Interact with results |

*spread of values*in GURPS by using

*differently shaped dice*. Today, I'll look at

*different distributions*along the series of integers

**3:18**.

### The Standard Distribution

All of these

*distributions*are the "*normal distribution*" or "*bell curve*" (Perhaps technically, not the*normal distribution*because it is a*discrete series*, but blah.) This is called a*bell curve*normally because it has an even*rise*and*fall*when looking at a*frequency chart*, with the*most common values*being*close to the mean (average)*. The second*graph*illustrates this. If you look at the*key in the graph*, you will see**two numbers**, the*mean (average)*and the*standard deviation*. The*standard deviation*is kind of a way to tell how*random the numbers are*. If it is a very big*standard deviation*, the*numbers will vary all over the place*; if the*standard deviation*is very small though, it means that the numbers will generally be*closer to the mean*.### GURPS Default: 3d6

From Wikipedia |

GURPS, by default uses a

**3d6***dice roll*for almost all*throws*besides a few*random lookups*,*damage*, and*social encounters*. When throwing**3d6**, the*standard deviation*is**2.96**. The*average*for all combinations is always**10.5**. The*standard deviation*is a*special number*that says, when using a*normal distribution*, that you will have a**68% chance of rolling the average**, plus or minus the*standard deviation*. For**3d6**this means a*range*of**7.54:13.46**, or probably since we are dealing with*dice*,**8-14**. Playing GURPS, you probably notice you get these*numbers*a lot. A*smaller**standard deviation*more greatly rewards*higher stats*, and a*larger standard deviation*lends leniency to*lower stats*.### No Curve: D&D style

If you look at the

*chart*, you can see a flat line that is matched to "**1d16 +2**". There is technically no (normal)**16-sided dice**, but it can be*simulated*by using**2d4**or**1d8**and a**1d2**among other things. My personal favorite when doing this is to use a normal*six-sided die*with an*8-sided die*. The value of the*8-sided die*is as shown, but add**8****more**to that*number*if the*six-sided die*has an*even number*(I hate*flipping coins*!) and you can do these**both**at the*same time*, You get the*biggest possible standard deviation*with this method:**4.61**, which gives a**68%****chance**of a*number*from**5.89**to**15.11**, or rounding to**6-15**. Each*number*has exactly a**1/16****chance of occurring**, which almost matches what we got when we*round*. Though, a**6.25% chance**makes for lots of*critical failures*and*successes*. If you really want to*play*this way, you might want to change*critical success*to only occur on**3**, and*failure*only on**18**... and it will still be more common than the normal**3d6**. Having*no curve*can be seen as more exciting because things feel a little less predictable. It becomes possible to get lucky and do*impossible feats*on*the regular*, or*catastrophically fail*on the*most**mundane tasks*.### The Smallest Standard Deviation: 15 pennies

We have a few more shown, but today has been busy, so I'll skip straight to the other extreme: throwing

**15 pennies**, counting the*number of heads found*, and adding**3**. This has a*standard deviation*of**1.94**, or a**68% range of 8.56 to 12.44**, or*rounding*,**9-12**. More than half of the results you can...*flip*, I guess instead of*roll*, consist of the**4 numbers**in the middle.**4 numbers**are**twice as likely**as*any of the other numbers**that outnumber them***3:1**. This*small standard deviation*makes*skill checks*and*contests*extremely reliable, and increases the*value*of*high attributes*much quicker... at the expense of*diminishing returns*kicking in much earlier as well.*Critical successes*and*failures*will be*extremely rare*at this rate. To be close to the same*ratio of chance*,*Critical failures*should occur when*rolling*a**15 or higher**, and a*critical success*should occur when*rolling*a**6 or lower**.### Other Notes and Wrapping Up

I'm not sure how practical using

*any other dice rolling scheme*would be. Like I said earlier, a*large standard deviation*favors*low skill levels*and increases the*odds*of*criticial failures*and*successes*; while a*smaller standard deviation*favors*higher stats*and*decreases*the*odds*of*critical failure*and*success*. I don't know if these should cost anything as a*quirk*or a*perk*, but practically speaking, at least, I'd be annoyed by anyone who wanted to*shake***15 pennies**every*skill check*. I didn't detail all the*other possible curves*which are just more or less gradients from a smaller to a*larger standard deviation*with less pronounced effects compared to the**two poles**I did discuss, but might be easier to handle.**5d4-2**, in fact, comes close to the*distribution*in*Fate*if that is something you like... I personally hate*4-sided dice*though... so, that's that.**Precis**- A look at other*dice distributions*in GURPS without changing the**3-18 spread**.
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