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The D20 Mechanic

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Anonymous

Hi all,

This is my first post here, and certainly not my last. I'm glad I found this place. I recognize a few people here from [TMP] where I post religeously. :wink:

Anyway, I'm hashing out an outline to a skirmish ruleset for starship combat and am trying to settle into a dice mechanism to use. My current infantry set uses a 2d6 system which I like and provides nice results. For this newest game I wanted to use something different.

Not to be confused with the "D20 System", I'm wondering what your thoughts are (scientific or otherwise) on using a 20-sided dice for the mechanism? I'll be using charts, tables and modifiers as well.

Thoughts?

-B6

GeminiWeb
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Joined: 07/31/2008
The D20 Mechanic

To oversimplify things ...

D20 is better than lower die for providing a wider range of outcomes, using a flat uniform distribution (i.e. all numbers have the same probability of being rolled). A d6 only offers 6 possibilities, so the range of options is limited ... Then again, a D100 offers an even wider range, but usually involved rolling two d10's ...

It also has a nice feature where a +1 or -1 adjustment corresponds to a 5% change to get a partiuclat number of higher (or lower dependign on your reference point). For example, there is a 50% chance of rolling an 11 or higher. With a +1 modifier to the die roll, this becomes 55%.

However, often a unifom probability isn't appropriate - the tails of the distribution are of specific interest - just imagine playing Setters of Catan with a d12. Okay, there is no '1' but you get the point - its the different probabilities that make it more interesting. There is were adding numbers from several die rolls together comes in (e.g. 2d6, 3d6). Adding more die rolls makes the extremes more extreme and the average results 'more common'. Different results can also be achieved be adding different types of die (e.g d6+d10).

Anonymous
The D20 Mechanic

Thanks for the insight GeminiWeb. So, would 4d6 be better average-wise than rolling 1d20?

-B6

GeminiWeb
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Joined: 07/31/2008
The D20 Mechanic

Quote:
Thanks for the insight GeminiWeb. So, would 4d6 be better average-wise than rolling 1d20?

Thanks for clarifying 'average-wise' ... otherwise I'd have had to say it always fun rolling more dice ;)

Let's think ...

4d6 gives scores from 4 to 24
- score of 4 (and 24) occurs 0.08% of the time
- score of 5 (and 23) occurs 0.31% of the time
- score of 6 (and 22) occurs 0.77% of the time

So you can see that the tails of the distributiom are quite rare!

Now, I'm a bit too lazy to work out the probabilities, so this is what happened with 100,000 random throws using Lotus 1-2-3

04,24 - 0.08%
05,23 - 0.30%
06,22 - 0.76%
07,21 - 1.54%
08,20 - 2.71%
09,19 - 4.34%
10,18 - 6.17%
11,17 - 8.01%
12,16 - 9.68%
13,15 - 10.78%
14 - 11.23%

(d20 gives 5% for each number)

Now, to look at the relative probabilities, we'll standardise it according to the number of times you expect to see a number rolled, compared to the number of times a 4 is rolled ...

04,24 - 1
05,23 - 4
06,22 - 9
07,21 - 19
08,20 - 33
09,19 - 53
10,18 - 75
11,17 - 97
12,16 - 117
13,15 - 131
14 - 136

(d20 would gives 1 for all numbers)

Thus, we get 136 rolls of 14 for very one roll of 4 ...

Really depends it this is what you want ...

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