"Bell curve 1 to 6 results on one d6" Topic

I like bell curve distribution dice results but I don't like the uneven jumps between numbers when you add in modifiers. It's not a perfect answer but for my own satisfaction I made a 6-sided die with the following distribution of results: 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, so the middle numbers occur more frequently than the high or low. You will note that this is in fact 12 results. I took a regular d6 and drew a line between the corners of the die on the 1 and 6 faces. Then on the '1' side, I wrote a '4' on one side of the line and a '3' on the other. On the 6 side, I did the same but wrote the numerals '6' and '1'. When die lands on the 'split' faces, I read the result that is pointing the nearest to me (the 3 or 4, or the 1 or 6). This gives me the distribution of 1 to 6 results that my tiny mind wanted. It works well and the reading of the split face results is usually clear. Obsessed I suppose.

Couldn't you just have used a 12 sided die?

I could have used a 12-sided die but that would involve me cutting out 12 little pentagon labels or waiting 2 weeks to get a blank d12 delivered. Is my laziness/cheapness/impatience showing?

Something is showing…

It's certainly an innovative solution. But 2 dice are an easier fix and slightly more Gaussian than your system.

so what good is it? you have the same problem that 2d6 have only with less room for mods before they become counter productive.

You can't roll buckets of dice with 2D6, which is, I presume, why he wants to do it with 1 die.

Another option which is a bit longer but eliminates any interpts with which side to read. Re-roll all 1s and 6s. Low is 3 and high is 4.

Here is a thought. A six sided die is a cube which is a 3 demensional object and doesn't need to be linear therefore make the die start at 345612. That way now the curve is on 4561. See just manipulate the data.

What??

Thanks for the comments thus far.
Quester: With 2d6 the jumps in percentage between dice results varies. For example, if you're shooting at someone and need a 4 or higher (16.7%), but have a -1 modifier because of cover, then the odds go up 11% for a 5 or higher (27.8%). If you needed a 6 or higher (41.7%) but have a -1 modifier then the odds go up 16.7% for a 7 or higher. The effect of the same modifier has different effects depending on what number you started with. That is why I wanted the same amount of variation with the odds between different numbers.

Tabletopwarrior: You are correct that the cube doesn't have to be linear however, no matter which way you number the sides, the odds of rolling any given result are the same. There is no "curve." All results have a 16.7% chance of occurring.

Pigbear: Okay, you made laugh. :)

And yes, BooneC is right, I want to roll a handful of dice so 2 dice per event doesn't work unless I have pairs of the same colored dice and sort thru them. Which again leaves the uneven jumps in odds between results.

Isn't it fun being a gamer so one can obsess about stuff like this?

"You can't roll buckets of dice with 2D6"

You can if you get the dice-in-a-dice that people are selling.

What about using averaging dice that already have this solved?

Also, technically, the 2d6 distribution is a step-function, not a bell curve (aka Gaussian distribution)

Pphalen: Thank you for the suggestion. I haven't seen any dice that have a range of 1 to 6 on a bell curve distribution. Can you tell me where I could get some? My handmade ones don't look very attractive.

pphalen, I didn't say that 2d6 were Gaussian, just that it's "more Gaussian" than Acharnement's cooked die. That's just based on a weak test for normality. I'm sure you will admit that the more dice you use, the closer you approach a Gaussian distribution.

Acharnement,

Pretty neat idea, but I'll bet you'll get arguments in critical situatiions as to what corner is closest.
--
Tim

Re-roll all 1s and 6s. Low is 3 and high is 4.

That should be reroll all 1s and 6s.
1-3 the roll remains the same.
4-6, 1s become 3s and 6s become 4s.

Yes, averaging dice might be an option – however the range of results is only 2 – 5.

They're created by changing the '1' into a '3' and the '6' into a '4' (or you can purchase them). This results in a primitive bell curve.

If your result must be between 1 and 6…

2D6 divided by 2 (rounded to closest) gives a fairly gaussian bell curve (broad normal distribution).

3D6 divided by 3 (rounded) gives a tighter bell curve (a normal distribution with less variance which is closer to a trangular distribution)

1D6 gives a uniform distribution of course (i.e. every outcome is equally proabable).

I ran 1000 simulations of each and charted the results to be sure.

I meant to say 2d6/2 is slightly skewed. Mean = 3.7, instead of 3.5. This results as convention dictates the x.5 outcomes get rounded up (e.g. 11/2 = 5.5, rounded to 6) .

3d6/3 gives a mean of 3.5 with a far higher probability of results in "the middle". 3 and 4 are twice as likely as 2 and 5. 1 and 6 are very unlikely.

Roll a d4 and a d6. Read the d4. If the d6 is 1,2, keep the result. On 3,4 add 1. On 5,6, add 2. That gives you the same distribution you have-- 122333444556

Thanks for the use of your brain power on this conundrum, especially Elcid1099. I will file all the suggestions in my notes but I really wanted a single die that gives results between 1 and 6 with a bell curve distribution.

Here is a thought. A six sided die is a cube which is a 3 demensional object and doesn't need to be linear therefore make the die start at 345612. That way now the curve is on 4561. See just manipulate the data.