[N.B. The following is a repost from the brief period when I did my Hearbreaker blogging on my miniatures blog. I wrote this for an audience of people who were mini painters but not necessarily gamers, so if it seems like I'm over-explaining basic d20 RPG concepts, that's why. I link to my first real Hearbreaker post; I'm not going to repost it here, but feel free to take a look if you're interested in some design manifesto kind of stuff.]
My preliminary Heartbreaker post was pretty squishy—big on theory, light on substance. Now begins some actual substance. Let's begin with the critical hit. d20 players are very familiar with how these work, and even non-gamers may have heard the term "natural 20." "Natural 20" means when you roll your twenty-sided die (or "d20"), and a "20" shows on the die (instead of the die roll + modifiers equalling 20). This usually means that you automatically succeed at whatever you were testing, no matter what the actual result. Likewise, rolling a "natural 1" often means automatic failure, again no matter how good the roll might be otherwise. These results can be called "critical successes" and "critical failures." When attacking, a critical success might also result in increased damage, while a critical failure might mean you've dropped your weapon, accidentally stabbed an ally, or worse, depending on the caprice of your gamemaster.
You can see why these rules were put in place. No task is so impossible that success might never transpire through a stroke of luck. And no hero is so competent that he might not suffer the occasional setback. But it seems that a 5% chance of fluke success or failure is a bit much to ask. Even I might play the lottery if there was a 5% chance of winning, and I don't believe anyone would ever step on a plane if it had a 5% chance of crashing. Luckily, there's a way to capture this idea without such wildly swingy odds.
Remember that in d20 games, you roll to beat a certain score, called the Difficulty Class or DC, that is higher or lower depending on the difficulty of the task. Let's redefine "critical success" and "critical failure" around this concept. A critical success is a result that is more than twice the DC of the task at hand. A critical failure is less than half the DC. So I'm attacking a goblin with a defense DC ("AC", for you D&D veterans) of 10. If the result is higher than 10, I've succeeded, but higher than 20, and I've critically succeed and get double damage. Huzzah! But if the result is lower than 5, I've not only failed, but critically failed, and stab myself in the foot. Curses! You can see that a character with a really high attack score is going to get double damage against that goblin all the time, which is already pretty neat and obviates the need for "minion" rules and suchlike. But how would even a mean peon ever score a critical failure?
Let's add a rule that I've heard called the "exploding 20." This isn't my idea, but it goes like this: When you roll a natural 20, you roll the d20 again and add the result to your total. So your modifier is +8, let's say. You roll a natural 20, so your total so far is 20+8=28. You roll again because of the natural 20 and get, say, a 13. So your grand total is 20 (initial roll) +13 (second roll) +8 (your modifier)= 41. Fantastic!
Likewise, you can have an "exploding 1" where if you roll a natural 1, you roll the d20 again and subtract the result from your initial total. So in the case above, if instead you started with a natural 1, your grand total is 1 (initial roll) -13 (second roll) +8 (your modifier)= -4. Against our goblin with a defense DC of 10, that would meet our definition of a critical failure. Better go see a podiatrist.
You could, if you liked, allow for an infinite chain of exploding 20s, creating the theoretical possibility of infinitely high rolls. Let's call this a "chained explosion." You could do the same for exploding 1s, but I find that the most sensible approach—by which natural 20s explode after the initial natural 1—is kind of hard to explain and usually overkill, as 1 -20 +modifiers is usually enough to guarantee critical failure anyway.
Here's another wrinkle; D&D players will know that for certain weapons, you can get a critical hit even if you don't roll a natural 20. A rapier, for example, might do double damage on any natural roll between 18 and 20. Let's call this a threat range of 3. A magically "keened" rapier does double damage on a natural roll between 15 and 20; it has had its threat range increased to 6. If you roll in your threat range, you have rolled a threat.
For our new system, we should say that any natural roll in a threat range should explode. A threat range of 1 works just like our "exploding 20" above, triggering a reroll as described, but a check with a threat range of 3, like an attack with a rapier for example, would also trigger that reroll on an 18 or 19.
We should also consider the opposite concept. An error range of 1 works just like the "exploding 1" above, but an error range of 3, perhaps for an attack with a cursed or poorly-made weapon, would also trigger the reroll for a 2 or 3. If you roll in your error range, you have rolled an error.
Skip this paragraph if you get the concept and don't care about precise mathematical definitions. But for the sake of precision, let's define a threat range of x as any natural die result between [21 -x] and 20, and an error range of x as any natural result between 1 and [0 + x]. A roll within a threat range triggers a threat, a reroll with the result added to the total, while a roll within an error range triggers an error, a reroll with subtraction instead.
Here might be a good place to add that if you are going to use the "chained explosion" rule, the error or threat range of the second reroll is always just 1. That is, if the threat range is 3, and you roll a natural 19 and then a natural 18, the first roll explodes but the second doesn't. Also, if you roll a 1 on the reroll after a threat, you don't then trigger some sort of error within the threat check. That's just silly.
And here's one more quick idea to really expand our minds around the implications of this new way of thinking, which I got from the surprisingly good Swashbuckling Adventures book. You can increase the threat range of any check by up to five, but you also increase the error range by the same amount! So you can gamble to increase the odds of a success or even a critical success, but with the increased chance of critical failure.
So where does this leave us? We basically now have four possible result types for any check: success, critical success, failure, and critical failure. We have the related concepts of threat and error ranges, though it should be noted that you can have a critical success without rolling a threat or a critical failure without rolling an error (and you can roll a threat without getting a critical success!). This makes the simple d20 check a lot more interesting than simple success or failure. But what might these results actually mean in the game? We'll consider that next time!