Different Dice Combos, Different Distributions

[dark cauliflower]

http://fromkickassistan.blogspot.com/20 ... -dice.html

this is a great blog post. I had no idea that diddling with dice combos would give us all these different distributions. I never thought about it this way. Its way cool that DCC is edging us into these new game freedoms. Makes me wonder if 3d6 for character abilities can be monkeyed with.

1d12 + 1d3 + 1d3 ....

big fat kudos to the blog author for putting the piece up there.

[cthulhudarren]

Personally I think the whole dice chain idea is money.

[dark cauliflower]

I was dorking around with a dice rolling/bell curve program and I got sum pretty interesting results with the 1d12 + 1d3 + 1d3 combo. It turns out that you have the same chance generating a 7-14 ability score, and that's the highest. That contrasts with having the same chance to as getting a 10 or 11, which is the highest with a 3d6.

I'm not sure to think about this. Maybe I'm using the program wrong!

I'm trying to look at this as increasing the chances of not creating a character with bleh ability scores.

[dark cauliflower]

heh, er...

I looked at the 1d14 + 1d2 + 1d2 combo, and its giving me equal chances for rolls from 5-16.

bell curvy

[GnomeBoy]

heh, er...

I looked at the 1d14 + 1d2 + 1d2 combo, and its giving me equal chances for rolls from 5-16.

bell curvy

This all makes sense, doesn't it? Am I just reading it into your posts that this seems strange...?

I mean, make an absurd example, by pushing your d14/d2/d2 example one further -- if you had a d16 + d1 +d1 to generate a 3 to 18 range, well... the chances of getting a result from 3 to 18 are all the same... because the probability of each result on the d16 is the same. In this case there is no curve at all.

Shifting to the d14 only changes things at the far ends. Another shift to the d12 is again only changing the ends of the 'curve'. The larger the 'big' die compared with the rest, the flatter the curve becomes.

[dark cauliflower]

man, I dont know... I'm justing having some fun with the friggin program and dice. Just altering the dice changes how things will play out.

a d10 + 1d2 + 1d6

gives me a equal probability for 9-12.

This is food for thought for me. Do I want to alter how I do my character ability rolls for the game? Would it break the funnel in some way?

[GnomeBoy]

...I'm trying to look at this as increasing the chances of not creating a character with bleh ability scores.

Well, assuming by 'bleh' you mean 'low', what about 6d3? That gives you a nice bell curve, with a minimum result of 6, and a strong average of 12.

[dark cauliflower]

6d3 looks like a good strong chance of middle ground. Im seeing

a 12 with almost 20% chance of happening
11 and 13 with what looks like a 17% each
10 and 14 with 13%

what is that, a 70% chance for a 10-14 range?


-----added----
that looks stronger than the 3d6 which seems to give you what looks roughly a 50% chance to score in that range.

[TheNobleDrake]

Changing the way ability scores are rolled has always been one of the things I fiddle with, spending hours checking the math and running some practical examples for myself... and then choose to leave alone.

For example, I know that my players absolutely love the character they manage to luck out and get an 18 on - enough so that I think significantly altering the chance of getting one is what usually talks me out of a particular change.

Rolling 6d3 would put a .14% chance of getting an 18, compared to the normal .46% chance, so I'd never use it.

Methods other than 3d6 that I have used from time to time, even though no one asked:

4d4+2

1d10,000 rolled on a chart so as to perfectly weight each score so that high scores have the same chance as 3d6, low scores have lower chance, and all the average scores pick up the extras equally.

And my favorite alternate method: Each score has a base of 8, then you roll 7d6. Each d6 is counted by its whole value and can be added to any score of your choice - no splitting a die result between two scores, and no adding more than 10 total to one score (so you have to roll two 5s, a 6 and a 4, or be willing to stack more than two dice on an ability to get an 18).

It's my favorite because it guarantees every character built that way to be average at minimum, but gives a pretty solid chance of having some positive modifiers - but without making it too likely that every score has a positive modifier.

I have not used any of these with DCC yet, but I will probably talk to my players about which one of them to use in the eventuality that I let them play characters with hand-picked occupations to fit their concept.

So that I am not entirely off-topic: I've been a fan of using "odd" dice combinations ever since reading the AD&D 2nd Edition DMG and then trying to figure out exactly why the random encounter charts were 1d8+1d12 instead of 2d10 or 1d20 with another encounter "slot".

[dark cauliflower]

4d4 +2 seemz to give me the same shape as the 6d3 thinger. The probabilities seem to be different though:
12 : 17%
11 and 13: 16%
10 and 14: 12%

which is I tink 73% chance appearing in the 10-14 range.
----------
I never really sat down an analyzed the tables in the dmg. I always was goking at the nudes in the books. That was more fun.

this is kinda fun too.

[dark cauliflower]

hah,

1d14 + 1d3 + 1

gives a great chart. Numbers 5-16 all have what looks like 7.2% of occuring. 4 and 17 almost have 5%. 3 and 18 have 2.4%.

This might be the method for me!

[bryguy]

I kind of like the old Call of Cthulhu way for some stats. 2d6+6 for some and 3d6 for others (of course in D&D, or DCC terms it would be for certain ability scores depending on class... since CoC there are no classes to choose from)

[dark cauliflower]

that's an interesting idea there. Not sure how I'd do a zocchi variation of it at the top of me head but sumtin could be worked out.

There seemz to be an ultimate equalizer with the d16 + 2, where every score has an equal percent chance of coming up. One big flat line.

[bryguy]

i just gave you the variation...
it works! use it!

[bryguy]

it still keeps you within the range but excites the players into thinking they are getting a BONUS!

[Relaxo]

Bit of a drift and maybe a stupid question:

on 3d3, how many doubles are possible? and what are the probabilities of getting one?
on 2d3, there can be only 3 doubles (1,1; 2,2; and 3,3) but in the 2-6, what's the probability of a double in 2d3?

thanks!

[GnomeBoy]

You could always make six rolls -- but the six rolls are different...

roll each set, one time:
3d6
6d3
d14+d4
d12+d5+1
d16+2
d6+d5+d4+d3

(or any other scheme you care to develop, obviously)

That way, you can skew things however you like; you can sorta make sure one or two stats are going to tend to be higher-ish (if that's what you want), but not everything goes that way... The players can roll them in whatever order they like, hoping to get a high Per or whatever stat their going for, but it's by no means guaranteed.

[dark cauliflower]

Bit of a drift and maybe a stupid question:

on 3d3, how many doubles are possible? and what are the probabilities of getting one?
on 2d3, there can be only 3 doubles (1,1; 2,2; and 3,3) but in the 2-6, what's the probability of a double in 2d3?

thanks!

the weird little program I have doesn't tell me this. It just gives me a graff. Maybe one of the math eggheads around here can give you a little equation to figure it out.

[TheNobleDrake]

Bit of a drift and maybe a stupid question:

on 3d3, how many doubles are possible? and what are the probabilities of getting one?
on 2d3, there can be only 3 doubles (1,1; 2,2; and 3,3) but in the 2-6, what's the probability of a double in 2d3?

thanks!

Note: all figures are rounded to the hundredths place.

On 2d3: Each double has an 11.11% chance of coming up, so chance that any double is rolled should be the combination of the chance of each double, or 33.33%.

on 3d3: Each double has a 22.22% chance of coming up as a double, but there is a 25.93% chance for each double to come up if you don't exclude the doubles that are actually triples. Then the chance of any double coming up is again the combined chance of each double, so 66.66%, or 77.79% depending on how you look at it.

[Relaxo]

See, this is why I studied English: I;m actually more confused now. LOL.

[TheNobleDrake]

See, this is why I studied English: I;m actually more confused now. LOL.

Allow me to re-phrase myself in an attempt to alleviate your confusion.

-2d3-
There is an 11.11% chance of both dice coming up 1.
There is an equal chance of both dice being 2, and an equal chance again for both dice being 3.

The chance that the dice are doubles, regardless of the number showing on the face, is 33.33%.

-3d3-
There is a 22.22% chance that exactly two of the three dice come up 1.
The chance that exactly two of the three dice come up 2 is the same, and for two of three dice coming up 3 as well.

The chance that at least[/1] two of three dice show the same number is 25.93%.

The chance that a double of some sort, with the third die never showing the same result as the double (i.e. results like 1, 1, 3 or 2, 2, 1, but not results like 1, 1, 1). is 66.66%.
The chance that a double of some sort, with the third die possibly making it triples (i.e. results like 1, 1, 3 and 1, 1, 1 all being included) is 77.79%