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).

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 ...