Tag Archives: Probabilities


The characters in our hypothetical game system already have Abilities – characteristics such as Strength, Dexterity or Intelligence – but they also need to have experience and training: Skills.

Untrained Use: Skills that can be used untrained receive a -3 Dice modifier. That makes dice checks one category harder. That’s pretty much the gist of our task resolution system, and it fits with the -3 for absolutely abysmal ability scores.

Basic Training: In the post on skill and ability modifiers, we determined that rank 0 in a skill is equivalent to basic training without practical experience. Rank 0 avoids the untrained penalty, and allows use of skills that can not be used untrained, but does not give any bonus to the check.

Flexible Skill Coupling: Some game systems strictly associate a skill with a particular ability, such as Dexterity for Archery. Other systems make it entirely dependent on situation. I prefer the flexibility of the later, but admit that some skills should usually depend on certain abilities. In our archery example, a ranger who tries to keep track of several identical-looking targets may have to substitute his Intelligence modifier for his Dexterity modifier.

So how do our characters gain skills?

Remembering that the maximum our system can comfortably support is a +8 skill rank, we do have to limit the number of skill ranks available to a character in some fashion. An easy solution would be to use skill points and to escalate the cost of skill points for higher ranks. However, I believe there are disadvantages to this: We either have to allow characters to “save up” skill points until they can afford to buy an expensive skill rank, or we have to accept a high level of book keeping, if skill points have to be spent directly on skills, even if it does not result in an immediate skill rank increase.

Both methods also mean that a character who is waiting to improve an expensive skill will not see any character improvement in quite a while.

Instead, I had this idea to keep character improvement at a fairly steady pace, but to reduce the magnitude of improvement over time. The only way I can come up with to implement this are character levels, something I wanted to avoid. But I think it might work, especially if we do not hook other power increases (“hit points” come to mind) to levels.

Let’s whip up a table.

LevelExpSkill PointsMax Skill Rank

(And so on for levels beyond 10.)

So basically, the Game Master decides what level the characters start on. Each level, they receive a number of skill points that they can directly spend to increase their skill ranks. Since there’s a maximum skill rank, based on level, players can not start their characters out with unrealistically high skill ranks.

The game master then rewards the players with experience points – say, 3-5 points per game session. Every 2-4 sessions, all characters advance by one level.

There’s another benefit to this system: Newer characters can actually catch up to older characters, at least to a point..

LevelTotal Skill Points

Older, more experienced characters will always have more skill points in total, but assume a character of level 10 and one of level 1. 18 points difference, but the maximum difference in a skill is 6 points.

By level 14 and 4, the difference will be 12 points; by level 17 and 7 it is 10 points. After that, the difference stays constant. That buys the more experienced character one additional skill at maximum level, or a total of three “+3’s”. It seems hardly game-breaking, especially if you consider that higher skill levels are subject to diminishing returns anyway.

In addition, the game master could reasonably hand out a few Rank 0 Skills to the “younger” characters. This is entirely within the scope of our definitions. Imagine if the newer character travels with an expert swordsman, the older character. Just watching him “in action” should give the young protege some basic hints about sword-fighting. It doesn’t really give the new character a big boost; spending even one skill point on a skill raises it to Rank 1 anyway, no matter whether the character had it at Rank 0 or not.

Such Rank 0 “Bonus Skills” should be awarded at the Game Master’s discretion. However, as a rough guideline, a number of Rank 0 skills equal to half the level of the level difference to the highest character may be appropriate. So if your new character starts at level 2, and the old hand has level 16, the Game Master could assign you a maximum of seven bonus skills at Rank 0. These should be in areas that other characters have high skills in, and should be awarded after you have traveled with your companions for some time (which might well be before the first session, if your Game Master allows it).

The exact numbers for skill points et al probably need to be based on how many different skills the system actually uses – and, of course, this all would have to be play tested to see if it actually works.


We still need to work out our actual abilities and their modifiers. In the last post in this series, Skill and Ability modifiers, I worked out a system of modifiers and how it affects task resolutions. I concluded that I have a +0 ..+8 range for positive modifiers, which includes both skill and ability modifiers. My gut feeling is that this should be split roughly into +2 for abilities and +6 for skills. By the definitions of the Skill and Ability modifiers post, +2 from abilities gives a talented person an advantage of 1-2 years of training, which does not sound unreasonable if you view a person’s entire career. Of course, in an abstract simulation such as an RPG this means high ability scores “front-load” skill use – that is, you gain a large boost to many skills before you ever receive any job training – but that’s okay; especially since I firmly believe that skills that realistically require training should also require so in a game; we can compensate with an “untrained skill use” penalty.

Anyway. Abilities. Since this is a genre-less game system, we will only define a few basic abilities. Specific genres could add abilities, such as a fantasy genre adding a magic skill. Also, I am a fan of having physical and mental abilities that roughly mirror each other.

  • Strength
  • Endurance
  • Agility
  • Intelligence
  • Willpower
  • Charisma

Let’s use 2d6 as our random generator for attributes. This gives us a range of 2-12, average 7, with a bias towards the middle of the spectrum. We have a few options on how to proceed, all based on what ranges we define for what modifier. I like symmetry, so I came up with the following:


Using random ability generation and this modifier system almost half of the characters will have a +0 in any given ability. Close to 20% will have either +1 or -1, and 8% will have a +2 or -2. Almost 28% in total will have a low ability modifier, another 28% a high ability modifier.

I think this should work fairly well, especially if you consider that player characters will likely improve ability scores that are vital to their “roles” – be that strength for a sword fighter, agility for an Imperial marines sniper, or intelligence for a wizard. Player characters tend to be trained professionals, who would hone their abilities and skills as best they can. John Doe, his only hobby being slouching in front of his TV every night, rarely ends up packed with muscles.

Point Buy: Not everybody likes to generate characters by random. Since the average roll would be 7 per ability, six ability scores mean 42 points on average. Let’s give our Point Buy characters those points to spread among their abilities. This actually results in slightly above-average characters, since 6 is still a +0 modifier, and such a character could buy two 9’s and four 6’s. Two other optimized sets would be:

  1. 1x 12, 5×6
  2. 2x 11, 2×6, 2×4

These all work out to an overall of +2 in ability modifiers. You can easily assign your character low scores in abilities you do not expect to use much, but this still doesn’t seem to be excessively powerful.

Larger Than Life: In a very “heroic” campaign, the Game Master may simply let players buy abilities for a higher point value (see Point Buy system), or let them roll 1d6+6 instead of 2d6. That eliminates negative ability modifiers altogether. Besides improving chances for high end abilities considerably, it also has the side effect of eliminating negative numbers from the character sheet, simplifying matters ever so slightly.

Skill and Ability Modifiers

A few months ago I began to theorize on task resolution and dice mechanics for a hypothetical game system. In those two posts, I concluded that using 3d6 seems to be a good dice mechanic, and for task resolution I decided on the following difficulties/target numbers:

DifficultyProbabilityRoll 3d6
Very Difficult9.26%15+

However, these decisions require that the bonuses given by skills, attributes, and so on stay within certain boundaries. Or, in other words, the capabilities we grant the characters need to be balanced against those difficulties.

So what happens when we modify dice rolls? We just shift the probability of achieving a certain result around. The following table shows the percentage of success for our difficulties for a range of dice modifiers of -6 .. +6:

DifficultyTrivialEasyRoutineDifficultVery DifficultImpossible
Dice Mod.

Judging by these numbers, +4 to +5 is the range that a trained, experienced professional will have. +5 turns Routine tasks into (almost) automatic successes, and lowers the chance of failure for difficult tasks to just under 10%. If our hypothetical trained professional can take things slowly, prepare, or otherwise gain a situational bonus, Difficult checks quickly become automatic successes for him.

At the same time, our +5 professional will still fail Impossible tasks 75% of the time. They are truly challenging, and will require good preparation or a lot of experience to complete successfully.

Freshly-created characters should probably have most of their skills no higher than +1 to +2, and their core skills – their specialization – should be +3 for a few skills, maybe +4 for one skill if they are really pushing it.

0You took the basic course or picked up some basics informally, perhaps as a hobby.
1You used the skill professionally for some time, or as a hobby for many, many years.
2You used the skill professionally for a year or two.
4Your professional specialization for several years, or a side skill used regularly for many years
6Expert in the field
8Top of the field

That’s not a very big budget for handing out numbers. It has to cover skills and, presumably, attributes. And we have to keep in mind that it has to allow for improvement during actual game play; if a character starts out “at the top of his field”, the players will quickly get bored with that.

It also means that attribute modifiers either need to be kept very low – if, say, an exceptional intelligence were to give +3 to all knowledge, science and similar skills it is easy to see that attributes would quickly dominate the game’s balance. That kind of bonus should be limited to exceptionally “gifted” individuals.

Perhaps there is another solution, though. For certain things, I will not argue that natural ability will give a person a head start. To continue our intelligence example: A really smart person has an easy time picking up mathematics. But math is not something you just invent for yourself (unless your are a Newton or a Leibniz, and even then you basically spend years teaching yourself). A less intelligent person who spends time studying math will outperform the smart person who has no training very quickly.

So instead of applying ability bonuses to skills, perhaps we should see the two independently from each other. A high ability score could make acquisition of associated skills easier, or it could perhaps allow for higher overall skill levels for this particular character. In the later case, though, we will have to allow a player fairly fine control over his ability scores, and the possibility to raise them in-game – doesn’t have to be easy, but it has to be possible.

However, this is getting to the point at which we have to formulate an actual character generation system and to actually play-test it to see if all this theory works out after all. And that’s for the next post in this series.

Task Resolution

After deciding that 3d6 is a dice mechanic that gives good, generally predictable results and a good granularity, let’s work on task resolution. “Task resolution” is any situation where a character is attempting to achieve something, but the mechanics will be used for other decisions as well. One example might be random encounters, where the probability is dependent on, say, weather or the time of the day.
Continue reading “Task Resolution” »

Dice and Probabilities

If I wanted to create a game system, one of the first things I’d tackle is the fundamental dice mechanic I’d like to use. Rolling dice, and the chances a player is supposed to have at succeeding different given tasks, obviously deeply influence many other design decisions – such fundamentals as attribute ranges and how they figure into the dice rolls, but all other aspects of the game system as well.

Continue reading “Dice and Probabilities” »