dex really early There are also STR belts littering the game
With proper equipment/spell swapping, higher rolls are less than needed and consoling them in will save you time which is more important that ethics in a single player game.
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
That is not true. It means that the number of possible results (from 6 times 3 [3,3,3,3,3,3] to 6 times 18 [18,18,18,18,18,18]) are reduced. Whenever system fails to throw at least 75 it will throw again. So, the throws when sum is below 75 should be subtracted from the possible throws and it means higher chances for a 6*18. It is true that it will be still extremely low but a bit higher then you calculated.
If you still not see it, just count the percentage of throwing 6*18 if system trhow again when sum is below 107. It means that there can be maximum one 17 throw. The chance for 6*18 is ~14% (1/7) in this setup.
90 or higher: 0.007423053208% 91 or higher: 0.003859754233% 92 or higher: 0.001938622967% 93 or higher: 0.000938360936% (Less than 1 in 100,000) 94 or higher: 0.000436533979% 95 or higher: 0.000194568202% 96 or higher: 0.000082779328% (Less than 1 in 1,000,000) 97 or higher: 0.000033469498% 98 or higher: 0.000012791892% 99 or higher: 0.000004591263% (You literally have better odds of winning the English National Lottery at this stage) 100 or higher: 0.000001534911% 101 or higher: 0.000000472980% 102 or higher: 0.000000132511% 103 or higher: 0.000000033132% (Less than 1 in 3,000,000,000) 104 or higher: 0.000000007203% 105 or higher: 0.000000001310% 106 or higher: 0.000000000187% 107 or higher: 0.000000000019% (Less than 1 in 5,000,000,000,000) 18s across the board: less than 0.000000000001% (Less than 1 in 9,000,000,000,000,000)
Just so ya know.
Edit -typo'd
As mentioned, certain race/class combinations greatly improve the odds of rolling in the low 90s. But your point about minimum stats having no effect on the uppermost roles is still valid (For a Paladin, everything up to the "107 or higher" mark is affected by the automatic 17 Charisma). But there's no way to get 18's across the board without rolling 18's across the board.
That said, if a sub-75 rolls get re-rolled, it drastically changes your percentages (they'd go from "*UNBELIEVABLY* unlikely!!!" to a much more reasonable "UNBELIEVABLY unlikely!") because the reroll happens instantly, so for the user, it effectively never happened. That would be great news for people trying to get high end rolls.
However, if sub-75 rolls get rounded up (the same way that individual stats get round up), then the probability of 18s across the board (both the real and the effective probability) would be as you listed.
In simpler terms, let's say I needed to roll a 6 on a d6. My probability is 1 in 6. If everything 3 or below was instantly thrown out and rerolled, my probability would be 1 in 3. But if everything 3 or below was rounded up to 4, my probability would still be 1 in 6 (4, 4, 4, 4, 5, 6).
Looking at Giosanti's numbers, with all those 75's, it's hard to tell if it's rounding, or just the tail of a normally distributed curve. Is anybody particularly good at statistics? What would the median and standard distribution of such a curve look like? I suppose the minimum stats/rounding makes that more difficult too.
Rerolls for sub-75 stats don't change the chance of getting higher than 75 though, it simply guarantees you'll roll at least 75.
That is not true. It means that the number of possible results (from 6 times 3 [3,3,3,3,3,3] to 6 times 18 [18,18,18,18,18,18]) are reduced. Whenever system fails to throw at least 75 it will throw again. So, the throws when sum is below 75 should be subtracted from the possible throws and it means higher chances for a 6*18. It is true that it will be still extremely low but a bit higher then you calculated.
If you still not see it, just count the percentage of throwing 6*18 if system trhow again when sum is below 107. It means that there can be maximum one 17 throw. The chance for 6*18 is ~14% (1/7) in this setup.
You're right if it's rerolling, yeah, my bad. If it's just force-rounding it's not doing it though. Still, the probability holds as a good guideline.
That said, if a sub-75 rolls get re-rolled, it drastically changes your percentages (they'd go from "*UNBELIEVABLY* unlikely!!!" to a much more reasonable "UNBELIEVABLY unlikely!") because the reroll happens instantly, so for the user, it effectively never happened. That would be great news for people trying to get high end rolls.
However, if sub-75 rolls get rounded up (the same way that individual stats get round up), then the probability of 18s across the board (both the real and the effective probability) would be as you listed.
Looking at Giosanti's numbers, with all those 75's, it's hard to tell if it's rounding, or just the tail of a normally distributed curve. Is anybody particularly good at statistics? What would the median and standard distribution of such a curve look like? I suppose the minimum stats/rounding makes that more difficult too.
75 means that average throw is 12.5. The average throw of 3 dices is 10.5. It means that if throws sub 75 are rounded up to 75 then we should see more than 50% of the results in that column. But the real case is far from it and it confirms that sub 75 throws are regenerated instead of rounding up.
If any roll below, say, a 10 and it gets rounded up it doesn't change the odds of getting an 11, just so ya know. Stat redistribution makes it a little easier to switch around but you can't really afford to be short-stacked for 93 as if you score the minimum (3) on one roll you've got to score 18 on everything else. (Probability approx 1 in two trillion). Nevertheless the simple fact you've been going for four days should demonstrate that the odds are massively against you.
This is where you've made your mistake, methinks. The totals of rounding mean that if you score the minimum "3" on one roll and it is increased to 9, then you need to roll an 84 across the other five stats; 16.8 average, not 18 average, for your 93+ (do the maths yourself if you're inclined, but most definitely not 1 in two trillion).
Likewise, if you have a minimum of 15 in a stat (some classes do), this means you only need to roll a 78 or better on 15D6, two minimum stats of 15, you only need a 60 or better on all other rolls to have a score of at least 90.
For Fighter/Mage/Thief there are two or three 9 minimum stats if I recall; so you need an 84 across fifteen dice so long as your low roll is on one of those three. It doesn't make it more likely to roll an 18 on a particular dice, or very likely in general, but it does indeed make it mathematically more likely to roll a 93, simply by making a larger number of the possible results total a 93+.
Like another poster said, 18/00 with 15 CHA is better than 18/99 with 18 CHA.
I know that but I keep thinking I'll just take any Str with 18s across the board (except for Wis score), play through the game, grab the Str tome and in the end my char will be better by 3 points.
Of course, at the same time, I realise that not taking this 18/00 and going for a lousy 18/23 might just as well turn out to be the decision that will kill me along the process :P
18/00 strength is three times more powerful than 18, and noticeably more effective than the low 18/xx rolls.
If you wind up with a strength of anything less than 18/50, you'll be getting +1 to hit and +3 to damage, compared with 18/00 granting +3 to hit and +6 to damage. So, the difference between 18/00 strength and 18/01-50 strength is +2 to hit and +3 damage. In other words, if you're willing to give that up, you may as well drop your strength to 15 now for that extra charisma.
Oh, and don't forget your weight limit. If you're soloing, being able to carry 400 lbs is going to be a lot better than only 220 lbs. You could carry extra suits of armor, if for example you want to wear full plate instead of your usual wizard robes. Carrying any sort of heavy loot would become much easier.
Ok, ladies and gentlemen, we have a decision @Madhax made me change my mind - the 400 lbs argument is a valid one. Since I'll have to carry a lot of back-up shit in my inventory, I need 18/00. Besides, chances are I won't ever make it to Candlekeep (tome) in a no-reload game :P
90 or higher: 0.007423053208% 91 or higher: 0.003859754233% 92 or higher: 0.001938622967% 93 or higher: 0.000938360936% (Less than 1 in 100,000) 94 or higher: 0.000436533979% 95 or higher: 0.000194568202% 96 or higher: 0.000082779328% (Less than 1 in 1,000,000) 97 or higher: 0.000033469498% 98 or higher: 0.000012791892% 99 or higher: 0.000004591263% (You literally have better odds of winning the English National Lottery at this stage) 100 or higher: 0.000001534911% 101 or higher: 0.000000472980% 102 or higher: 0.000000132511% 103 or higher: 0.000000033132% (Less than 1 in 3,000,000,000) 104 or higher: 0.000000007203% 105 or higher: 0.000000001310% 106 or higher: 0.000000000187% 107 or higher: 0.000000000019% (Less than 1 in 5,000,000,000,000) 18s across the board: less than 0.000000000001% (Less than 1 in 9,000,000,000,000,000)
Ok, ladies and gentlemen, we have a decision @Madhax made me change my mind - the 400 lbs argument is a valid one. Since I'll have to carry a lot of back-up shit in my inventory, I need 18/00. Besides, chances are I won't ever make it to Candlekeep (tome) in a no-reload game :P
Enough of rolling. It's time to play some BG!
Good luck! No-reload soloing takes more stones than I've got.
Ok, ladies and gentlemen, we have a decision @Madhax made me change my mind - the 400 lbs argument is a valid one. Since I'll have to carry a lot of back-up shit in my inventory, I need 18/00. Besides, chances are I won't ever make it to Candlekeep (tome) in a no-reload game :P
Enough of rolling. It's time to play some BG!
Good luck! No-reload soloing takes more stones than I've got.
Well, so far I had to run from 3 battles including Tarnesh... For the moment I'm avoiding Silke and Spiders in Beregost, did Marl and Dunkin, made it to Nashkel, doing Carnival at the moment. I'll have to go and finish off Basilisks soon.
I managed to survive a bandit ambush thanks to high AC (Ankheg Plate, Ring + 1, Tower Shield, Girlde of Piercing), not a signle arrow got through, which is quite lucky as I had 9 HP at the time.
I don't sure if what I did is good or poor attempt but this what I did:
For Human Fighter or Mage or Thief the minimum stats are 3 to 18 except of one attribute which is 9 to 18, So I rolled random numbers in those ranges for the 6 attributes and summed them for 100,000,000 times using the Monte Carlo method, this is what I got:
Total Attributes Points - The probability For :
24 or above: 99.999985% ~100%
70 or above: 37.49698% 71 or above: 34.08948% 72 or above: 30.802113% 73 or above: 27.65485% 74 or above: 24.665297% 75 or above: 21.848886% 76 or above: 19.216507% 77 or above: 16.779232% 78 or above: 14.538583% 79 or above: 12.495214% 80 or above: 10.652605% 81 or above: 9.006138% 82 or above: 7.5449004% 83 or above: 6.262758% 84 or above: 5.1477375% 85 or above: 4.189241% 86 or above: 3.3714936% 87 or above: 2.6825159% 88 or above: 2.108718% 89 or above: 1.6376128% 90 or above: 1.2529601% 91 or above: 0.9462681% 92 or above: 0.7026591% 93 or above: 0.51330805% 94 or above: 0.368005% 95 or above: 0.25827% 96 or above: 0.17688198% 97 or above: 0.11827499% 98 or above: 0.076478004% 99 or above: 0.047884006% 100 or above: 0.028689003% 101 or above: 0.016348% 102 or above: 0.008794% 103 or above: 0.0043760003% 104 or above: 0.001976%
The probability For:
Exactly 70 is 3.4074981% Exactly 71 is 3.287366% Exactly 72 is 3.147263% Exactly 73 is 2.9895499% Exactly 74 is 2.816411% Exactly 75 is 2.632378% Exactly 76 is 2.437274% Exactly 77 is 2.240652% Exactly 78 is 2.0433679% Exactly 79 is 1.842609% Exactly 80 is 1.646467% Exactly 81 is 1.4612371% Exactly 82 is 1.282143% Exactly 83 is 1.11502% Exactly 84 is 0.958497% Exactly 85 is 0.81774706% Exactly 86 is 0.688978% Exactly 87 is 0.573798% Exactly 88 is 0.471105% Exactly 89 is 0.384653% Exactly 90 is 0.306692% Exactly 91 is 0.243609% Exactly 92 is 0.18935099% Exactly 93 is 0.14530301% Exactly 94 is 0.109735005% Exactly 95 is 0.081388% Exactly 96 is 0.058607% Exactly 97 is 0.041797% Exactly 98 is 0.028594002% Exactly 99 is 0.019195002% Exactly 100 is 0.012341% Exactly 101 is 0.0075540002% Exactly 102 is 0.004418% Exactly 103 is 0.0024% Exactly 104 is 0.00119%
Sum of Probabilities Is: 99.99999199999999 ~100
I might be wrong, me and statistics are not good friends, but it seems reasonable..
Comments
Oh, and may I say again, the odds for straight 18s on 6 dice is approx. nine-quadrillion to 1. Kind of dizzying, isn't it?
Anyway, absolutely take the 18/00 roll. Obviously there's a 1 in 100 chance of getting that strength. But you've got that strength AND an amazing roll of 90. That's as good as you're likely to get for a long, long time. Like another poster said, 18/00 with 15 CHA is better than 18/99 with 18 CHA. The way I roll is, I work out what stats I'd like before I start, and if it'd take more than like 150-200 rolls to get, I consider it too difficult and instead aim lower. Your roll statisticallly takes a lot longer than 150-200 times.
- in some cases 3-18
- in others 9-18
- and in some even 15-18
Of course, at the same time, I realise that not taking this 18/00 and going for a lousy 18/23 might just as well turn out to be the decision that will kill me along the process :P
I looked into the stats of rolling a while back but I don't remember everything. I saved some test rolls to get an idea of the chances at opposite ends of the spectrum. Small sample sizes of 100. Human Fighter gets low rolls and Human Ranger gets high rolls:
HUMAN RANGER
75 3
76 5
77 12
78 8
79 13
80 12
81 10
82 9
83 7
84 4
85 6
86 2
87 1
88 1
89 5
90 1
91 0
92 0
93 1
HUMAN FIGHTER
75 32
76 16
77 17
78 11
79 6
80 6
81 4
82 3
83 1
84 4
I remember a good test was looking into how often a Paladin rolled a 17 vs an 18 for charisma. Again, don't remember results.
Friend spell was already mentioned
You also get the bracers of Dex really early
There are also STR belts littering the game
With proper equipment/spell swapping, higher rolls are less than needed and consoling them in will save you time which is more important that ethics in a single player game.
If you still not see it, just count the percentage of throwing 6*18 if system trhow again when sum is below 107. It means that there can be maximum one 17 throw. The chance for 6*18 is ~14% (1/7) in this setup.
That said, if a sub-75 rolls get re-rolled, it drastically changes your percentages (they'd go from "*UNBELIEVABLY* unlikely!!!" to a much more reasonable "UNBELIEVABLY unlikely!") because the reroll happens instantly, so for the user, it effectively never happened. That would be great news for people trying to get high end rolls.
However, if sub-75 rolls get rounded up (the same way that individual stats get round up), then the probability of 18s across the board (both the real and the effective probability) would be as you listed.
In simpler terms, let's say I needed to roll a 6 on a d6. My probability is 1 in 6. If everything 3 or below was instantly thrown out and rerolled, my probability would be 1 in 3. But if everything 3 or below was rounded up to 4, my probability would still be 1 in 6 (4, 4, 4, 4, 5, 6).
Looking at Giosanti's numbers, with all those 75's, it's hard to tell if it's rounding, or just the tail of a normally distributed curve. Is anybody particularly good at statistics? What would the median and standard distribution of such a curve look like? I suppose the minimum stats/rounding makes that more difficult too.
75 140
76 100
77 80
78 50
79 49
80 31
81 20
82 18
83 10
84 10
85 6
86 2
87 2
88
89 1
Likewise, if you have a minimum of 15 in a stat (some classes do), this means you only need to roll a 78 or better on 15D6, two minimum stats of 15, you only need a 60 or better on all other rolls to have a score of at least 90.
For Fighter/Mage/Thief there are two or three 9 minimum stats if I recall; so you need an 84 across fifteen dice so long as your low roll is on one of those three. It doesn't make it more likely to roll an 18 on a particular dice, or very likely in general, but it does indeed make it mathematically more likely to roll a 93, simply by making a larger number of the possible results total a 93+.
If you wind up with a strength of anything less than 18/50, you'll be getting +1 to hit and +3 to damage, compared with 18/00 granting +3 to hit and +6 to damage. So, the difference between 18/00 strength and 18/01-50 strength is +2 to hit and +3 damage. In other words, if you're willing to give that up, you may as well drop your strength to 15 now for that extra charisma.
Oh, and don't forget your weight limit. If you're soloing, being able to carry 400 lbs is going to be a lot better than only 220 lbs. You could carry extra suits of armor, if for example you want to wear full plate instead of your usual wizard robes. Carrying any sort of heavy loot would become much easier.
Enough of rolling. It's time to play some BG!
Never tell me the odds!
I managed to survive a bandit ambush thanks to high AC (Ankheg Plate, Ring + 1, Tower Shield, Girlde of Piercing), not a signle arrow got through, which is quite lucky as I had 9 HP at the time.
For Human Fighter or Mage or Thief the minimum stats are 3 to 18 except of one attribute which is 9 to 18, So I rolled random numbers in those ranges for the 6 attributes and summed them for 100,000,000 times using the Monte Carlo method, this is what I got:
Total Attributes Points - The probability For :
24 or above: 99.999985% ~100%
70 or above: 37.49698%
71 or above: 34.08948%
72 or above: 30.802113%
73 or above: 27.65485%
74 or above: 24.665297%
75 or above: 21.848886%
76 or above: 19.216507%
77 or above: 16.779232%
78 or above: 14.538583%
79 or above: 12.495214%
80 or above: 10.652605%
81 or above: 9.006138%
82 or above: 7.5449004%
83 or above: 6.262758%
84 or above: 5.1477375%
85 or above: 4.189241%
86 or above: 3.3714936%
87 or above: 2.6825159%
88 or above: 2.108718%
89 or above: 1.6376128%
90 or above: 1.2529601%
91 or above: 0.9462681%
92 or above: 0.7026591%
93 or above: 0.51330805%
94 or above: 0.368005%
95 or above: 0.25827%
96 or above: 0.17688198%
97 or above: 0.11827499%
98 or above: 0.076478004%
99 or above: 0.047884006%
100 or above: 0.028689003%
101 or above: 0.016348%
102 or above: 0.008794%
103 or above: 0.0043760003%
104 or above: 0.001976%
The probability For:
Exactly 70 is 3.4074981%
Exactly 71 is 3.287366%
Exactly 72 is 3.147263%
Exactly 73 is 2.9895499%
Exactly 74 is 2.816411%
Exactly 75 is 2.632378%
Exactly 76 is 2.437274%
Exactly 77 is 2.240652%
Exactly 78 is 2.0433679%
Exactly 79 is 1.842609%
Exactly 80 is 1.646467%
Exactly 81 is 1.4612371%
Exactly 82 is 1.282143%
Exactly 83 is 1.11502%
Exactly 84 is 0.958497%
Exactly 85 is 0.81774706%
Exactly 86 is 0.688978%
Exactly 87 is 0.573798%
Exactly 88 is 0.471105%
Exactly 89 is 0.384653%
Exactly 90 is 0.306692%
Exactly 91 is 0.243609%
Exactly 92 is 0.18935099%
Exactly 93 is 0.14530301%
Exactly 94 is 0.109735005%
Exactly 95 is 0.081388%
Exactly 96 is 0.058607%
Exactly 97 is 0.041797%
Exactly 98 is 0.028594002%
Exactly 99 is 0.019195002%
Exactly 100 is 0.012341%
Exactly 101 is 0.0075540002%
Exactly 102 is 0.004418%
Exactly 103 is 0.0024%
Exactly 104 is 0.00119%
Sum of Probabilities Is: 99.99999199999999 ~100
I might be wrong, me and statistics are not good friends, but it seems reasonable..