A different kind of RNG for D&D 3.X
Posted: Mon Jun 06, 2016 11:20 pm
Another RNG thread? Really?
Yes.
So, with the current RNG system (d20+bonuses vs DC), and the usual situation (the number that actually matters in most cases is not a probability of succeeding, but rather an average number of attempts between failures/successes), the +1 bonus can actually have a vastly different effect on your survivability depending on both the DC and your current bonus. Also, there's the annoying effect where, at high levels, even characters of same level that are both supposed to be able to do something can have bonuses to doing that thing, that are not on RNG within each other, due to accumulation of a lot of little +1's little bullshit modifiers.
I've seen some people here that wanted to switch to a dicepool system, but dicepools have a negative side in that, while it's harder to technically get off RNG, practically you do so even faster than in d20 system, and again, that +1 bonus can have vastly different effects, depending on whenever you start near the center of the bell curve or in its tail. Also, it's very hard to figure out how to convert the existing D&D numbers so that they'll continue to make sense.
So, I've tried to make a RNG system that would be:
1) At least somewhat compatible with D&D 3.X and existing numbers in it (so you can theoretically plug it in).
2) Have the system be based around the "average number of attempts before success/failure" as directly as possible.
3) Have a +1 bonus mean the same thing on as large range of possible bonus values and DCs as possible.
4) Do not have a "get off RNG" effect at all.
The result is this algorithm: when you have to roll against a DC, you add all your bonuses and maluses together, add 11 to the result, then substract the DC from it. You should arrive at a number +N, +0, or -N, where N - some integer number. For later reference, I'm going to call it "resolution number".
If it's +0, then you simply flip a coin, or roll a d6 and succeed on 4,5,6 - 50/50.
If it's a positive number, you then roll a number of d10's equal to that number plus 6, and if at least one of them has 10 on it, you succeed.
If it's a negative number, you roll a number of d10s equal to the (module of that number + 6), and if at least one of them has 1 on it, you fail.
What is this shit and why is it so complicated?
The reasoning here is that every +1/-1 in this system, unless it flips the sign of the resolution number, increases/decreases the average number of attempts between successes/failures by 10%, because every new d10 die adds a separate and independent 10% chance to succeed/fail, probabilty of a event "all dices don't roll a certain number" is equal to a multiplication of probabilities for each dice to "not roll a certain number", which means it scales exponentially, and average number of attempts is inverse of probability, so it scales exponentially, too.
Which is about equal to an effect of +1/-1 bonus in in D&D if you roll against DC 11 with +0 modifier - 50% success chance turns to 55% and 45%, which results in about +10%/-10% relative difference in average number of attempts between successes/failures.
So in effect, it's mostly similiar to d20 near the region where chances of success/failure are equal, and diverges as you go away from it.
That also explains why the heck I'm using d10's here, and not d20's.
Where the heck did that "+6" came from?
It's to make it relatively smoothly transition from "likely success" through "50/50" into "likely failure" zone. With 7 d10, chances of at least one of them rolling up 1 (at negative resolution number) or 10 (at positive resolution number) is about 52%, which results in about 2.09 average rounds between failures/successes. It's not as smooth as I'd like it to be, but that's the best you can get with d10s.
This system has me rolling piles of dices, fuck this non-D&D bullshit.
Well, it's not actually that hard, especially seeing that you only have to watch out for dices that roll a certain number - and that's very easy to spot. It's also very easy to extend towards very large numbers - since you don't actually have to keep in mind any numbers (as in most dicepool systems), you can just, instead of rolling all dices at once, roll the first 10 d10s, then, if it didn't show up a single 1/10, roll a second dozen of d10s, and so on. Pretty easy, as long as you remember how many dices you've already rolled.
Wait, does this "no to getting off RNG" business mean that my uber-armored-character can no longer be effectively invincible to the low-level plebs?
You can still become effectively invincible, because the average time between failures scales exponentially with the bonus you get.
For example, at resolution number of +10 (equal to DC 21 - which is already off RNG in normal d20 system), you get 5.4 attack attempts between someone sticks it through the armor. Not that high, right?
If your resolution number on AC check is +20, the average number of attack attempts is about 15.5. Getting there...
With resolution number of +30, it rises up to 37.7 - which is more than a d20 system's maximum 20.
And for +40, it's more than a hundred - 127.3 average attempts, before the poor low-level shmucks get one attack through your armor.
As you can see, there's still enough space in the system for numerically-ridiculously-overpowered shit, unlike in 5e with its "bounded accuracy" crap. And what's more, all these additional little +1 bullshit modifiers that you simply forget about in normal D&D play, they all still matter, even at such high level - because every single one of them still increases that number by 10%. And, they also don't break RNG.
Any criticism?
Yes.
So, with the current RNG system (d20+bonuses vs DC), and the usual situation (the number that actually matters in most cases is not a probability of succeeding, but rather an average number of attempts between failures/successes), the +1 bonus can actually have a vastly different effect on your survivability depending on both the DC and your current bonus. Also, there's the annoying effect where, at high levels, even characters of same level that are both supposed to be able to do something can have bonuses to doing that thing, that are not on RNG within each other, due to accumulation of a lot of little +1's little bullshit modifiers.
I've seen some people here that wanted to switch to a dicepool system, but dicepools have a negative side in that, while it's harder to technically get off RNG, practically you do so even faster than in d20 system, and again, that +1 bonus can have vastly different effects, depending on whenever you start near the center of the bell curve or in its tail. Also, it's very hard to figure out how to convert the existing D&D numbers so that they'll continue to make sense.
So, I've tried to make a RNG system that would be:
1) At least somewhat compatible with D&D 3.X and existing numbers in it (so you can theoretically plug it in).
2) Have the system be based around the "average number of attempts before success/failure" as directly as possible.
3) Have a +1 bonus mean the same thing on as large range of possible bonus values and DCs as possible.
4) Do not have a "get off RNG" effect at all.
The result is this algorithm: when you have to roll against a DC, you add all your bonuses and maluses together, add 11 to the result, then substract the DC from it. You should arrive at a number +N, +0, or -N, where N - some integer number. For later reference, I'm going to call it "resolution number".
If it's +0, then you simply flip a coin, or roll a d6 and succeed on 4,5,6 - 50/50.
If it's a positive number, you then roll a number of d10's equal to that number plus 6, and if at least one of them has 10 on it, you succeed.
If it's a negative number, you roll a number of d10s equal to the (module of that number + 6), and if at least one of them has 1 on it, you fail.
What is this shit and why is it so complicated?
The reasoning here is that every +1/-1 in this system, unless it flips the sign of the resolution number, increases/decreases the average number of attempts between successes/failures by 10%, because every new d10 die adds a separate and independent 10% chance to succeed/fail, probabilty of a event "all dices don't roll a certain number" is equal to a multiplication of probabilities for each dice to "not roll a certain number", which means it scales exponentially, and average number of attempts is inverse of probability, so it scales exponentially, too.
Which is about equal to an effect of +1/-1 bonus in in D&D if you roll against DC 11 with +0 modifier - 50% success chance turns to 55% and 45%, which results in about +10%/-10% relative difference in average number of attempts between successes/failures.
So in effect, it's mostly similiar to d20 near the region where chances of success/failure are equal, and diverges as you go away from it.
That also explains why the heck I'm using d10's here, and not d20's.
Where the heck did that "+6" came from?
It's to make it relatively smoothly transition from "likely success" through "50/50" into "likely failure" zone. With 7 d10, chances of at least one of them rolling up 1 (at negative resolution number) or 10 (at positive resolution number) is about 52%, which results in about 2.09 average rounds between failures/successes. It's not as smooth as I'd like it to be, but that's the best you can get with d10s.
This system has me rolling piles of dices, fuck this non-D&D bullshit.
Well, it's not actually that hard, especially seeing that you only have to watch out for dices that roll a certain number - and that's very easy to spot. It's also very easy to extend towards very large numbers - since you don't actually have to keep in mind any numbers (as in most dicepool systems), you can just, instead of rolling all dices at once, roll the first 10 d10s, then, if it didn't show up a single 1/10, roll a second dozen of d10s, and so on. Pretty easy, as long as you remember how many dices you've already rolled.
Wait, does this "no to getting off RNG" business mean that my uber-armored-character can no longer be effectively invincible to the low-level plebs?
You can still become effectively invincible, because the average time between failures scales exponentially with the bonus you get.
For example, at resolution number of +10 (equal to DC 21 - which is already off RNG in normal d20 system), you get 5.4 attack attempts between someone sticks it through the armor. Not that high, right?
If your resolution number on AC check is +20, the average number of attack attempts is about 15.5. Getting there...
With resolution number of +30, it rises up to 37.7 - which is more than a d20 system's maximum 20.
And for +40, it's more than a hundred - 127.3 average attempts, before the poor low-level shmucks get one attack through your armor.
As you can see, there's still enough space in the system for numerically-ridiculously-overpowered shit, unlike in 5e with its "bounded accuracy" crap. And what's more, all these additional little +1 bullshit modifiers that you simply forget about in normal D&D play, they all still matter, even at such high level - because every single one of them still increases that number by 10%. And, they also don't break RNG.
Any criticism?