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20190709, 09:02 PM (ISO 8601)
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 Jul 2009
Need a dice mechanic for unlimited stat growth
Does anyone know any good examples of a dice mechanic in a game that has unlimited growth for stats/skills/etc.?
I'm really fond of the dice rolls in PbtA games, but they typically cap their stats at +3 to keep the success/failure/mixed thresholds relevant.
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.
Are there any good examples out there of a dice mechanic that stays equally relevant regardless of the numbers of the characters involved?
Thanks in advance.

20190709, 09:55 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
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.

20190710, 05:10 AM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
I'd look at dice pool systems like Shadowrun, World of Darkness, or (if I remember right, it's been a few years) Burning Wheelbased systems like Mouse Guard. If you aren't familiar with systems like this, essentially you roll a number of dice based on whatever character stats you use, and count up the number that meet some specific condition (Shadowrun uses d6s and counts 5s or 6s, World of Darkness d10s and counts 8 and up).
A core function of roll and add mechanics is that bonuses shift both the maximum and the minimum outcome for a check. In order to keep challenges nontrivial for someone with a +10 bonus but still possible for someone with a +1 bonus, you need to have possible dice outcomes with a larger range than those two numbers (if I use a d10, every outcome that the +1 bonus can receive, the +10 bonus is guaranteed to receive, so either the +1 can't ever succeed, the +10 must always succeed, or I bypass it with some sort of guaranteed success or guaranteed failure for certain roll results like DnD does with attack rolls). So any roll and add mechanic is going to be less than ideal for your system.
A dice pool system means that regardless of how arbitrarily large your pool gets, it is still technically possible to have every result come up fail. It still doesn't resolve the "impossible to succeed" challenge for someone whose pool is smaller than the minimum number of successes. They also struggle to manage penalties to rolls that would exceed the benefits (if you have a net 1 to your roll, how do you resolve that within the existing system?). This covers infinite increasing, but fails with infinite decreasing. It also leads to a lot of dice in hand, which slows down play.
Any dice system is going to come with some baggage. And as Amechra pointed out, there are practical physical limitations to what you can do with dice. If you can give some ideas of what you'd expect for a likelihood of success for a few example values, someone around here can probably get you in the ballpark.Currently operating the 5e Subclass Contest and the 5e Base Class Contest. Check them out if even just to vote or give feedback, we love that in there.
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20190710, 08:39 AM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Me, I'm curious why you want this at all. Why have a system where each +1 doubles your strength if someone with +500 is still competing with someone who only has +1? The +500 is going to be over a google times stronger than the +1. There's no conceivable way for them to compete. The +500 is going to win no matter what.
If you're going with a dice pool, this might be represented by saying "If you have at least X more dice than your opponent/the ranking of the challenge, you automatically succeed."Hi, you can call me Void. I prefer she/her or they/them pronouns, please. Yes, "they" is a singular pronoun. I write a superhero webserial called Paternum  check it out!
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20190710, 09:37 AM (ISO 8601)
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 Jan 2009
Re: Need a dice mechanic for unlimited stat growth
This is going in a very different direction, but Grod the Giant's STARS system has something that sorta helps with this.
You have stats similar to in Mutants & Masterminds, but it also has a concept of tiers. So there's something like a "normal human" tier up to a "cosmic" tier. A cosmic 1 is still multitudes better than a normal human's 10. Normally play has folk be on the same tier, but I could envision saying "this guy has Cosmic Strength 10 but is otherwise mundane".
It's been over a year since I looked at his system, so I forget the details, but you could probably use it as inspiration, and it's avoid the issues of having dozens to hundreds of dice to roll.
On the other hand, I don't think his system would allow you to precisely say "this is +500", but you could probably easily map ranges of numbers to his categories. Or just homebrew something of your own, using that as a resource.
Edit: here's a link to a post I found by him. The links to his system (I think one has a price, the other is a short version for free) are in his signature.Last edited by JeenLeen; 20190710 at 09:39 AM.

20190710, 10:05 AM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Part of the issue here is also that you're doubling the fictional value of a stat with each +1 boost. There isn't really a dice system that can accurately represent that  in most systems, +1 to your stat becomes less valuable as you go along (+1→+2 is a +100% to your bonus, while +4→+5 is a +25%). I say most because there are a few outliers (Roll and Keep and the One Roll Engine come to mind), but those systems also tend to have a sharp cutoff where any bonuses past that point just make you automatically succeed (or close enough to it that they need to modify how bonuses work (see Roll and Keep)).
Are you sure that you aren't going too broad? For reference, someone with a +20 Strength in your system is over a million times stronger than a +0. Someone with a +40 is over a million times stronger than that.

20190711, 01:38 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Roll 1d4+your stat. To succeed, you must meet or exceed a difficulty of 3+the target stat. On a natural roll of 4, add an exploding 1d21. On a natural roll of 1, add an imploding 1d22.
If I haven't bungled my math entirely, that should give you a 50% chance of success against an equal stat, a 25% chance of success against stat+1, and halve your chance of success against each successive point of stat difference.A role playing game is three things. It is an interactive story, a game of chance, and a process in critical thinking.
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20190711, 03:03 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Honestly, if it's really a doubling each time, look to Diceless. If you have more Stat than the guy you're competing with, you win. Tasks have simple stat checks: do you have the minimum required to pull it off?
Exponential growth of any sort (which compounded doubling qualifies as) makes rolling to compare relative stat potency pointless.

20190711, 03:57 PM (ISO 8601)
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 May 2018
Re: Need a dice mechanic for unlimited stat growth
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.

20190711, 04:08 PM (ISO 8601)
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20190711, 04:55 PM (ISO 8601)
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20190711, 05:32 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
The one issue with the dΣ system is that it really rapidly runs into diminishing returns. It also runs into the "my hands are insufficiently huge for all of these dice" issue (unless you've got a set of Ubiquity dice, but that only goes so far).
...
3d6 roll under, but the d6s are backgammon doubling dice. No, I don't think this is very workable...

20190711, 05:39 PM (ISO 8601)
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 Sep 2016
Re: Need a dice mechanic for unlimited stat growth
Doubling seems a very crude jumps, perhaps split it into an octave?
...
If it is literally doubling and you just want a pass fail, effectively rolling a D 2^La against D 2^Lb/.....
Then perhaps a binary expansion of a coin toss might do the trick even more simply?
The conceit is you throw one coin for the most significant bit, a second for the next and so on, so if your level is 2^5 you effectively throw a D32
In practice if they get anything on the 64, 128, 256... positions they win straight off, so first they throw all these coins, if they get any heads they win.
If they don't then at this point then you both throw coins until only one player gets a heads (as this is 5050 you could just add that coin to a stack).
Realistically it could be argued someone twice as strong ought to win vastly more than twice as often (in chess an increase in 40 points ECF grade wins 90% of the time), but at that point the power system is far to crude to handle it anyway.Last edited by jayem; 20190711 at 05:41 PM.

20190711, 06:48 PM (ISO 8601)
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 Jul 2009
Re: Need a dice mechanic for unlimited stat growth
Alright, first some background information.
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.Me, I'm curious why you want this at all. Why have a system where each +1 doubles your strength if someone with +500 is still competing with someone who only has +1? The +500 is going to be over a google times stronger than the +1. There's no conceivable way for them to compete. The +500 is going to win no matter what.
The doubling of stats with each bonus is just an abstraction to avoid needing to know the exact numbers within the setting. Within the fiction, the monster threatening the party has 1264 Strength (or whatever arbitrary number). But at the tabletop you only need to know if it's Strength is "cakewalk", "fair fight", "don't let your guard down", or "curbstomp". If two characters have Strength +3, one might actually be stronger, but not by enough to make a significant difference.
The reason characters' power can rise indefinitely, is basically because that's what I decided, back when it was all just stories. But now that I wanna try to act it all out with some friends, I need to attach some ACTUAL game onto the fictional game.
Are you sure that you aren't going too broad? For reference, someone with a +20 Strength in your system is over a million times stronger than a +0. Someone with a +40 is over a million times stronger than that.
The reason it's a doubling is because it's the only number that's easy math. To go higher would mean each +1 is a tripling or more, making the problems happen faster, and to go lower means each +1 is a x1, which has no effect. To say "each +1 is x1.5" or something like that, stops it from being easy to calculate in your head. Powers of 2 are just easier to keep track of.
That being said, you probably could do something decent with a variation on a dice system I've been sitting on (snip)I'd look at dice pool systems like Shadowrun, World of Darkness, or (if I remember right, it's been a few years) Burning Wheelbased systems like Mouse Guard.
(snip) I say most because there are a few outliers (Roll and Keep and the One Roll Engine come to mind), (snip)Roll 1d4+your stat. To succeed, you must meet or exceed a difficulty of 3+the target stat. On a natural roll of 4, add an exploding 1d21. On a natural roll of 1, add an imploding 1d22.
If I haven't bungled my math entirely, that should give you a 50% chance of success against an equal stat, a 25% chance of success against stat+1, and halve your chance of success against each successive point of stat difference.Honestly, if it's really a doubling each time, look to Diceless. If you have more Stat than the guy you're competing with, you win. Tasks have simple stat checks: do you have the minimum required to pull it off?
Exponential growth of any sort (which compounded doubling qualifies as) makes rolling to compare relative stat potency pointless.
What's important isn't the size and number of dice used, it's what your chances are of succeeding or failing. Once you know that, THEN you can find a range of dice that covers those numbers.
On the surface I really like the "50% chance between equal stats, going up or down logarythmically from there" that Quelliandyrae suggested. But the more I think about it, the more I want to avoid a pure "success/failure" kind of mechanic.
This setting started purely as a story, and so I want to have a more narrativestyle resolution mechanic.
I really like the Apocalypse Engine's "fail forward" storydriven philosophy, but like I said, it doesn't deal with this specific setting. Also, looking at OneRoll Engine, the idea of separately resolving different aspects of a task such as degreeofsuccess and timetocompletion with a single roll blows my mind. THIS is exactly the kinda stuff I was hoping someone would show me. Offthewall new ideas that common games don't use.
This setting also allows for extremely mismatched power levels, and I wanna try to work with that as much as possible. I want people climbing up the back of a towering colossus and plunging their sword into its neck, and being thrown off as it howls in pain. I want people trying to survive the elder dragon's attacks long enough to bait it into the ravine where the king's army waits in ambush to take it down with the might of a nation. I want people coming up with clever ways to get around the massive strengths of extremely powerful enemies. A simple Succeed/Fail mechanic really doesn't seem suited for this.
Any dice system is going to come with some baggage. And as Amechra pointed out, there are practical physical limitations to what you can do with dice. If you can give some ideas of what you'd expect for a likelihood of success for a few example values, someone around here can probably get you in the ballpark.
And when I definitely fail to achieve this, with any luck, I'll at least have a system that will do MOST of what I want, with baggage I can most easily tolerate.
I'm thinking perhaps of using a d%. It all boils down to "what are your chances of success?" And most people most easily understand probability as percentages. Just figure out your chances, then try to roll that chance directly with a d%. If I can only figure out how to shoehorn more than Yes/No results in, I'll be well on my way.

20190711, 07:27 PM (ISO 8601)
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 Jul 2009
Re: Need a dice mechanic for unlimited stat growth
Wow, a lot of responses happened while I typed. Life distracted me a lot today.
A sigmoid curve is definitely the spirit I was going for. And going "difference in rank" rather than "objective bonus" will definitely help keep things simpler.
Realistically it could be argued someone twice as strong ought to win vastly more than twice as often (in chess an increase in 40 points ECF grade wins 90% of the time), but at that point the power system is far to crude to handle it anyway.
if:
0 difference is 50% / 50% success rate, and
1 difference is 25% / 75%, and
2 difference is 12.5% / 87.5%, and
3 difference is 6.25% / 93.75%, and
4 difference is 3.125% / 96.875%, and
5 difference is 1.5625% / 98.4375%, and
6 difference is 0.78125% / 99.21875%, and so on...
then your chances at 6+ difference in rank is negligible. If you just give up at that point, and call it certain/impossible, (and round some decimals), then I can eliminate a lot of recursive dice rolling/coin flipping with a single d%.
So, if you roll a d%, with a chance of:
0 diff. 50% / 50%,
1 diff. 25% / 75%,
2 diff. 12% / 78%,
3 diff. 6% / 94%,
4 diff. 3% / 97%,
5 diff. 1% / 99%,
6 diff. Don't Roll,
Then I think I have the beginning of a barebones basic system. It'll probably be rollunder for easy calculation. It will require players and DM to memorize these percentages, though. Maybe rollunder when you're the one with higher stats, and rollover when you have lower? Then you only have to remember 50,25,12,6,3,1... Or maybe just print the percentages directly on everyone's character sheet.
It's a little clunky, but does a lot of what I want...
Now to try to flesh it out. I'll think on it as I go to bed, and work tomorrow...
Thanks for everything so far. I think this may just be the most constructive help I've ever gotten on a message board...

20190711, 09:07 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Another thing you may wish to consider, especially for like the "lesser characters can hold off overwhelming ones for at least a brief time/pull epic stunts like climb a dragon to attack it" sort of thing is to use a system with a more normal probability distribution for determining chance of success, while letting results scale much higher.
Like, you could use a d20 system (or some sort of bell curve, or whatever) for making most skill checks, attack rolls, etc. Those stats scale much more slowly, every +1 being a relatively marginal improvement or whatever. But for things like damage and hit points, you have the exponential scaling.
Like, say you have a level 5 warrior with Accuracy, Defense, Strength, and Toughness 5. It's facing a giant with Accuracy 2, Defense 2, Strength 8, Toughness 8 (the giant's probably higher level than the warrior, since its higher stats are the ones with greater scaling). Say checks roll on 3d6+stat against difficulty 11+stat, and each three points you beat the difficulty by essentially adds one to your effect stat. Your "hit points" are your Toughness scaling times five, and your "damage" is your Strength scaling times one. So in a normal fight against an even foe you're looking at five hits to win.
The warrior attacks at 3d6+5 vs. 13. It deals 32 damage per hit, and has 160 hp. The giant attacks at 3d6+2 vs. 16. It deals 256 damage per hit, and has 1,280 hp. Now, the warrior might actually be able to hold out for a bit there, because it's more likely to hit, the giant's more likely to miss, it may even rack up some decent damage sine if it rolls 16+ it deals double, 19+ quadruple, etc. But if the giant lands even a single hit, the warrior's done.
More "skill" style checks would also use the normal roll. So when the warrior tries to climb on the giant's back and the giant tries to dislodge it, they're rolling 3d6+5 vs. 3d6+8 or whatever (or maybe the warrior has an Athletics skill that can roll higher or something). So it's tough but doable.
I dunno, just some more thoughts.A role playing game is three things. It is an interactive story, a game of chance, and a process in critical thinking.
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20190712, 08:20 AM (ISO 8601)
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 Jan 2009
Re: Need a dice mechanic for unlimited stat growth
This seems a very simple and elegant situation. And it avoids the issue of 'too many dice'.
You can 'fast track' it by always rolling 3d4, but using different colors. So you know which one is your base die and which one is your boon/bane die if you roll a 1 or 4. Or, really, I guess you could roll 2d4 and have one as base and one as the modifier you use if it's a 1 or 4. (Since the explode/implode is a d2, count 1 and 2 on a d4 as 1 and 3 and 4 as a 2, or something similar.)
Or literally roll a d4 and flip a coin, but rolling 2d4 is probably easier for most players.

20190712, 06:34 PM (ISO 8601)
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 Oct 2014
Re: Need a dice mechanic for unlimited stat growth
Gamers are too focused on integers. Games like Warhammer 40k only use 6sided dice and still manage to create a system with stats that work by using attack/defense comparisons.
If you don't want to do stat comparison tables, just use JRPG growth and mechanics. Divide attack by defense and that gets you a multiplier for flat damage amounts. Other games have slightly more complicated formulas but they all do a variation of this because the goal is to have damage scale infinitely. The issue here becomes that at very high totals it becomes easy to minmax and break the game which is why the games generally end and the end boss resorts to oneshot kills. Except Disgaea because you can go to level 9999 in those games and hit for millions of damage.
Point is you can use existing RPG systems that have huge stat totals in the hundreds and merely use the formula they have for working out the damage. Typically based on fractions.Trolls will be blocked. Petrification works far better than fire and acid.

20190712, 06:44 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
I have a LOT of Homebrew!
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20190712, 07:05 PM (ISO 8601)
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 Sep 2016
Re: Need a dice mechanic for unlimited stat growth
I still feel that's a bit crude. It's when things are near your level that you care. Putting me and Usain bolt in the same speed category is flattering, but...
Spoiler: that saidIf you take it as being odds to win, then it probably is a bit more reasonable. Say Usain Bolt wins 99.9% of the time (tripping the other time) that puts him at my level +10. I.E 10 levels is twice as fast and 1000 times more likely to win, 1 level is noticeably faster (7%) and twice as likely to win (which all sounds more reasonable to me)
It doesn't really make much difference if something 500 levels of strength above youor 10 (1024 times stronger), in either case you are toast. That basically gives the DM about 5 options of nontrivial fights.Spoiler32733906078961418700131896968275991522166420460430 64789483291368096133796404674554883270092325904157 15088668412756007100921725654588539305332852758937 6 times stronger
Also if something is. Then it deserves a really high level, even if you called it a level 1,000,000 creature the players would still be vastly underrating it's strength.Spoiler32733906078961418700131896968275991522166420460430 64789483291368096133796404674554883270092325904157 15088668412756007100921725654588539305332852758937 6 times stronger
In addition if these fights are of several rounds then that will mess things up further. So I think you want to build that in.

20190712, 07:26 PM (ISO 8601)
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 Jul 2009
Re: Need a dice mechanic for unlimited stat growth
I think I've had an epiphany about this whole mess today while I worked.
I've been wondering how to add in degrees of success, AND builtin narrative hooks,
AND multiple axes of succes, AND this and that and the other, and figured I'd have to come up with all these extra conditions for the dice to determine, and that calculating it all after the dice have rolled would take an annoying amount of time, and that I'd have to make a bunch of sacrifices and compromises to get a system that worked...
But today I think I've come up with something that lets me add in a lot of my moving parts without making it too complicated.
It came to me when I was thinking about opposing rolls. Most games treat opposing rolls as normal rolls with variable DC. You roll, he rolls, you compare numbers, you find out who succeeds. But when you think about it, it all comes down to two people trying to succeed at something. What if each roll checked success separately?
What happens if they both succeed? Or both fail?
The more I thought about it, the more it felt like it could fit all the crap I wanna throw in.
Imagine you're a guy trying to get into a building, but there's a guardian standing in your way, trying to keep you out.
You roll to violently get past him, and he rolls to violently repel you. Normal games would just say whoever rolls highest gets to have their way. But a much broader range of options exist.
There are the obvious ones:
Attacker succeeds, Defender fails.
"You shove your shortsword into his gut, then kick him to the side. He lays on the ground, clutching his stomach as you run inside."
Defender succeeds, Attacker fails.
"You try to attack him, but he dodges and grabs you by the collar. He lifts you up, punches you in the face, and throws you into the bushes next to the entrance. As you recover, he crosses his arms, and glares at you."
But there's more that can happen.
Attacker fails, Defender fails.
"You try to slash at him, and he dodges in the middle of trying to grab you. You're both offbalance, and collapse into a heap, limbs tangled."
Attacker succeeds, Defender succeeds.
"You slash him in the side, and manage to push past him, but as you do, he stomps down hard on your knee, injuring your leg. You're inside, but slowed down, and the fight's not out of him yet..."
I think this could bring back the flavor of the "mixed success" of Apocalypse Engine games. There'd have to be some interpretation of the results, but I think that would be more of a bonus for my needs. Heck, if I added in a crit/fumble range on rolls, then the possible outcomes should have more than enough fuel for creative DMs and players to determine success, completion time, costs, collateral damage, etc.
Obviously the DM would have to either roll for "static DC" obstacles, or maybe "take average" or something, when the character's roll isn't opposed, but I think the meat of it would still work.
I haven't crunched any numbers yet, but I think this might get me like 80% of what I want, with just two rolls for each check.
Any thoughts?

20190712, 07:50 PM (ISO 8601)
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 Jul 2009
Re: Need a dice mechanic for unlimited stat growth
Wow, why do most replies come while I'm writing my own post?
Oh well...
I can address JNAProductions's and jayem's comments at the same time.
Within the setting, people actually can reach Disgaealike levels of power. But I don't want to have sets of twelvedigit numbers on character sheets, so I abstracted the numbers. While people inworld will say "Wow, JimBob's Strength is 1500!", players at the table will only need to know that JimBob's Strength is "+10". I want to avoid videogamey JRPG type mechanics, because they're just too hard to use at the tabletop with paper, pencil, and maybe a calculator. The numbers reach those heights mainly for narrative purposes. When the enemy is way too high level, the party can find out by exactly how much, and know when it IS possible to take them on by something a little more structured than DM fiat. Also, it helps keep highpowered NPCs organized, cuz' I can tell who's likely to come out on top when they have reason to oppose each other.
I mainly want this to be a narrativefocused game, but in this case, the numbers are PART of the narrative.

20190712, 09:48 PM (ISO 8601)
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Re: Need a dice mechanic for unlimited stat growth
Oh man. Oh man.
I think I just found the simplest way to do this.
Your stat doesn't affect your roll. It affects what you can achieve with that roll.
To clarify: Torchbearer has a system where different creatures have different levels of Might. When you're dealing with beings of higher Might, you start running into limits on what you can do to them in combat. For example, if their Might is 2+ levels higher than yours? You can't kill them  you can drive them off or capture them or whatever, but you can't kill them.
You could do something similar (but more general) with your stats  then you could make it so skills with a saner range of values (or ideals, or whatever) actually determine your modifiers.

20190712, 10:50 PM (ISO 8601)
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 Nov 2006
Re: Need a dice mechanic for unlimited stat growth
A boxer's punch has about 150 Joules. That is about 2^7 Joules.
Someone +500 over a boxer can punch 2^507 Joules, or about 10^152 Joules. That energy has a weight of 10^135 kg.
The massenergy of the observable universe is about 10^53 kg.
So only the energy of the punch has more mass than the entire visible universe by a factor of 10^80.
I know, cat girls, but what I'm trying to say is "what do you mean by 2x every +1 so that +500 has meaning".
Relative probability of winning at arm wrestling? That isn't loglinear; but you could talk about collections of people such that group A_i beats A_{i1} 2 times out of 3 when arm wrestling.
The person +500 won't be lifting 2^500 times as much stuff. It will still be insane.
Suppose being 5% stronger gives you a 2/3 chance of beating someone at arm wrestling. Then 500 such steps is 1.05^500 times stronger, or 39323261827x. Your punch would carry 5898489274050 J of energy, or about 10^12 J.
To reach a punch capable of shattering the Earth, you need to hit 10^32 J. On this scale, that is around +1500.
To have a punch with as much energy as the mass of the galaxy, that is 10^42 kg * c^2 or about 10^58 J. You hit that around +3000.
If your hand is ~10 cm in diameter, it forms a black hole when there is 67331765482045288639033395 kg, or about 10^42 J, which happens around +2000 strength.
Is that the kind of scale you are looking for? You'll note it actually caps out at 2000 strength, because at that point you cannot use your strength without collapsing into a singularity (or, more accurately, already being a black hole, as punching doesn't create energy, it just moves it around).

20190713, 12:51 AM (ISO 8601)
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 Oct 2014

20190713, 06:58 AM (ISO 8601)
 Join Date
 Jun 2018
Re: Need a dice mechanic for unlimited stat growth
Never use Exploding Dice.
The creator of exploding dice cannot do math properly.
Example:
Roll a d6 get a natural 6.
Roll a second d6, get a non6 value, add 6 to it.
How the **** do I get a natural 6 value?
Not possible.
You get a 5 or a 7, but never a 6 because of the exploding dice mechanics.Level Point System 5E
Poker Roll
Tier 1 Master of All
Tier 2 Lightning Bruiser
Tier 3 Lethal Joke Character
Tier 4 Master of None
Tier 5 Crippling Overspecialization
Tier 6 Joke Character

20190713, 10:49 AM (ISO 8601)
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 Dec 2010
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 Where I live.
Re: Need a dice mechanic for unlimited stat growth
If you make your explosion 1dX1 or implosion 1dXX (like Quelliandyrae did), this problem goes away.
As an aside, the only games I can think of where this is an issue are Palladium's games (where a normal human has stats going from 315 and 1724¹), and Savage Worlds (there are potential edge cases where, for example, it's slightly easier to hit DC 6 with a d4 than a d6). Most of the other ones I can think of with explosions are dice pools that don't involve direct addition.
¹ Only stats that are 17+ matter, by the way.

20190713, 02:00 PM (ISO 8601)
 Join Date
 Jun 2015
Re: Need a dice mechanic for unlimited stat growth
Your stats are infinite,ranging from + 0 to + infinity
Each time 2 characters roll one against other, you roll 1d6+ stat and compare them. Whoever rolls higher wins, ties goes to whoever has more stat.
This means, of course, that someone with +6 will Always win against someone with +1. But also, he's 32 times stronger, so I doubt the other guy could win anyway.Final Fantasy RPG 4th Edition:
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20190715, 01:37 PM (ISO 8601)
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 Jan 2006
 Location
Re: Need a dice mechanic for unlimited stat growth
L5R also uses exploding dice in their rollandkeep system. Abraviation is NkX, where N is how many dice you roll, and X is how many dice you may keep. Sum your kept dice to get your result, and see if it's over the target number (TN). It uses d10s, and 10s explode. Because you're rolling multiple dice, the fact that no single die will ever be a 10 usually doesn't matter; it just slightly diminishes the probability of getting exactly a multiple of 10 as your result. The more dice, the more slightly. (Exploded dice count as a single die for purposes of "keeping," so if you roll a die and get a 10, explode it to a 20, then a 28, you keep the 28 as a single die.)

20190716, 02:27 PM (ISO 8601)
 Join Date
 Nov 2006
Re: Need a dice mechanic for unlimited stat growth
Exploding d6s, where you add 5+explode d6 on a 6, don't have the "can't roll 6 problem". And adding 5s is easier than adding 6s.
One problem I have with it is that exploding is quite rare, you need huge numbers of rolls to see it very often.
We can "fix" that with exploding d10s; with these dice, 0 is 0 (not 10), and any roll of a 56789 is 5+another roll. Then we get about 2/3s of an explode per roll (on average), smoothing the curve.
Results from a few trials:
2
4
0
2
0
4
3
1
9
2
2
3
8
1
1
4
6
0
4
20
10
2
4
2
0
7
5
5
04 each have a 10% chance each
59 has a 5% chance each
1014 has a 2.5% chance each
1519 has a 1.25% chance each
etc
You have a 5050 chance to roll a 5+, a 1/4 chance to roll a 10+, a 1/8 chance to roll an 15+, etc. This mimics a "exploding coin flip" system, but with 5 times more granularity.Last edited by Yakk; 20190716 at 02:29 PM.