Does anyone know what the average would be for the "roll four dice, and take the best three" method?  I tried to figure it out myself, and came up with 12.132716 as a result, but I'm not certain if I crunched the numbers correctly or not.

I asked my number-crunching friendly statistician, and he came up with  12,244599. I can't say I understand exactly how he got there, but I trust him when it comes to numbers.

Edit: More exactly his result was 12,25 - 7/1296.

I did a quick and dirty emprical check on that average and agree with your friend.

Aggregate sum of the values for all permutations = 15869.  Number of permutations is 6^4 = 1296. Result is 12 317/1296, which indeed does work out to 12 324/1269 - 7/1269.

BTW since it's a quick thing to do, and averages can lie , here is the data for the probability of each possible value from 3 to 18.  The chance is the number on the left divided by 1296.
Result Occurances
3 1
4 4
5 10
6 21
7 38
8 62
9 91
10 122
11 148
12 167
13 172
14 160
15 131
16 94
17 54
18 21

Remember I said averages can lie to you? Just from the average you might think that the single most common result is 12, but in truth 12 is edged out slightly by 13, and 14 & 15 are moreso common than 11 & 10, respectively.

If I remember correctly, that's very close to the result that a bunch of math/programmer geeks came up with on ENWorld.  They also determined that a 31 point buy creates characters equivalent to the average results of 4d6k3 dice rolling, confirming my suspicions that 25 point buy creates bitch ass wimp characters.  

Ah, so I did miscalculate.

Thanks for the info.

@Cyberzombie: It depends partially on what BP cost you assign to rolls below 8. If you just assume those are 0BP, the same as 8, then the average is just over 29 BP before you factor in the reroll rules. The reroll rules, which i don't remember off the top of my head, is likely how they are getting to 31BP.

So yes, 25BP is pretty damn weak. But 28BP is quite comparible because with random rolls you can get a lot of those "wasted" odd numbered rolls (almost exactly 1/2 the rolls result in an odd number).

They used the rules for hopeless characters -- ones so pathetic you trash them and reroll -- to come up with the 31 points.  After all, a variant house rule like point buy should follow the same criteria as the ACTUAL character creation rules.  :deviousgrin:

-- Point buy hatah Spikey

Huh?  Point Buy isn't a house rule.  It might be listed as an offical variant in core books (been so long since i even looked at that part of the rules i don't remember what the base method is), but that is something entirely different than a house rule.

I'm not sure exactly WTF you are talking about with "same criteria"? Which criteria?

I'm OK with giving point-buy slightly less power than random rolling, because you do get more control. So if rolling 4d6 keep 3 combined with the hopeless rule gives an average of 31 points (which sounds reasonable), I'd have point-buy give 28 points.

Quote from: blakkieHuh?  Point Buy isn't a house rule.  It might be listed as an offical variant in core books (been so long since i even looked at that part of the rules i don't remember what the base method is), but that is something entirely different than a house rule.

I'm not sure exactly WTF you are talking about with "same criteria"? Which criteria?

Sorry.  I have a long-term hate going on for the supporters of point buy over at ENWorld.  The thing that annoys me the most about it is that they act like it is the official way to create a character, when it's an optional rule buried in the DMG.

The "house rule" part comes in because most of that same group of people are rules Nazis who get all snooty over any sort of variant rule, or any interpretation of the rules different than their own.  I find it ironic and annoying that that same group also clings to an optional rule that, if they use it, means that they have house rules.

Let me try again on my last sentance of the previous post: 4d6k3 creates average characters that are the equivalent of a 31 point buy character.  Therefor, if the two generation methods are supposed to be equivalent, then the "standard" point buy should be 31.  I think that the mathematical analysis backs up my anecdotal evidence that the point buy amounts in the DMG create retard sub-standard characters.  

If anyone wants to try to find the ENWorld thread -- and has the Search capability -- it was started by Charwoman Gene (which is why I clicked on it in the first place) and is at least one year old.  It was darn interesting reading.  

How 'bout this? People roll their stats, 4d6 drop lowest, in order. No rearranging. The first roll goes in str, second in dex, etc.

But here's when it gets fun.

Let them swap! Anybody can swap their Strength or Intelligence or whatever stat for anybody else's. "I'll swap Str scores if you'll swap Wis scores, too - I want to play a cleric." "OK, I'll get a high dex from her, and then swap it with that guy who has the high con I want..."

thought I guess this would only work in groups that have lots of players.

I haven't been back to ENWorld in a very long time. But now I get where you are coming from. Ya, that is a rather odd view to have. Likely what it is is that Point Buy fits their personality. Plus that it is right there in the Chargen program gives it an extra level of authority that satisfies their "canon" itch. *shrug*

Quote from: CyberzombieLet me try again on my last sentance of the previous post: 4d6k3 creates average characters that are the equivalent of a 31 point buy character.  Therefor, if the two generation methods are supposed to be equivalent, then the "standard" point buy should be 31.  I think that the mathematical analysis backs up my anecdotal evidence that the point buy amounts in the DMG create retard sub-standard characters.  

Unfortunately I find that a flawed, and incomplete analysis. In no small part because of those odd numbered rolls I talked about. Usually you'll have one, maybe two stats that you'll want to raise as you rise in levels. Of that average of 31 there are therefore approximately 3 BPs (actually more) of that is tied up in odd values. Only some of those points are going to be of any real value, and once you get to 2 odd rolls or more (which is the norm, not the exception) some of those BPs you'll have to wait 8 levels if not more to take advantage of. That translates to a lot of extra +1's to rolls in the meantime that a Point Buy character can have.

In short, averages have a tendancy to lie.

Now that is the first case I've ever seen that actually makes some sense!    I still don't entirely buy it -- if I remember right, odd scores are pretty much unavoidable with 31 pb, too -- but at least you have a point, unlike the ENtards I've fought with in the past.  

So -- what do you think a pb equivalent to 4d6k3 is?

Quote from: CyberzombieNow that is the first case I've ever seen that actually makes some sense!    I still don't entirely buy it -- if I remember right, odd scores are pretty much unavoidable with 31 pb, too -- but at least you have a point, unlike the ENtards I've fought with in the past.  

Well there IS a reason I don't go to ENWorld anymore. :heh:

With 31 Point Buy you end up with one (or three or five) odd numbers. But it is your choice to keep it to one, and your choice which one it goes into, and that is the difference.  It is easier to target that extra odd one in a stat you intend to raise. Then you only have to wait till you hit 4th for the payoff.

As for exactly how many BP i'd value it at, that is a bit more subjective in what you value the risk of rolling crappy at.

Me i tend to like to encourgage people to take risks, or at least reward them for it. That is why I see 28 BP as more acceptable. However 29BP is likely closer, maybe even edging into 30BP. I haven't done a full analysis, including looking at the full distribution of the rolls. That's just a gut feeling, although typically my mathematical "gut feelings" are fairly accurate.  The wildcard, like i mentioned before, are those sub-8 rolls and how you view those.

That said what we often do is allow 2 full sets of rolls, and the player takes whichever of the 2 full sets they like better.  That falls a lot more in line with 30-32 BP. We tend to have more grinding type games, so to save character generating time and coffin costs we have that extra filtering of the weak out right up front. :mourn: