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Bosh
2011-02-17, 11:29 PM
Take a deck of cards and discard all of the cards except for:
Two Aces (which represent 1's)
2 Twos
2 Threes
3 Fours
4 Fives
4 Sixes
1 King (which also represents a six)

Shuffle the cards well and deal them out into six piles of three. Add up the cards in each of the six piles of three and those are your six stats.

This way everyone has a stat total of 74 or an average of 12 and a third, which I just a hair higher than the average value of 4d6 drop the lowest. Some characters will still be more powerful than others (since it's better to have some high and some low stats rather than all mediocre) but the variance will be greatly reduced. It can be tweaked by using a different set of cards, of course.

Probably the fairest way I can think of to do fairly even random characters without doing math to randomly distribute a given point buy among the six stats.

Thoughts?

Fax Celestis
2011-02-18, 12:04 AM
At my most recent game, I tried letting everyone roll1 their own set, and then rolling my own set3. Each player could then choose between their own set or my set: in this fashion, every player was given a choice to ignore the RNG and get the same thing available to everyone else.

15d42, seven times, drop the lowest group, arrange as desired).
25d4 (http://img.photobucket.com/albums/v216/FaxCelestis/bellCurve5d4.png) has a steeper curve than 3d6 (http://img.photobucket.com/albums/v216/FaxCelestis/bellCurve3d6-1.png), and has about the same center point as 4d6b3 (http://www.superdan.net/images/4d6curve.gif). As such, it makes for more average scores in what I feel is a better range and with a better centerpoint. The minimum of 5 helps those people (like me) who roll one stat atrociously low, and the max 20 makes for a once-in-a-lifetime god stat.
3Actually, I rolled three sets and kept the one I liked the best.

Fiery Diamond
2011-02-18, 12:08 AM
At my most recent game, I tried letting everyone roll1 their own set, and then rolling my own set3. Each player could then choose between their own set or my set: in this fashion, every player was given a choice to ignore the RNG and get the same thing available to everyone else.

15d42, seven times, drop the lowest group, arrange as desired).
25d4 (http://img.photobucket.com/albums/v216/FaxCelestis/bellCurve5d4.png) has a steeper curve than 3d6 (http://img.photobucket.com/albums/v216/FaxCelestis/bellCurve3d6-1.png), and has about the same center point as 4d6b3 (http://www.superdan.net/images/4d6curve.gif). As such, it makes for more average scores in what I feel is a better range and with a better centerpoint. The minimum of 5 helps those people (like me) who roll one stat atrociously low, and the max 20 makes for a once-in-a-lifetime god stat.
3Actually, I rolled three sets and kept the one I liked the best.

I Like that idea. If I ever get the chance to run another game, I'll do something along those lines.

HunterOfJello
2011-02-18, 12:25 AM
I wish I had paid more attention in my probability course so I could analyze this method or remember a program that could assist me, but I think I can remember enough to do some pencil and paper work.

~

I'll start with comparing this method to the 3d6 method.

First of all, the card method should end up giving a much better spread of stats because of the larger number of high values compared to rolling 3d6. It does have the flaw of removing the chance of a lucky player rolling several very high rolls and getting 18 for every stat.

-The average outcome of a 3d6 roll is 10.5 where the average outcome of the card method is 12.3

-The chance of having an 18 in one of your stats is 0.463% in the 3d6 method where you have 1.226% chance in the card method.

-An even better factor is that you cannot get a 3 for one of your scores using the cards method

-For the new lowest score (4), the chance of gaining such a score in the 3d6 method is 1.85% and in the card method is 0.0817%

~

Compared to a Point-Buy, the highest point-buy equivalent you're going to come out with will be around 36. The lowest point buy i did was 26 points, although you may be able to go a bit lower.

Point-Buy has the advantage of never giving a character a natural stat lower than 8, but also limits how high those stats go above the 8 starting value.

~

If anyone has a better knowledge of probability than I do, I'd love to see some comparison graphs and information about this idea.

Bosh
2011-02-18, 12:36 AM
Note: also for my system (and any rolling system dammit) I prefer rolling down the line instead of arranging to taste, makes things truly random :)

Fax Celestis: like you said, rolling more dice works very well if you want a smaller average range of stats. Having a tiny chance of getting a god stat is also fairly interesting, of course your set-up is trying to do something very different from my set-up.


I'll start with comparing this method to the 3d6 method.
I tried to set it up to match 4d6 drop the lowest results (at least roughly). If you want to match 3d6 results, then just get three Aces and three of each from 2-6 and shuffle and deal those out instead.


It does have the flaw of removing the chance of a lucky player rolling several very high rolls and getting 18 for every stat.
Feature, not bug. That's exactly what it's intended to do. Basically give people random stats without having anyone be too unlucky or lucky. Although, as you do point out there is still some point buy variance, but I reduced it as much as possible without using more math (for example writing up a list of every possible point buy configuration and randomly choosing one).


Compared to a Point-Buy, the highest point-buy equivalent you're going to come out with will be around 36. The lowest point buy i did was 26 points, although you may be able to go a bit lower.
Depends on how you value stats lower than 8 wrt point buy.

The main point about using cards is that while it is random each event is not independently random. For example if you get an 18 on one stat it lowers your average for all of the other stats, which dice doesn't do. This limits the variance greatly and makes for less point buy differences while still making it random.

Serpentine
2011-02-18, 12:43 AM
I have one, that I give people the option of using, which is something like this: one 9 or less, one 10-11, one 12-13, one 14-15, one 16-17 and one 17-18. I had another version I liked more, but I forget it...

RS14
2011-02-18, 02:03 AM
I think it is better than 4d6b3, but summing the ability scores does not accurately measure the value of that set.

I tried something similar, except generating scores with the same point buy value. Even then, there were some that were weaker than others, due to the weaknesses of point buy. (It was, however, a low-powered game, in which those small differences were magnified)

Here, for instance, a character could have

13 13 13 13 11 11,

or

18 17 15 12 8 4

which is likely more powerful.

Still, I think it's a good idea.

HunterOfJello
2011-02-18, 02:19 AM
The main point about using cards is that while it is random each event is not independently random. For example if you get an 18 on one stat it lowers your average for all of the other stats, which dice doesn't do. This limits the variance greatly and makes for less point buy differences while still making it random.

Very true.


I wrote out the statistics for some of the stuff to show the differences. I thought you and others might be interested in the percentages that pop up.

I didn't write out the 4d6b3 method before because I couldn't remember how it worked. I think I got it now. It should go something like this:

-Average outcome of 4d6b3 is about 12.2 where the cards give 12.3

-The chance of getting a 3 with 4d6b3 is 0.0772% and with cards is 0%

-The chance of getting a 4 with 4d6b3 is 3.086% and with cards is 0.0817%

-The chance of getting an 18 with 4d6b3 is 1.8519% and with cards is 1.226%

-The chance of getting a 17 with 4d6b3 is something like 4.63% and with the cards is something like 4.902%. (This part is harder to calculate).

If any of my math is wrong, I welcome corrections. For more info:

I stole the average rolls for 4d6b3 from this post (http://forum.rpg.net/showthread.php?t=94134) on another forum. It looks legit enough and sounds right.
~
The chance of getting a 3 from the card method is 0% because you can't pull out 3 aces.

However, you can get a 3 when rolling 4d6b3. The only way to accomplish this is to roll four 1s all together. The odds of any six sided die rolling a 1 is 1/6, so the probability of rolling four 1s is (1/6)(1/6)(1/6)(1/6) or 1/(6^4) which is equal to 1/1296 or 0.000772 . By moving the decimal place over we can get a percentage of 0.0772% for the chance of rolling a 3 from 4d6b3.
~

The chance of getting an 18 with the cards is simple to calculate. For the first card, there are five possible 6s to pull out of the deck, so the first card's chance of being a 6 is 5/18. Since you do not replace cards, there is one less 6 in the deck and one less card, so the possibility of the next 6 is 4/17. The third is then 3/16. Multiplied together to obtain the probability we get (5/18)(4/17)(3/16)= 0.012255 or 1.2255%.

The chance of getting an 18 by rolling 4d6b3 is also fairly easy. In this instance we must roll threes 6s and then a 1, 2, 3, 4, 5 or 6 on another die. We must also consider the order that the die roll in. So, we get a set of numbers that look like
666X
66X6
6X66
X666
where X=any number from 1 through 6. Therefore we have 6 possibilities for the outcome of the extra die and four possible arrangements of where that random die appears in the order. In which case we have 6x4=24 possible arrangements in which three 6s and a number from 1 through 6 can appear. We divide this by the total possible outcomes to get 24/1296 = 0.018519 or 1.8519%.

~
Last but not least I wanted to see what the probability of getting a 17 for each instance was. So, for the card method we have to draw two 6s and one 5 from the deck. These can appear in one of three patterns
656
665
566
and the possibilties of drawing each card are different each time. The probability for 656 is (5/18)(4/17)(4/16), 665 is (5/18)(4/17)(4/16), 566 is (4/18)(5/17)(4/16). In the end we realize that each of these is equal to one another so we take the three and add them up to get the probability of 0.04902 or 4.902%.

The explanation for getting a 17 out of 4d6b3 is a bit more complicated. We use the same method as we did for getting the 18. Getting a 17 can only be accomplished by having a 665 combination from three of the die. The fourth die can be any number between 1 and 5, but cannot be a 6. So we generate all the possible arrangements:
665X
656X
6X56
65X6
6X65
66X5
566X
56X6
5X66
X566
X656
X665
That's 12 different arangements using the variable X which has 5 possible outcomes so we get 12x6=60 and compare that to the total possible outcomes of 1296 to get 60/1296=0.046296 or 4.6296%.

~


~

Generating probabilities for anything outside of the rarer outcomes is going to be more difficult since I've forgotten how to use probability formulas.

Overall, I think the card method will give you slightly better stats than 4d6b3 when considering a single stat roll, and a lower total value for your overall stats. This could be good for generating more 'natural' characters and allowing a larger possibility to have low and high stats for different abilities on the same character (a feature which is absent from the other stat generating methods).

Considering all of this, I think I'll use this method for the next campaign I run. I like the idea of characters with both high and low stats, but haven't come across a system that allows such outcomes easily.

~

Oh! It's also worth noting that the widest stat spread that this card method can give is
112 = 4
233 = 8
444 = 12
555 = 15
566 = 17
666 = 18
which would actually make a very fun character.

PetterTomBos
2011-02-18, 03:08 AM
I'll have a look at it when I have free time :)

Currently having statistics 101, and programming, so I'll get a little practical practice :)

Dr.Epic
2011-02-18, 03:56 AM
Sounds like it would take too much time: going through the deck and removing the cards and you can one have one person generate the stats at a time.

Kurald Galain
2011-02-18, 04:34 AM
Making a "less random" method of random stat generation strikes me as self-contradictory. If you don't like random stats, don't use random stats.

Totally Guy
2011-02-18, 04:52 AM
Dice are memoryless. Card's aren't. I can see the advantage in doing that. Good idea!

Bosh
2011-02-18, 05:00 AM
Making a "less random" method of random stat generation strikes me as self-contradictory. If you don't like random stats, don't use random stats.

In order to randomize how your stats are distributed instead of randomizing how high your stats are. Sure some people want characters to start off sometimes more powerful than other times but that's not only ONLY reason to have random char gen (I like having random numbers act as a Rorschach test to give me character ideas).


Sounds like it would take too much time: going through the deck and removing the cards and you can one have one person generate the stats at a time.

Yup, takes more time. But if you're going to play a character for a year...


This could be good for generating more 'natural' characters and allowing a larger possibility to have low and high stats for different abilities on the same character (a feature which is absent from the other stat generating methods).
Yup, just what I was trying to do. You can also easily change the value of the results by changing what cards you shuffle out.

FelixG
2011-02-18, 06:33 AM
the best system my friends and I have found?

2d6+6

gives you an 8-18 range with an average of 13 which is pretty nice

Frozen_Feet
2011-02-18, 09:06 AM
Less random? Need no such thing. My favorite is still roll 3d6, in order, for each stat. If total modifiers add to less than 0, roll again. Means everyone has at least average of 10 overall. If someone happens to roll three 3s and three 18s, that's their problem. :smallbiggrin:

PetterTomBos
2011-02-18, 09:09 AM
Less random? Need no such thing. My favorite is still roll 3d6, in order, for each stat. If total modifiers add to less than 0, roll again. Means everyone has at least average of 10 overall. If someone happens to roll three 3s and three 18s, that's their problem. :smallbiggrin:

Problem? What problem? Did anyone see a problem? :D

(Unless the 3's are in con and int tho) But a 18 int/con/dex mage could be awesome!

randomhero00
2011-02-18, 02:28 PM
Easiest way is to roll 3d6, reroll all ones. Which gives a min score of 6 and max of 18. Perfect.

If you want even higher, but still random do the above but add an extra die. So 4d6 and drop the lowest die + reroll all ones.

navar100
2011-02-18, 03:56 PM
Roll 4d6 drop lowest three times. Those are three of your scores.

Take any one score and subtract it from 27. That is your 4th score.

Take one of the remaining scores and subtract it from 25. That is your 5th score.

The last number subtract from 23 for your 6th score.

Add +2 to any one of the six scores.

Options: Must have minimum of 7 in a score. Must have maximum of 18 in a score even after adding the +2. Don't add the +2.

Results: If you roll average or low, subtraction gives you good scores anyway. Say you roll 11, 7, 10.

27 - 11 = 16
25 - 10 = 15
23 - 7 = 16

Your array is 16, 16, 15, 11, 10, 7 which is rather nice. You have a +2 to play around with. One of the 16s can be an 18. Having the 15 be a 17 instead is cool too. The 11 can become a 13 if you need it for feat prerequisites. There are also racial modifiers to consider.

Say you rolled well: 18, 15, 14.

27 - 18 = 9
25 - 15 = 10
23 - 14 = 9

With the +2

20, 15, 14, 9, 10, 9 (possibly for a high-powered campaign)
18, 17, 14, 9, 10, 9
18, 15, 16, 9, 10, 9
18, 15, 14, 11, 10, 9

Bosh
2011-02-18, 05:35 PM
Oh another quick statistical comment, technically my system has just slightly higher results than 4d6 drop the lowest, but a small portion of 4d6 drop the lowest characters will have such low stats that they're unplayable and are tossed out, if you remove these characters, the average 4d6 drop the lowest stats rise (by how much, I don't have the stat-fu to figure out) which probably puts them just a hair higher than my system on average.

BenTheJester
2011-02-18, 10:31 PM
Take a deck of cards and discard all of the cards except for:
Two Aces (which represent 1's)
2 Twos
2 Threes
3 Fours
4 Fives
4 Sixes
1 King (which also represents a six)

Shuffle the cards well and deal them out into six piles of three. Add up the cards in each of the six piles of three and those are your six stats.

This way everyone has a stat total of 74 or an average of 12 and a third, which I just a hair higher than the average value of 4d6 drop the lowest. Some characters will still be more powerful than others (since it's better to have some high and some low stats rather than all mediocre) but the variance will be greatly reduced. It can be tweaked by using a different set of cards, of course.

Probably the fairest way I can think of to do fairly even random characters without doing math to randomly distribute a given point buy among the six stats.

Thoughts?

I had a DM do something similar, but I think the values he used were different.

After the cards were distributed, you could also take 2 piles and trade any number of cards between them, allowing for some stat customization.

Murphy80
2011-02-19, 12:24 PM
Take a deck of cards and discard all of the cards except for:
Two Aces (which represent 1's)
2 Twos
2 Threes
3 Fours
4 Fives
4 Sixes
1 King (which also represents a six)

Shuffle the cards well and deal them out into six piles of three. Add up the cards in each of the six piles of three and those are your six stats.

This way everyone has a stat total of 74 or an average of 12 and a third, which I just a hair higher than the average value of 4d6 drop the lowest. Some characters will still be more powerful than others (since it's better to have some high and some low stats rather than all mediocre) but the variance will be greatly reduced. It can be tweaked by using a different set of cards, of course.

Probably the fairest way I can think of to do fairly even random characters without doing math to randomly distribute a given point buy among the six stats.

Thoughts?

We use 20 cards, 18 divided (in order) for the 6 stats + a 6 and a 1(added after the other 18 are revealed). The 6 allows each player to get a decent score where they want (max 18). The 1 will turn an odd score into an even score.

Dalek-K
2011-02-19, 12:29 PM
I just roll

1d8 + 10

or

2d4 + 10

For each stat... Easy, effective, and I don't need to go buy a pack of cards :smalltongue: