Captain Anorak's Guide to Gaming
The Dicex System
The Dicex System is a system I use in my own games, based on the old Star Wars game. It's also discussed in my essay on dice rolling systems. I'm planning to mention it a lot so I thought I should set it out in one place.

To make a stat roll you need an input value. This is the value of the stat you're rolling on, plus any modifiers. Note that it's important to add these modifiers before any dice are rolled as they may affect the number of dice rolled.

From the input value, a dice value is determined. This is 1D6 for every three points of input value, plus one for each point of input value left over. Thus an input value of 7 would have a dice value of 2D6+1, and an input value of 9 would have a dice value of 3D6. (For input values below 3, see below.) The dice of the dice value are then rolled and the result is the output value.

To resolve a task, the GM assigns it a difficulty level. Then the dice roll is made. If the output value is greater than or equal to the difficulty, then the task is a success with a success level equal to the difference. If the output value is less than the difficulty then the task is a failure with a failure level equal to the difference.

Input value	Dice value	Minimum output value	Average output value	Maximum output value
0	0	0	0	0
1	1D3-1	0	1	2
2	1D3	1	2	3
3	1D6	1	3.5	6
4	1D6+1	2	4.5	7
5	1D6+2	3	5.5	8
6	2D6	2	7	12
7	2D6+1	3	8	13
8	2D6+2	4	9	14
9	3D6	3	10.5	18
10	3D6+1	4	11.5	19
11	3D6+2	5	12.5	20

Note how the average output value is very close to the input value. It's generally about 10-20% higher, but that's not a big thing. The beauty of Dicex is that it produces an output value between a roughly zero and twice the input value, with the central and most probable result around the input value.

This avoids a problem with many dice-dased systems in which a stat is added to a dice roll, where a 'step' being introduced into the numbers. Under Dicex, doubling the input value and doubling the difficulty level results in the same probability of success. Doubling the input value doubles the typical output value.

Let me illustrate what I mean. Imagine a system called Rollover where a task is resolved by adding a stat (typical human value 10) to the roll of 3D6, giving a success if the result equals or beats a target number. This introduces a 'step' of 11 points: a stat of 10 requires a difficulty level of 21 to give a 50% chance of success.

Now consider this as a combat system. A fighter has an Attack and a Defence: to hit in combat an attacker's Attack is rolled using the defender's Defence as a difficulty level. If a combatant fights multiple enemies he has to split his Defence between them. Under Dicex, an Attack of 10 with a Defence of 12 requires a roll of 12+ on 3D6+1, giving a 50% chance of hitting.

Splitting this Defence between two attackers to give Defence 6 against each, we end up needing a roll of 6+ on 3D6+1 resulting in a 95% chance of hitting. So it's very hard but not impossible to defend against two attackers at once.

Under Rollover on the other hand an Attack of 10 requires a Defence of 21 to give a 50% chance of hitting: to hit needs a roll of 21+ on 3D6+10. Dividing this between two attackers as Defence 11 and Defence 10, to hit now requires a roll of 11+ or 10+ on 3D6+10, which can't fail.

Rollover's introduction of the 11-point 'step' has skewed the numbers. Doubling the stat (10 to 20) and doubling the difficulty (21 to 42) in Rollover won't result in the same probability, it will result in a much more difficult roll.