I worked up this as an introduction for my players, and thought I'd post it here also:
Cold Iron, like many RPGs, is based on a task resolution system. The player will declare some task they want to attempt (I try and hit the troll with my sword). The character will have some ability with this task (for attack, the ability is hit, often abbreviated to H). There will be some difficulty of the task. Some tasks have a static difficulty, others, like hitting trolls with big pointy things, are opposed checks, the target will resist with some ability (the troll might defend with a parry, often abbreviated as D, or a dodge, often abbreviated as Db). All check use the same randomizer. Some systems use a single die and add (d20+ability), others roll dice against the ability (d100 <= skill).
Cold Iron has a clever chart that utilizes the normal distribution to generate a modifier (often called a chance adjustment). The probabilities of getting particular modifiers follow the bell curve of the normal distribution. The clever trick is in how the probabilities are generated.
Probabilities are always a number between 0 and 1 (when expressed as percentiles, the number is multiplied by 100). Gamers have long used a pair of d10s to generate percentile values between 1 and 100 (sometimes 0 and 99). One die is labeled the 10s digit, and the other the 1s digit, and the pair is rolled and read as a two digit number (00-99, where 00 is usually read as 100). The normal distribution however requires infinite precision, more than two digits. So the concept of rolling two digits is just extended to rolling as many digits as are necessary. The way the probabilities are arranged in the normal distribution, it's not always necessary to roll a bucket full of dice.
Here is a chart that uses the normal distribution to express the probabilities for a range of values:
The left hand column is the cumulative probability (for example, on 2d6, there is a 1 in 36 chance of getting a 2, a 2 in 36 chance of getting a 3, a 4 in 36 chance of getting a 4, up to a 6 in 36 chance of getting a 7. The chance of getting a number, N, or less is the sum of all the individual probabilities of each number less than or equal to N, this is known as the cumulative probability, so the cumulative probability of a 4 or less on 2d6 is 6 in 36 or 1 in 6). The right hand column is the modifier (chance adjustment, or CA). The chart above shows the decimal point, however, it is common practice to leave the decimal point out of chance adjustment tables.
One more bit about the probability math behind this chart, the chart is designed so that a +20/3 (+6.666667) is one standard deviation "above average").
To generate a chance adjustment using this chart, the player should roll a pair of d10s, identifying which digit is first (if it's easier for you, consider it a d100 roll - except 00 will NOT be read as 100). If you look at the chart, most of the time, the number will fall in the range from 12 to 88, which corresponds to chance adjustments of -8 to +8. If you roll between two numbers, you use the lower chance adjustment (so a 51 results in a +0 CA). If you roll in the range of 90-99 or 00-09, you will note the chart has additional digits and multiple rows. In this range, you will need to roll additional d10s to generate additional digits to distinguish between the different chance adjustments. There is a simple rule which lets you roll the dice, then look at the chart. You will see that each number in these ranges starts out with a string of 0s or a string of 9s, and after that string are
2 more digits. So basically, if you roll a 90-99, for each leading 9 you roll, you need to roll an additional digit, for a 90-98, you roll one more digit. For a 99 you roll two more (which may result in rolling even more digits).
Note that if you roll a 99 and then your subsequent pair is a 09, you do not need to roll any more d10s. Your roll is a 9909, which is a +15.
Rolling low is always bad, which is kind of fun if you roll a 00, it's probably an oh-oh kind of moment...
Once you have a chance adjustment, you add it to your ability and compare to the difficulty. If your ability equals the difficulty, you will note that you have a 50% chance of success. If you roll lots of 9s and are confident your result will be a smashing success, feel free to narrate something ("The troll slips in the mud as my axe falls on his neck, I hit him with a 35 (having rolled a +24 on an 11 attack, knowing the troll has a 20 defense).").
A really good result with an attack (and some other abilities) results in a critical success. Generally, a critical success occurs when the adjusted attack is 7 or more higher than the defense. With an attack, this will cause double damage. With attacks, it's possible to get even more than double damage (normally 9 better is triple, 11 better is quadruple, etc., however, armor does modify this).
Here are some more examples:
A fighter with an 11 attack (H, typical of a 3rd level fighter) swings at a goblin with a parry (D) of 14. The fighter rolls an 89, which is a +8, so hit net attack is 19, since this is greater than the goblins D the fighter hits. Later the fighter rolls a 999985, which is a +27, and will probably smear the goblin all over the floor! Shortly thereafter, he rolls a 00045 (-23) which will cause him to fumble. The fighter needs a +3 (67) or better to hit the goblin.
The chart seems daunting at first, and there is some fancy math behind it, but after some play, most players find it easy to use, and you don't need to understand the fancy math. Many players even end up memorizing some of the numbers that come up the most, and mean the most. Normally, D is higher than H, so negative chance adjustments often don't hit. So memorizing 50, 56, 62, 67, 73, 77, 82, 85, and 88 will suffice for a large percentage of rolls.
Another thing is that since the difference between a hit and a critical is 7, you can often look at the dice and see a 60 something, and you know you hit with a +0 CA and crit with a +5 CA, so it doesn't matter if you got a +1, +2, or +3. You hit. Of course the situation could have changed, so the GM should pay attention to the rolls and may ask the player to figure it out (because now a +3 chance adjustment might score that character a crit).
For those interested in exploring the math a bit, the following Excel formula can be used to generate the chart:
The first parameter is the chance adjustment you desire the value for, notice the 20/3 standard deviation is the third parameter (the second parameter indicates the average on the chart is +1, while the fourth parameter indicates cumulative probabilities should be used). I have an Excel sheet on my website that shows how the table can be generated.