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## Comments

3,684251Rolling at 1 re-roll a second you would expect perfect 18s to turn up once in 101559956668416 seconds on average. I make that 3218240.825 years at 365.25 days a year.

So sure you could roll it, but it would take an average of 3.2 million years. Imagine the frustration when you notice it just as you click re-roll.

124I'm thinking a joint effort here, I can muster 4 comps myself, obviously a lot more is needed, I guess we want the time down to less than a year.

3,684214251Having one stat between 17-18 (Paladin) decreases the odds hugely - you would multiply the rest of the combined odds by two, rather than 216, assuming they're equal chance.

251Bear in mind this is an average, not a guarantee - it could happen first roll, or it could take 20 million years.

1,4182,989Usually ctrl-8 is faster.

1,050Windows' Calculator says... 9,8464004200485121993638286900206e-15... That comes up to about... 0.00000000000001% chance of rolling it?

168they give 0,000000000018413% to roll 108 points...

3,00953,415If the game uses a standard number generation method for every score from 3-18, checks the scores against class/race minimums, and raises them to the minumum if necessary, then the odds of "rolling" an 18 are unchanged (i.e., before you re-assign points). In this method, a paladin would get a 17 Charisma like 95%+ of the time, since every generated score of 16 or below would get bumped to 17, but he'd still have to "roll" an 18 to have 18 Charisma (before you reassign points). So, to get all 18s, you'd still have to have the random number generator generate six "raw 18s".

If the game uses a mechanic that first looks at the allowed range for each score (based on class & race), and then generates a score based on a certain min and max, then yes, the paladin's high minimum Charisma increases the odds of "rolling" an 18.

168the column on the right shows the chance to roll *exactly* the value on the left, and its modelled for a mage (who has only one minimum score - INT must 9 or higher), paladin has usually 3 points more than the table shows (Paladin has 75% to have CHA17 and 25% to have CHA18)

2,029Obviously, figuring out the actual probability in the game is somewhat complicated, given uncertainties in the RNG, different racial/class minimums, and the fact that the game won't ever roll below 75 total. If we figure out precisely how the RNG works and define a race and class we can theoretically compute a probability of rolling all 18s, or if we don't want it to be a pain in the ass we can write a computer program to brute force most of it for us.

5,018Needless to say the DM disallowed the character. The DM told me later that he almost allowed the character but fully intended to infect him with stat reducing diseases that magically bypassed the Paladin's immunity, starting with Charisma. My DM could really be a piece of work sometimes. I thought it was awesome.

6,4563,009If, on the other hand, you are concerned only about the *sum total* of the dice, not the individual die results, then you will find that the possible outcomes collapse from 216 into only 56. Let me expand on my earlier example. Suppose you roll a 2, a 3, and a 4, giving you a result of 8. You could have rolled 2, 4, and 3 to arrive at the same result. Since we care only about the sum and not the individual results, the rolls of 2/3/4 and 2/4/3 are the same. When you examine the results this way, what you will find is that the results are as follows:

3 has 1 outcome, 4 has only 1, 5 has 2, 6 has 3, 7 has 4, 8 has 5, each of 9 through 12 has 6, 13 has 5, 14 has 4, 15 has 3, 16 has 2, and 17 and 18 both have only 1, for a total of 56.

Following this analysis, p(rolling an 18) = 1/56. Given that the end result is our goal rather than the individual rolls, this is a more accurate method, *in my opinion*.

You may continue to disagree with me if you so desire but that does not invalidate my results. Fortunately for you, my username is irrelevant and thus you need not waste any mental energy worrying about it.

168But you do not roll a dice with 56 faces on each with sum of the numbers but you roll six times 3 dices with 6 faces. There is no difference if you roll 18 times dice with 6 faces altogether or each separately or if you roll six times 3 dices with 6 faces. The probability of 18 in some stat is 1/216. The probability of all max stats is 1/(6^18). But due to the fact that you cannot have a PC with stats like 3/3/3/3/3/3 the probability of 18/18/18/18/18/18 is somewhat higher that 1/(6^18) (the table here http://baldur.cob-bg.pl/bg2?pg=1,1,0 is assumed to a character minimum is 3/3/3/3/9/3 (mage) - if higher are the minimum stats the easier is to get very high stats)...

2513,0092512513,009251251168are you studying math (I hope not :E) or the math in your nick is just for camouflage? Take 2 dices with 6 faces and roll about 100 times (if you roll a 1000 times it would be better), note the scores and then look how many times you rolled sum 2, 12, 5 and 7

I say that you will have

2 about 2,8% times

12 about 2,8% times

5 about 11,1% times

7 about 16,7% times

You say you will have

2 about 4,8% times

12 about 4,8% times

5 about 9,5% times

7 about 14,3% times

Then come back and say who was closer to truth...

3,6842,269