Normalized d20 dice

[Marvinrah]

With the proliferation of d20 games, I was wondering if the concept of a "normalized" die would be popular amongst players. This normalized die would generate results from 1 to 20, but would have more than 20 sides and would have weighted probabilities toward the median value by duplicating certain numbers. The goal is to simulate a more "typical" result instead of a uniform probability for all results. The most important factor is to remain fully compatible with the d20 system. This normalized d20 could be interchangeable with the regular d20 whenever a situation called for a less uniform distribution.

Using a thirty-sided (30) die, number the facets in the following configuration:
01-06 x1
07-09 x2
10-11 x3
12-14 x2
15-20 x1

If this idea is popular, maybe we can suggest it to a dice manufacturer since they have existing d30 molds.

 

[Mr Fidgit]

personally, i like the idea of having an equal chance to roll any number (good, bad or average) rather than a weighted chance to get a 'typical' result. just IMO

and welcome to the boards Marvinrah

 

[Kamard]

Huh, thats interesting.

Simulates a sort of bell curved d20 on a d30...

I'd buy one, just to have one more goofy dice.

 

[dafrca]

Huh, thats interesting.

Simulates a sort of bell curved d20 on a d30...

I'd buy one, just to have one more goofy dice.

I have to agree, I would buy one just for fun. However, I would not use it as I like the even chance rather then a forced bell curve.

dafrca

 

[Harlock]

Actually, this is a good idea I think for skills in the D20 system. I rather prefer a 3d6 approach to those as it places more emphasis on buying ranks in skills and less on dumb luck. A higher skill rank mean that even on the greatl increased median rolls of 3d6 you have a good chance of success. Also, the decreased chance of a "lucky" high roll to compensate for those 2 crummy skill points you slapped into diplomacy suits me just fine. I'd be interested in a die like this since the molds are already made. I'd more interested in a ratio-weighted 36 sided die.

 

[MThibault]

On the other hand, you could just roll 2d10 and simultaneously translate the rules that refer to a "Natural 1" to "Natural 2". Wouldn't that provide a bell curve with pretty much the same range of possibilities. Average roll will increase from 10.5 to 11 due to the loss of the number 1, but that isn't much difference.

Cheers.

 

[Quickbeam]

Certainly a very interesting concept. But for my part, I'm happy with my d20 having only one of each number, instead of weighting the odds towards the median. Besides, this would make having a "lucky" die less likely to occur .

And welcome to EN World as a member and poster, Marvinrah!!

 

[tarchon]

A lot of systems already do that by various means, though I think with d20, the system is really designed with an implicit assumption that the d20 will have the large variance that it does (SD ~ 5.8, over 1/2 the mean). The magnitudes of the modifiers in particular derive a lot of their relative significance from the size of the variance and the flatness of the distribution.

I've actually thought about implementing a software die roller with customizeable variance or even mass function, but I doubt if there would be that many people interested in it.

 

[ced1106]

Familiar with GURPS? GURPS uses a normalized resolution (3d6) **but** its skill-level purchasing system uses marginal utility (it costs more points to go from N to N+1 when N is high vs. when it is low). D&D, meanwhile, uses a linear resolution (d20) but its skill-level purchase is also linear (1 point = 1 skill level, with a cap).

D&D skill levels remind me more of a percentile based system, similar to BRP. Interesting that with a d20, threads for normalized resolution are much more common than with percentile systems.


Cedric.
aka. Washu! ^O^

 

[Drawmack]

For easy bell cuvre just roll 2d20 and divide the result by 2, rounding down. Of use 2d10 and loose a number, as mentioned earlier you can loose 1 or one that I saw a while ago rolled 2d10-1 unless you rolled a natural 20 which effectively got rid of the 19. The logic was that 1 is a critical fumble and 20 is a critical pass so 19 was a much less important number then either of those two. It also did something wierd to the average roll
(1+2+3+...+18+20)/19 ~ 10.05.

You can vary the dice find any combination of dice that totals 20 when rolled to max.

a) 5d4
b) 3d4 + 1d8
c) 2d4 + 2d6
b) 2d4 + 1d12
e) 2d6 + 1d8
f) 1d8 + 1d12
g) 2d10

Then subtract N-1 where N = the number of dice rolled, in all cases except when all dice maxe out.

a) - 4
b) - 3
c) - 3
d) - 2
e) - 2
f) -1
g) - 1

The number that you eliminate is 20-(N-1).

a) 20 - 4 = 16
b,c) 20 - 3 = 17
d) 20 - 2 = 18
e,f) 20 - 1 = 19

so you averages become
a) (1+2+...+15+17+18+19+20)/19 ~ 10.21
b,c) (1+2+...+16+18+19+20)/19 ~ 10.16
d) (1+2+...+17+19+20)/19 ~ 10.11
e,f) (1+2+...+18+20)/19 ~ 10.05

Since the average is a function of the number eliminated the higher the number you can eliminate the better of you are. Now let's look at the d30 distribution and average to see if what you propose is better then what can easily be done with dice we already have.

01-06 x1
07-09 x2
10-11 x3
12-14 x2
15-20 x1

(1+2+3+4+5+6+7+7+8+8+9+9+10+10+10+11+11+11+12+12+13+13+14+14+15+16+17+18+19+20)/30 = 315/30 = 10.5 comes out the same as 1d20. Though I if you talk probability you have a 3 1/3 chance to roll any given side so you have a
3 1/3% chance of rolling 1,2,3,4,5,6,15,16,17,18,19,20
6 2/3% chance of rolling 7,8,9,12,13,14
10% chance of rolling 10,11

I don't feel like doing anymore math but I bet the the best bell curve is going to come from 5d4.