I thought I would review some of the "old ways" to test stats and then offer some thoughts and opinions.
AD&D
Player's Handbook (1E, 1978), p. 76 in the "Dig" spell description:
Any creature at the edge (1’) of such a pit uses its dexterity score as a saving throw to avoid falling into the hole, with a score equal to or less than the dexterity meaning that a fall was avoided.
This is the first explicit example of an ability check that I could find in the rules. It would be great if someone with greater knowledge of the materials could find examples pre-dating this one.
The ability check given here may be written concisely as
d20 <= Dexterity
And it generalizes to
d20 <= Ability score
This is the classic "roll under" mechanic. It uses a discrete uniform distribution (d20). There is no reference to "situational modifiers" or any other kind of bonus or penalties.
AD&D
Dungeon Master's Guide (1E, 1979), page 110, in the section on "Conducting the Game," "Rolling the Dice and Control of the Game":
There will be times in which the rules do not cover a specific action that a player will attempt. In such situations, instead of being forced to make a decision, take the option to allow the dice to control the situation. This can be done by assigning a reasonable probability to an event and then letting the player dice to see if he or she can make that percentage. You can weigh the dice in any way so as to give the advantage to either the player or the non-player character, whichever seems more correct and logical to you while being fair to both sides.
This method is fairly arbitrary. The words "make that percentage" imply percentile dice are to be used. This yields the formula:
d100 <= Percentage chance given by DM
This is a "roll under" mechanic. It uses the discrete uniform distribution with granularities of 1%.
Basic
Dungeons and Dragons (Moldvay Edition, 1981), page 60, in the "DM Instructions":
"There's always a chance." The DM may want to base a character's chance of doing something on his or her ability scores (Strength, Dexterity, and so forth). To perform a difficult task (such as climbing a rope or thinking of a forgotten clue), the player should roll the ability score or less on 1d20. The DM may give a bonus or penalty to the roll, depending on the difficulty of the action (-4 for a simple task to +4 for a difficult one). A roll of 1 should always succeed, and a roll of 20 should always fail.
This looks like what we saw in the 1E PHB, but now we have have the first glimpse of difficulty modifiers. The template is
d20 + difficulty <= Ability score
where the difficulty ranges from -4 (easy) to +4 (difficult). Note that the difficulty modifier is added to the dice roll rather than the target number (ability score) making difficulty positive and ease negative.
There's a new concept here of a "critical success" (1) and "critical failure" (20). Note that these are the reverse of what we normally think: A "natural 20" always fails!
"You’ve always got a chance: Use ability scores to determine success or failure" by Katharine Kerr in
Dragon #68, Vol. VII, No. 7, December 1982, pages 81-82
This article pertains to AD&D 1E. It makes use of the percentile roll we saw in the 1E DMG, rather than the d20 roll we saw mentioned in the 1E PHB:
the DM may turn the score into a percentage chance for the character to use the skill in question. Multiplying the ability score by 5 gives a number we may call the basic skill percentage.
Applying this to the ability scores of the fighter in the earlier example, we get:
Strength of 18, times 5 = 90%
chance of using strength
Intelligence of 8, times 5 = 40%
chance of thinking correctly
Wisdom of 9, times 5 = 45%
chance of wising up
Dexterity of 14, times 5 = 70%
chance of manipulating objects
Constitution of 17, times 5 = 85%
chance of withstanding stress
Charisma of 10, times 5 = 50%
chance of persuading others
Later we read something new and innovative. Sometimes 2 or more abilities are relevant to a test. If so, average them:
two or more skills play a part in one action. To get the base chance in these circumstances, simply average the percentages required, rounding up if necessary. In the example, the fighter will need both strength and dexterity to pull himself onto the ledge once he’s made the climb; 70 + 90 divided by 2 = an 80% base chance of scrambling over the ledge successfully.
We also get a discussion of situational modifiers, their granularity and typical values:
size of the bonus/penalty increments goes, the DM should pick one consistent with the rest of the game system, then stick to it despite wheedling from the players. Since many penalties and bonuses in the AD&D rules come in increments of 05% or 10%, a logical choice would be to make normal factors affect chances for success at the 05% rate and exceptional ones at 10%. If our fighter were standing on slippery ground for his jump, he would be penalized -05%, but if he were up to his waist in water, the penalty could justifiably be increased to -10%
So the basic formula is
d100 <= (5 x ((Ability score) or (averaged ability scores))) +bonus/-penalty of 5% or 10%
AD&D
N5: Under Illefarn (1E, 1987) by Steve Perrin, page 6, in the "Modifying Ability Checks" section:
Ability checks are sometimes modified by the difficulty or ease of task to be accomplished. The Dungeon Master may modify the chance of success in one of two ways.
The simplest way is to add a difficulty modifier to a roll. For example, a climb up a steep slope could call for a Strength check. If the slope is particularly steep, add 1-5 to the number rolled before comparing it to the character's Strength. If the modified roll is too high, the Ability check fails.
So far this is just like Moldvay, except the difficulty modifier ranges from 1-5 rather than -4 to +4. But next we get a whole new, innovative system...
Another way to modify an Ability check is to use different dice. For example, rolling 3d6 instead of 1d20 means that characters with high abilities will almost always succeed, while those with low abilities will usually fail. This is because the usual roll on 3d6 is between 9 and 12. More difficult Ability checks can be resolved by calling for the use of 4d6 or even 5d6, making success almost impossible for all but characters with the highest abilities.
We can extrapolate this to the following formula:
Nd6 <= Ability
...such that N equals...
| 2d6 | Easy |
| 3d6 | Average |
| 4d6 | Hard |
| 5d6 | Nearly impossible |
This is a "roll under" mechanic too, like the previous ones. But now we get bell-like distributions for the first time, and we also get a rationale for using them: Nd6 rolls have a smaller spread than d20 rolls, meaning random variates will tend to cluster together close to the mean.
3E/3.5E d20 SRD Sometimes a character tries to do something to which no specific skill really applies. In these cases, you make an ability check. An ability check is a roll of 1d20 plus the appropriate ability modifier. Essentially, you’re making an untrained skill check.
In some cases, an action is a straight test of one’s ability with no luck involved. Just as you wouldn’t make a height check to see who is taller, you don’t make a Strength check to see who is stronger.
The formula is
1d20 + Ability modifier >= DC
where Ability modifier is (Ability score - 10)/2 rounded down, and DC is 10 for average tasks, higher for harder tasks. That's innovative. Old school systems look at the whole ability score, not just the modifier.
Also, prior ability checks were all "roll under" mechanics. Here we see a mechanic where rolling higher is better. This jives with some players better. Your proposed d10 mechanic works this way too. "Basic Fantasy" and "Microlite 74 " are two examples of old-school style systems that make use of this "roll high" mechanic. One can always transform a "roll under" mechanic to a "roll high" mechanic if one so desires.
4EThe formula is
1d20 + ability score modifier + ½ character level >= DC
This adds Level into the mix. In other words, as you gain experience and go up in level, it becomes easier to make an ability check against a fixed test.
OK. Here is the checklist I'd use when deciding how to test stats.Uniform distribution, triangular, or bell-like?d20, d100 (and your proposed d10) mechanics have a discrete uniform distribution. This makes the effect of a +1 difference easy to calculate: 5% for d20, 1% for d100, and 10% for d10. Using a bigger-sided die (d20 or d100) gives you "finer granularity." Using a small-sided die (d6 or d10) gives you big granules. Something to consider.
When you're dealing with sums of discrete uniform distributions (2d6, 3d6, 4d6, 5d6, etc.) things get tricky. Considering the triangular 2d6 distribution, a +1 may change the percentages by 16.67% or 8.33% or 2.78%. It all depends on where you are on the curve.
On the other hand, uniform distributions have the widest spreads. As a rule of thumb, as the curve becomes more bell-like, you can expect about 68% of rolls to be within +1/-1 spread of the mean. Here are some tables for comparison. First uniform distributions. Then bell-like distributions.
Uniform distributions| Roll | Mean | Spread |
| d6 | 3.5 | 1.70782512766 |
| d10 | 5.5 | 2.87228132327 |
| d20 | 10.5 | 5.76628129734 |
| d100 | 50.5 | 28.8660700477 |
| Roll | Mean | Spread |
| 2d6 | 7 | 2.4152294577 |
| 3d6 | 10.5 | 2.95803989155 |
| 4d6 | 14 | 3.41565025532 |
| 5d6 | 17.5 | 3.81881307913 |
"Roll high" mechanics bring to mind 3E and 4E. "Roll under" mechanics are quintessentially "old school" for me.
Critical rolls?Does a certain roll spell automatic success or failure like Moldvay Basic?
Can more than one ability come into play?If so, consider averaging the relevant abilities like in the Dragon Magazine article cited above.
Ability scores or ability modifiers?Using scores is "old school" to me. Using modifiers seems very 3E/4E.
Does class matter?Is this something a fighter can do better than an MU? If so, consider a class modifier. We see this with thief skills. I'm not sure why we don't see it for other classes. Aren't fighters more athletic? Shouldn't they be able to run faster/longer, and leap higher/longer than other classes, even versus an opponent with the same ability score but a different class?
Does level matter?Is the task at hand something a more experienced PC can do better than a less experienced PC? If so, consider a level modifier, like 4E.
How do situational modifiers work? What is their typical range?Finally, consider using something like the
Troll dice roller and probability calculator to simulate and experiment with your system before unleashing it on your players!
how about 2d6 
The premiere issue of The Dragon, Vol.1, No.1, June 1976, on page 7, in an article entitled, "How to Use Non-Prime-Requisite Character Attributes," by Wesley D. Ives. His system is fairly complicated. The main formula is
