Need a dice mechanic for unlimited stat growth

[Breccia]

In the system I want to use it for, each +1 to a stat doubles its power, and they can rise indefinitely. Meaning a guy with +3 strength is twice as strong as a guy with +2, who is twice as strong as a guy with +1, who is twice as strong as +0 (the average), who is twice as strong as -1, etc... But guys with +500 strength can totally exist.

You're not the first to try to do this.

I've played a gaming system called DC Heroes. It did exactly what you are talking about: +1 means twice as good. This was done to keep Superman and Jimmy Olson on the same chart. In their system, the average stat was 2, allowing the average human to pick up "two points of weight" which was two hundred pounds (therefore the average PC weight was also 2, as it covered 100 to 200 pounds) without having to make a Strength check. A car weighs 6, the Empire State Building weighed 23, and Mt. Everest weighed 43, the Earth "weighs" 78, the Sun "weighs" 96 and the Milky Way "weighs" 144. +500 Strength would, therefore, allow the character to lift the known universe.

And one hundred thousand million billion trillion quadrillion quintillion sextillion septillion of its closest friends -- nearly a google of copies of our known plane of existence.

Your system is designed to be ridiculous. Which is fine if that's what you're going for, but keep that in mind when going further.

Okay with that out of the way, odds are, you're not putting +500 Str on the same field as +0 to +2 people. Such situations are in the "dice don't matter" territory. You're looking at something in which someone with an actual chance tries something. Here's how DC Heroes did it:
1) All actions are resolved with 2d10. An 11 was average, of course.
2) If you roll doubles, you may roll again and add. You can do this indefinitely...until the dice are double 1's, which even on the first roll is a critical automatic fail.
3) The result was then looked up on the aforementioned chart, where stats were in groups of expanding values.


Now, to be fair, D&D has dabbled in doubling as well. In 3rd Edition, +5 Str was twice as strong, forever. But even the strongest of D&D monsters, with a D&D Str of, say, 50, would "only" be eight doublings more than the average Str of 10, meaning the DC Heroes table above would only have to go up to the 10 row/column. And epic-level monsters lived there. You could easily get to 10th level without seeing anyone with a D&D stat of 25, where the 5 row/columns would be needed. It's at this point I should point out that the table above is for holding a truly ridiculous stat difference on one page. You probably don't need to do that, therefore, probably don't need to make 3-4 share a category, 5-6 share a category, 7-8 share, etc etc.

So let's port a pair of low-level D&D characters into the DC Heroes chart above. "Fingers" McGee is a rogue proficient in his short sword and between his Dex and training has an AV ("to hit roll") of 4, and the sword (being twice as good as a club) has an EV ("damage roll") of 3. "Ironbutt" Floyd is a fighter with only average Dex having an OV ("touch AC") of 2, but has sturdy full plate mail granting an RV (um..."saving throw"?) of 5.

The AV/OV chart says Fingers needs to roll a 9 to land a blow (read across and down). That's going to happen a lot.
A) If Fingers rolls exactly a 9, he hits...but then we read the EV/RV table. There's a N there, meaning "No effective result". Basically, Fingers' attack hit the plate mail and bounced off.
B) If Fingers rolls an 11, he reads across one more column to the right, finds he hits that one too, and says "I hit by one column". This means, the RV is pushed one column to the left to the 3-4 spot. There's a 1 there, the minimum (duh) result. Ironbutt takes 1 BODY, but with a D&D high Con and high level, probably has 4 or more of those and isn't down yet.
C) If Fingers rolls an 19, he reads across a total of four more columns to the right to the 18 (stopping before the 21) and says "I hit by four columns". Once again, the RV is pushed to the left by four, through A ("All of it", or the EV of 3) to the +1 (so, "All of it plus one more") to do 4. Again, Ironbutt's BODY is likely 4. This is a major success: getting all of your opponent's defense in a single attack. In a normal hit, the target would be knocked unconscious. Major successes are also needed for related "one-hit win" situations, such as mind control or encasing your enemy in a cage made of green energy from your enchanted ring.
D) In the extremely unlikely chance that Fingers rolls a 36 (such as by rolling a pair of 10's, then a 9 and a 7), which is unlikely in the extreme, he would push another five columns and do 9. This is over double what Ironbutt's BODY is, and Ironbutt is instantly killed. These overwhelming successes are needed not just for "one-hit wins" but real game enders, such as disintegration, making someone your permanent mind slave, or reading their mind so well you find things they don't even know they've forgotten. This should not happen against even opponents. These level of results are supposed to happen only when one side is comically (literal and/or figurative) superior to the other, such as "ancient red dragon breathes fire on level 1 commoner".

A lot of D&D would live comfortably in the DC Heroes chart columns up to 5-6. Remember, even a longsword+5 the hands of a high-level fighter with high stats and feats isn't doing eight times the damage of an unmodified 1d8. An 8d8 spell would, of course, and since a 1d8 longsword is an EV of 3, eight times as much would make it EV 6 in this context. In your system, everything just moves two spaces down, and is relatively identical.

I'm biased, but I liked this system. Specifically, the two-chart system with an increasingly harder and harder required roll for going after tougher targets. If Commissioner Gordon shoots his standard issue police handgun (EV 4) at a villain henchman wearing full body armor (RV 5), he's a good enough shot and trained enough with that armor to know where to hit the guy, whereas the average police officer will typically hit center mass and do no damage without a lucky shot. Dozens of cops, however, will take the villain down by sheer odds. But ain't none of them going to put a scratch in a solid steel wall (RV 12) unless they have hundreds of bullets, each.

Okay, with all of that said, maybe you can find something in there you like. Others have suggested exploding dice, which is fine, but they haven't suggested an exploding target which a difficult foe is. Remember, +1 to resistance is twice as tough, and it needs to be paid the same respect. Regardless, good luck, and let us know what you come up with!

[Yakk]

That DC Heros system sure loved charts.

In a more modern system, you can rewrite it to use pretty simple math.

Your DEFENCE is your ability +10.

To ATTACK, roll your stat +2d10. 1+1 on the first roll auto-fails. Explode (recursively) on all other doubles. The EFFECT is equal to the amount you beat the defence; 0 or less means no effect.

If you get a 1 or higher effect, add 1/5 of your ATTACK as a bonus (round down).

It isn't identical to those charts, but it is pretty darn close.

[punctured spoon]

Your Stat Minus Opponent's Stat	Your Roll
-N (your stat is N lower)	N+1 dice, keep only the worst one
-3 (your stat is 3 lower)	4 dice, keep only the worst one
-2 (your stat is 2 lower)	3 dice, keep only the worst one
-1 (your stat is 1 lower)	2 dice, keep only the worst one
0 (a tie)	1 die
1 (your stat is 1 higher)	2 dice, add up successes
2 (your stat is 2 higher)	3 dice, add up successes
3 (your stat is 3 higher)	4 dice, add up successes
N (your stat is N higher)	N+1 dice, add up successes

Each die has a 50/50 chance of being a success or failure. So when you're in the "add up successes" part of the table, the odds that you will fail are cut in half each time you add a die. And when you're in the "keep only the worst one" part of the table, the odds that you will succeed are cut in half each time you add a die.

I'm tentatively calling it the dΣ system.

This is interesting I might have you use this thank you

[BerzerkerUnit]

I'm vaguely curious why you feel that you need a system that can cover 500 doublings. That seems like quite a lot, to be honest. More to the point, I don't think there's any kind of useful dice system that can handle truly unlimited growth - you can only hold so many dice.

That being said, you probably could do something decent with a variation on a dice system I've been sitting on (you'll have to figure out DCs yourself, though - there's a reason I've been sitting on it):

• When your stat is a +1, you roll a d4.
• Increasing your stat by 1 steps the die up - d4→d6→d8→d10→d12
• If you would step a die past a d12, reset your die to a d4, and roll an extra d10.

So someone with a +7 (for example) would roll 1d8+1d10. Someone with a +17 would roll 1d8+3d10. The advantage here is that every +1 increases your maximum result by 2 and your average by 1, then every +5 increment also bumps up your minimum by 1 and your average by 0.5, so scaling stays pretty smooth indefinitely.

Honestly, though, you'd need to give people alternatives to rolling 1d12+99d10 for their person with a +500 Underwater Basketweaving skill, so I'm not entirely sure it's the best solution.

EDIT: Just noticed that you also want to go into the negatives - I'd just hand other people bonus dice for working against you at that point.

Is mint that basically the Step system from Earthdawn?

[GGambrel]

I have a dice system I've been tinkering with that adheres to a sigmoid curve. So modifiers can go infinity far up and down without odds of success hitting 100% or 0% (or running into any other cap).

Your Stat Minus Opponent's Stat	Your Roll
-N (your stat is N lower)	N+1 dice, keep only the worst one
-3 (your stat is 3 lower)	4 dice, keep only the worst one
-2 (your stat is 2 lower)	3 dice, keep only the worst one
-1 (your stat is 1 lower)	2 dice, keep only the worst one
0 (a tie)	1 die
1 (your stat is 1 higher)	2 dice, add up successes
2 (your stat is 2 higher)	3 dice, add up successes
3 (your stat is 3 higher)	4 dice, add up successes
N (your stat is N higher)	N+1 dice, add up successes

Each die has a 50/50 chance of being a success or failure. So when you're in the "add up successes" part of the table, the odds that you will fail are cut in half each time you add a die. And when you're in the "keep only the worst one" part of the table, the odds that you will succeed are cut in half each time you add a die.

I'm tentatively calling it the dΣ system.

This is basically identical to the resolution mechanic I'm using in my system. My biggest inspirations were probably Dark Coast by Torben Mogensen and Ubiquity. It's good to see others think the probabilities have merit.

Really this whole thread is kind of spooky since I'm using a log scale for stats as well.