Hi!
I created a table of probabilites for the LUG rolling system (What percentage chance of getint a 5 or higher for example). Would anyone be interested in a copy?
Dave M
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"Nothing ever rocks, nothing ever rolls, and nothing is ever worth the cost"
- Loaf, Meat
I just had a go at the statistics myself (I included the "6 on the D dice" rule, but not the "1 on the D dice" one), and I must say that the results were somewhat surprising (logical ... but surprising nonetheless and not extremely realistic).
The good news is that the mean values for results rise rather steadily:
<tt>Dice/..........Approx.
Attribute......mean value
..1.............4.0
..2.............5.2
..3.............5.7
..4.............6.0</tt>
However ... basically, what happens is the following:
<tt>1 dice
--------..........
........._______..
-------------------
2 dices
......._-^........
...__--...|______.
-------------------
4 dices._^........
.....__-..|....._.
..._-.....|..__-..
-------------------
.1........6.....12</tt>
(Not sure how readable this is ...)
So ... higher attributes have exactly the same probability of reaching above 6 as lower ones (which is already a bit arguable). Staying below 6, they have a better chance to obtain a higher result than lower attributes have. Above 6, higher attributes have a very low chance to get a 7 or an 8, but a better chance to get an 11 or a 12.
This is a bit weird I think, because for attributes of 4 or 5, chances are extremely high that they will either get a 5 or a 6, or possibly an 11 or a 12, and very low that they get anything else. So in less mathematical terms, either an "above average" result (most of the time), or an "exceptionally good" result (less often), but almost never a "good result" or a "very good result". This does not strike me as extremely realistic ... or is it somehow?
I'm trying to find a house rule to fix this ... has anyone run into that problem too? I checked Kuranov's table, but it tackles the problem the other way round so the discrepancy is not striking (of course: if you need a "good result" for a task, an "exceptionally good" result will do as well)
[This message has been edited by Calcoran (edited 02-26-2001).]
Sorry ... I'd really like to make the "graphics" more readable, but I can't seem to get fixed width fonts to work ... shouldn't it be tt /tt ?
[This message has been edited by Calcoran (edited 02-26-2001).]
####So ... higher attributes have exactly the same probability of reaching above 6 as lower ones (which is already a bit arguable).####
Sure, it's always only one die (the D die) which can raise the result above 6. So the chance to achieve a result above 6 is always 1/6 or 16,67%.
####Staying below 6, they have a better chance to obtain a higher result than lower attributes have. Above 6, higher attributes have a very low chance to get a 7 or an 8, but a better chance to get an 11 or a 12. This is a bit weird I think, because for attributes of 4 or 5, chances are extremely high that they will either get a 5 or a 6, or possibly an 11 or a 12, and very low that they get anything else.####
Why that? Keep in mind, that you don't have to reach exactly a 7 or 8, but that you have to achieve "at least" a 7 or 8.
I'd like to see your calculations, could you email me?
I once made an Excel sheet by myself, listing the possibilities of rolling a certain minimum result with one to seven dice. Anyone interested?
As I said, if you tackle the problem from the other way around, the gap is not as noticeable. http://www.trekrpg.net/Board/ubb/For...ML/000527.html lists the probabilities to reach a given "difficulty" with a given number of dices (in a better table than I could have done ) ... you'll notice for instance that 5D6 have just about the same chance to succeed at reaching 7 than 8, or 9 (and even 10), which is just another way of saying that they will almost always get an 11 or a 12 if they get a 6 on the D dice.
Since I always try to interpret the results of my players to tell them how well they succeeded, this is still rather annoying (characters with a high attribute just know they will either get a "you narrowly succeed" or a "you acchieve an exceptionnally good success" for standard difficulties even before throwing dices).
(P.S.: wait ... e-mail ... let's see)
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LUG Probabilities
) ... you'll notice for instance that 5D6 have just about the same chance to succeed at reaching 7 than 8, or 9 (and even 10), which is just another way of saying that they will almost always get an 11 or a 12 if they get a 6 on the D dice.
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