I'm really sorry to be a necromancer and res this from 5 years ago. I just saw this thread when searching back archives on how to balance thief skills with non-thieves trying to find traps, and really liked the proposal, and crunched some numbers on it.

Aplus wrote:**ABILITY CHECKS**
Assume a red (or whatever) d6 acts as the "target die". You roll it along with a different die based on your ability score and try to meet or beat the number showing on the target die.

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```
Score Die
3 d2
4-5 d3
6-8 d4
9-12 d6
13-15 d8
16-17 d10
18 d12
```

There is no real reason to do this. It's just for the sake of variety. You would use it for anything you would normally use a generic ability check for. If you wanted to get fancy, you could also change the target die for tasks of varying difficulty. On the one hand it seems kinda wonky, but I can easily memorize it (d6 for no modifier, and steps up or down from there), and I doubt telling players which die to roll is any more difficult than explaining roll-under for the millionth time.

Thoughts? I think I'll try it out next time and see what the players say...

I thought this sounded really cool. I like that it uses the dice chain and the swingy nature of it.

However, doing the math on it, the percentages don't work.

Consider an INT check. Maybe your PCs have found an ancient scroll describing the workings of a fantastical engine of war whose complexity was understood only by the Ancients. A PC with a dog-level INT of 3 still has a 25% chance of grasping this esoteric knowledge.

Consider STR check to force open a door that has been buttressed from the far side. A nearly paralytic person with a STR of 4, who almost requires the other PCs to carry him in a wheelbarrow, still has a 33% chance to knock the door down, even though the able-bodied turnip farmer only has a 58% chance.

Contrariwise, at 18, the chance of success only goes as high as 79%. So while your mentally disabled PC has a 1 in 4 chance of understanding the complex diagrams, your genius with an IQ above 180 has a 1 in 5 chance of not understanding it. That just seems kind of backwards and unbalanced towards and inferiority.

What does work out is that the 9-12 range has a little better than even odds of success (58%).

Here's how the probabilities break down:

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```
Score Die % success
3 d2 25%
4-5 d3 33%
6-8 d4 42%
9-12 d6 58%
13-15 d8 69%
16-17 d10 75%
18 d12 79%
```

If you bumped up the target die to a d8, the resulting tables are:

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```
Score Die % success
3 d2 18%
4-5 d3 25%
6-8 d4 31%
9-12 d6 43%
13-15 d8 56%
16-17 d10 65%
18 d12 70%
```

YMMV on whether that's much better. This system looks like it will always be biased towards low-ability characters.

Bumping the target die all the way up to a d12, an ability of 3 still has a 1 in 8 chance of success and an ability of 18 only a little bit higher than 1 in 2.

This might still work for opposed checks. Opposed checks before modifiers are statistically identical to a d2, with failure on a 1; or another way, on a d20, an opposed check before modifiers is statistically equivalent to a DC 10. This system doesn't obviously to reduce to that, since the dice you roll are different; the check is still 50/50 if you have the same attribute and hence same die, but if you're not at same attribute, then that isn't the case anymore. Of course, I'm not sure if it alters the probabilities that much more than the resulting 5% modifiers from +3 and -2. I don't feel like doing the math right now. It sure feels cooler, though; when the ogre rolls his d12 in the STR check against your d4, you get a more immediate sense of what you're up against.

I tried a few different permutations of the dice chain as you have it here (which I notice skips d5 and d7), and I think a 3 having 25% of success is basically guaranteed with this system, if the target die and 9-12 die are the same.

Anyway, interesting system that seems to get the swingy and unpredictable feel of the core rules, but I don't like how great the odds are for terrible characters opposed to how sucky the odds are for good characters. I wish there were a way to make it work better.