Complete Dark Heresy Rules Rewrite based on Gaussian Die

get the rules pdf here: http://www.serbitar.de/stuff/DHGB.pdf
get the zip file including character sheet, character generator, gaussian PC die (all Open Office documents) mobile phone gaussian die, rules pdf and some other stuff here: http://www.serbitar.de/stuff/DHGB.zip

Interesting Features:

* Tested system (in use for 3 month now)
* Gaussian Based System that removes any scaling problems and behaves realistically without
* Character sheet that does all the calculations for you, easy skill tests
* Close and ranged combat moves, traits, gear, drugs, purity seals, balanced psy powers, vehicles, corruption and insanity rules, clerical oratory and morale, and much more (91 pages of rules)

Might keep you away:

* Uses normally distributed die (Bell or Gauss curve), mobile phone java die and calc sheet Gaussian dies are included
* Lots of stuff still uncommented
* Work in progress

Further explanations:

can give a short introduction:

A normal d100 has the same probability to roll for example a 45 or 23 or 19. The probability to roll any of these numbers is exactly 1%. The probability to roll between (and including) 1 and 10 is 10%.

The gaussian die has different probabilities. In DHGB I use a gaussian die with a sigma of 10 and a mu of 0.

Mu is the number where 50% of the rolls are below and 50% are above. This means that my dice roller spits out positive and negative rolls, but the average is 0. For quick calculations and the statistical average the die does not do anything. So if you have a skill of 40 and your skill roll is 40 + the Gaussian die, the average result will be 40. This makes estimating your performance easy.

Sigma is the number where 68% of the results lie in. In a gaussian distribution with a sigma of 10, 68% of the results are within the range -10 to 10,
95.4% of the rolls will lie within -20 and 20,
99% of the results will lie within -30 and 30.

The figure below shows the probability distribution.

So why all the hassle?

Imagine an opposed strength check.
In real life everybody would say that there are four possible setups:
A) Both characters are equally strong
B) One character is stronger
C) One character is much stronger
D) One Character is overwhelmingly stronger

In case A) the outcome should be about 50% chance to win for any of the contenders.
In case B) the stronger one should have an advantage, but the other one should have some chance
In case C) the stronger one should almost always win, but there should be some tiny tiny chance of luck that the weaker wins.
In case D) the stronger one should almost always win with the exception of some rare ocurances.

How does a linear system like D100 perform in cases A-C?

Both characters roll and the difference between their strength and their roll decides the outcome.

Case A:
Both have strength of 30, both have equal chances to win. Everything is ok.

Case B:
On has strength 30 and the other 40. The guy with a strength of 40 has an approximately (not totally correct) 20% higher chance. Not that much difference for somebody who is 33% stronger than the other one

Case C:
One has strength 30, the other one has strength 60. The chances are 75% to 25%. The linear system totally fails this test. Somebody which is two times as strong will almost always win in reality.

Cade D:
One has strength 30 the other 130. The stronger one will always win. the chance for the weaker one to win are 0. The linear system fails (though, this is not much of an issue,a s the chance that the weaker ones would win is very small even in the gaussian system).

This is the problem with linear dice rolling systems. Easy tasks are not easy enough (even with an attribute of 30 a skill of 30 and a 30 bonus for very easy test will fail 10% of the time), hard tests are not hard enough, or their chance is zero. And comparative tests scale miserably.

This is different with a gaussian system. As 68% of the numbers lie within a -10 to 10 range, you know that if somebody has a value of 10 more in some stat, you will eventually be able to beat him. But if he has 20 more in one stat chances decrease exponentially, you will only beat him when you are very lucky.
On the other hand, you will almost always succeed in very easy test.

The thing what a gaussian die does is give a range, where the outcome is indefinite, but give ranges where the outcome is very clear BUT also gives a tiny chance to still do it. In a linear system, when you have to roll below 0 because of modifications, your chance is zero, or if you have to roll below 100, your chance is 100%.

In a gaussian die system there is always a chance of succeeding or failing, no matter how hard or easy, but most of the time, the result is the expected one.

A gaussian die is also a good approximation of the real world, as most real system behave in a gaussian way. There is an expected performance level (for example of an athlete or a machine) which varies by a certain degree, but the further you go away from that performance level the more unlikely the result will be. imagine a sprinter running the 100m in 10 seconds. He will maybe run them in 9.8 seconds od 10.2 second, but the probability that he runs them in 12 seconds is much smaller than the probability that he runs them in 10. Thats what a gaussian die does. In a linear system, the probabilities for the runner to run the distance in 12,11, 10, 9 or 8 seconds are the same (and they suddenly stop at some level where the 0-100 range ends).

Hope that explanation helps.

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The character sheet does all the maths for you. In the game you only have to add the dG to your skill and thats the result. Its actually even easier as the vanilla DH.

Example:
Climbing this rock is a difficulty 30 test.
The player has an effective skill of 40, so he rolls the dG (he rolls a -5) and adds 40 which is 35. That is better than 30 and he just makes the climb.
Effectively the skill of 40 is calculated using the attributes of the character (weight, strength, agility), his bare skill, and the armor he is wearing, but all this is done by the character sheet.

The dG is available as a mobile phone application in java and as an OpenOffice sheet (get them in the .zip file posted above).
And, as I mentioned before, that is the biggest drawback of the system. Most people just want to roll real dice.

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Well, that is not that easy.

To make the system scaleable you need a logarithm.
Why is that?
Scaling means that a competition between Str 20 and Str 40 must have exactly the same probabilities as with Str 200 and 400. The relative strength ratio, and that is the only thing that counts in a competition, is 2:1 on both cases.

Using a gaussian die or linear die (does not matter in this case) with an average of X and a standard deviation (this is the "spread" of the of results around the expectation value) Y to resolve the test the situation is as follows:

If you resolve the test by adding the die result to the attribute value, the chances for the weaker guy are much better in the 20/40 case, than in the 200/400 case. This can immediately be seen in the case of a d100. Even when rolling 100, you will never be able to beat 400 when your base is 200. But you will be able to beat 40 when your base is 20. So there is a chance to win for the weaker guy in the first case when you rol for example 90 and the other guy rolls only 40.
The same is true if you have to roll below your rating like in DHGB, its just a negative sign.

This is a non scaling system.

Taking the logarithm (any logarithm will do, the base is irrelevant) as base makes the system scalable.

Look at case 20/40: The difference in log scale (base 10 is)
log(20)= 1.3
log(40)=1.6
difference = 0.3
and the 200/400 case:
log(200) = 2.3
log(400) = 2.6
difference=0.3

Suddenly the system scales. You roll your die and ad the log of your attribute, and no matter what attribute value you have, the difference before rolling, and thus your chance to beat hi

m, will be the same (namely 0.3 with a log of base 10) if the other guy has 2 times your strength.

Thats why you absolutely need this math. In DH vanilla the system almost breaks down when space marines battle (and certainly does when primarchs or others fight), my system copes with them easily.