Designing a d20 RNG

[Iduno]

For a 2d10 RNG, you roll doubles 10% of the time. You can crit on any double that hits. If you need an 11+, you crit on double 6s, double 7s, double 8s, double 8s and double 10s. That works out to 5% of the time.

If you wanted fumbles, you could do the same (fumble on double 1, 2, 3, 4 and 5)

Isn't that the same terrible crap that Games Workshop roleplaying games pull? It's the same as saying you have an unreasonably high 10% chance to crit or crit fail, but also means your skill-ups have higher or lower value for no reason.

I don't think so.

If you're rolling 2d10, your range is 2 (double 1s) to 20 (double 10s). Since there is only one combination of dice for each result, you have a 1% chance of the most extreme results.

In 3.x, your chance of a critical is a function both of how often you roll a 'threat' and how likely you are to confirm. You're always 5% likely to roll a 20. If you need an 11+ to confirm, your chance of a critical is 2.5% (5% chance to roll a threat and 50% chance to confirm). If you're threatening on a 17-20 and you confirm on a 2+, you have an 18% chance of rolling a critical. Clearly there is a range of what is acceptable before you get to 'unreasonably high'.

In 2d10, you have a 2% chance of rolling a 19 and a 3% chance of rolling an 18; if you crit on an 18-20, you have a 6% chance of rolling a critical. You could also require a confirmation roll (a la 3.x) so 18-20 w/ confirmation. The issue is that as you add additional values to the threat range, the incremental benefit is higher. If you threaten on a 17, that adds 4% (10% total); if you threaten on a 16, that adds another 5% (15% total). So 18-20 is like 3.x natural 20 only; 17-20 is like 3.x 19-20; and 16-20 is like 3.x 18-20. You can map over the threat ranges relatively easily and get something that works out pretty closely, but there's also a cost - you're adding up two numbers before you add your bonus. If you roll a 9/8, you need to confirm that that is in the threat range before you add the attack bonus. If I had a +9 bonus, I'd probably prefer to add 9+9+8 - for me that's just a hair faster than 9+8+9.

Adding doubles is easy for anyone that's learned their x2 multiplication table. The way the brain works, you can recognize it before doing the actual addition. We know that there is a 6% chance of rolling an 18 or better (3% chance of an 18 [10+8; 9+9; 8+10], but we then have to recognize each of those combinations as potential threat. If you use doubles instead of a range of results, each possibility adds +1%. The highest it can ever be is 10% (all possible double results) - there's nothing saying 'doubles always hits, even if it is a very low roll, unless you choose to. But assuming you like ~5% crit range, and you like people who are better at attacking critting more often, you can pretty easily make a roll that 'if you roll doubles and you hit, it's a critical'. If the rogue hits on a 16+ and the warrior hits on a 12+, the rogue has a 3% chance of a critical and the warrior has a 5% chance. You've eliminated the confirmation roll as a requirement and more skilled attackers are rolling criticals more often.

Personally, I don't think you need 'doubles fumble on a miss'. If you use that roll, the rogue has a 7% chance of a fumble; the warrior has a 5% chance. The higher the roll needed to hit, the more likely they are to suffer a fumble. If you think those odds are too high, you just make snake eyes the only fumble result (1%); the rogue just misses on a double 7.

Since you're making the dice rolling take longer (adding two dice always takes longer than taking a value from a single die), you want to look for ways to save time in other places. Removing re-rolls (like confirmations) is one way to do that.

Re-reading, I missed the "doubles that hit" and "doubles that miss" part. So it's a 10% total of getting a critical success or failure. It still means some skill-ups increase your critical range while others don't, with no reason behind it, but it is at least predictable.

[deaddmwalking]

Re-reading, I missed the "doubles that hit" and "doubles that miss" part. So it's a 10% total of getting a critical success or failure. It still means some skill-ups increase your critical range while others don't, with no reason behind it, but it is at least predictable.

Sorry for any confusion.

If you use 'doubles that hit', there really isn't a 'skill up' that doesn't increase your chance of a critical success. At the very least, every +2 to hit is +1% chance of a critical success.

TN is dependent on the opponent. It is possible to have a low-AC opponent and a high-AC opponent at the same time (say 14 and 23). If you have a +10 to hit, you can hit the AC 14 on a 4+ (9% critical rate), but you need a 13+ to hit the higher AC (4% critical rate). A +1 wouldn't make a difference against the first opponent (you can't get doubles with a roll of 3), but it would for the higher AC opponent. You could now roll double sixes (12) so your critical rate would increase to 5%.

[DenizenKane]

I think I'm leaning towards the percentile crit scheme. A weapon that would crit on a 20, would instead have a 5% crit chance. You roll a 2d10, and one would be the tens, and one would be the ones place. And, also you add them together for your curved to-hit if you don't crit. If your roll is 95, 96, 97, 98, or 99 you confirm a crit. I don't think it takes much more time time to see you've rolled a high percentile. And, one of the features of this crit scheme is that a 10%/x2 weapon is balanced with a 5%/x3 weapon just like 3e.

You could even integrate the miss-chance mechanic into this same roll if you wanted. So, if the opponent had blur, you'd miss automatically if you rolled 00-19 on your percentile. Also, you could use this percentile mechanic with other functions, like if you wanted an ability to proc on 30% of your hits.

[Chamomile]

Are you going to have any weapons with an 8% chance of critting? I'm guessing not, and that all crit chances will always be a multiple of 5. Since you've already got to keep track of multicolored dice in the system you have, you may as well swap it for one in which you roll two different colored d20s and one of them is the crit die.

[DenizenKane]

Are you going to have any weapons with an 8% chance of critting? I'm guessing not, and that all crit chances will always be a multiple of 5. Since you've already got to keep track of multicolored dice in the system you have, you may as well swap it for one in which you roll two different colored d20s and one of them is the crit die.

Well, this is a solution for crits on a 2d10 RNG. At this point and I'm trying to consider ways to make crits in that system most similar to 3e. (Because the curved RNG causes crit ranges to be weird). I wouldn't even need to consider it using a d20, you'd just use the 3e system. Maybe just rolling a d20 with your attack would be okay, but your crit wouldn't correspond to rolling high on your to-hit dice, so there may be a flavor disconnect.

To clarify, I'm talking about doing the percentile and the to-hit on the same 2d10 roll. So, a 14 would crit if the roll was 95. Then you roll to confirm.

[Chamomile]

Ah, that does make a difference. I must've got mixed up on what the primary RNG was somewhere along the way, I remember 2d10 coming up but apparently lost track of it. Having the flat 2d10 roll also double as a percentile crit check is probably going to take a bit of getting used to, but after the initial learning curve I expect it'd work fine. It'll eat a little bit into how many new rules players need to learn, which is something to keep an eye on, but shouldn't be a big deal by itself.

[erik]

If you paint the die then it would be visually obvious when both painted sides are up that’s a crit. You may be in odd situations where a crit isn’t a hit. Maybe to balance that paint the 9 and 0 on both. Only 4% chance but it is 18-20 on the dice.

[pragma]

What you're measuring is the odds the PCs get 5 hits before the monsters get 6 hits, or something similar turning up to spoil the mood, that's the thing people notice. The time it takes you to get 5 hits is basically a bell curve, as is the time it takes the monsters to get 6 hits. Happily, the result of comparing a bell curve to a bell curve is a bell curve, and with dice easily enough described as a single pile of both side's dice.

This is also wrong. The roll on which you get your Nth success in a series of rolls is described by a Pascal random variable, which can look decidedly non-bell-like for certain parameter values (1). The chance that you roll 5 successes before a dragon does is the difference of two Pascal random variables with different parameters, which will look a little more bell shaped by the central limit theorem but won't necessarily be well described by a bell curve.

(As an aside, when you say bell curve I assume you mean a Poisson random variable, which is a discrete random variable that is well approximated by a normal random variable over appropriate intervals. Usually the term bell curve refers to a normal random variable, which is inappropriate for die rolls because it is continuous.)

You just need to move the probability involving a PC going down off the rare events and toward the vanishingly rare events, or even into the crazy outliers, so people notice the steps over time. The standard deviation of your bell curve is SQRT(x(y+1)(y-1)/12) for xdy. That's the probability you want to noticeably shift, the percent of time the monsters gank someone, and how far you have to shift it to do that is proportional to the standard deviation. Because it's roughly a bell curve.

The expression you've given is the standard deviation for the sum of die rolls, but you aren't summing your to hit dice. It's different from the variance of whether a monster gets N hits before you get M hits, which is given by N*(1-p)/p^2+M*(1-q)/q^2 where p is the probability of your success and q the probability of monster success. Your modifier is related linearly to p in the second expression.

(By the way, I now see that the square root you were talking about is for the standard deviation, which is indeed the square root of the variance.)

And even this analysis isn't entirely correct. What you really care about is total damage over N rounds, not total hits. That calculation doesn't have a closed form because the DPR random variable is actually a pretty weird one with a lot of probability mass at zero to reflect miss chances. You can get a look at one of these distributions by pasting the code below into http://topps.diku.dk/torbenm/troll.msp

Code: Select all

\ Greatsword damage 
tohit:=7;
bonus:=5;
critrange:=2;
critmult:=2;
hit:=1d20; 
confirm:=1d20;
dmg:=sum 2d6; 
if hit<tohit then 0 else 
if hit>&#40;20-critrange&#41;&confirm>tohit then critmult*&#40;dmg+bonus&#41; else dmg+bonus 

(1) https://www.probabilitycourse.com/chapt ... _distr.php

[DenizenKane]

Been thinking about this more, and I think rolling a d20 alongside your 2d10 for your attack rolls is the best choice for crits.

It gives you even 5% crit chance increments like 3e and still gives you a curved attack roll, its easy to read, adds negligible time or complication, plus you get to use the d20 and all the fun of hitting that nat 20 on it.

Also, since you're rolling them together already, you can use the 2d10 attack roll to confirm your critical as well. Also, you can make the 1d20 roll a roll for your miss percentile for blur effects (because you only care about increments of >=5% anyway), and percentage based procs at the same time. So, on the low end of the d20 roll you miss because of blur, and on the high end you get a crit to confirm.

[Username17]

Been thinking about this more, and I think rolling a d20 alongside your 2d10 for your attack rolls is the best choice for crits.

I hope not. People had the option of rolling a crit confirmation die alongside their to-hit die in 3rd edition. But they don't do that, because it's an incredible pain in the ass.

-Username17

[DenizenKane]

Been thinking about this more, and I think rolling a d20 alongside your 2d10 for your attack rolls is the best choice for crits.

I hope not. People had the option of rolling a crit confirmation die alongside their to-hit die in 3rd edition. But they don't do that, because it's an incredible pain in the ass.

-Username17

Yeah, you're right. The percentile idea is better. So, the player rolls 2d10 that is both a 2d10 attack roll, and d100 percentile to check for crits and miss. One of your dice is the tens, one is the ones. Before checking your attack roll, you see if you need to confirm a crit. A 5% crit weapon crits on 100, 99, 98, 97, and 96. If the opponent has blur, you would miss if you rolled 1-20.

For the Stats, I've been thinking about dropping them to 4. Strength (Str), Agility (Agi), Intellect (Int), and Presence (Pre). Strength is Con and Str combined, Presence is Wis and Cha combined. This means that characters that are strong, also have high HPs and fort saves. And, characters that are convincing now have strong wills and are less likely to fall for their own BS.

Modifiers for stats are never negative.
0 = +0
1-2 = +1
3-4 = +2
...
17-18 = +9
...

A Barbarian with 20 STR is gaining +10HP per HD, and the Wizard with 8 Str is still getting +4 HP per HD instead of -1.

A character with 8 STR has a +4 to jump instead of a -1, allowing them to consistently jump a foot into the air.


Skill ranks are Untrained (+0)/Trained(+3)/Expert(+6)/Master(+9). Class Skills are skills that your class automatically has Trained (or possibly more, I can see Wizards starting as Masters of Arcana without spending a skill point), and you gain +Int skill points at level 1. Classes may gain skill points as they level, at a rate of 1/2 to 2 a level.

Athletics (Str)
Uses: Climb, Jump, Swim, Run, Ride

Acrobatics (Agi)
Uses: Tumble, Balance, Fly, Hide, Move Silently

Sleight of Hand (Agi)
Escape Artist, Open Lock, Sleight of Hand, Use Rope

Perception (Pre)
Uses: Spot, Listen, Search, Sense Motive

Persuasion (Pre)
Uses: Bluff, Disguise, Diplomacy, Perform, Gather Information

Survival (Pre)
Survival, Heal, Handle Animal, Knowledge (Nature, Geography)

Linguistics (Int)
Uses: Decipher Script, Language, Forgery, Knowledge (History, Local, Nobility)

Arcana (Int)
Spellcraft, Concentration, Use Magic Device, Knowledge (Arcana, Religion, Planes)

Craftsmanship (Int)
Appraise, Craft, Disable Device, Profession, Knowledge (Engineering, Dungeoneering)

[DenizenKane]

Perception (Pre)
Uses: Spot, Listen, Search, Sense Motive

Persuasion (Pre)
Uses: Diplomacy, Perform

Deception (Pre)
Bluff, Disguise

Connections (Pre)
Gather Information, Knowledge (Local, Nobility)

Linguistics (Int)
Uses: Decipher Script, Language, Forgery, Knowledge (History)

Athletics (Str)
Uses: Climb, Jump, Swim, Run, Ride

Acrobatics (Agi)
Uses: Tumble, Balance, Fly

Stealth (Agi)
Hide, Move Silently

Sleight of Hand (Agi)
Escape Artist, Sleight of Hand, Use Rope

Devices (Int)
Uses: Use Magic Device, Open Lock, Disable Device

Arcana (Int)
Spellcraft, Concentration, Knowledge (Arcana, Religion, Planes)

Craftsmanship (Int)
Appraise, Craft, Profession, Knowledge (Engineering, Dungeoneering)

Survival (Pre)
Survival, Heal, Handle Animal, Knowledge (Nature, Geography)

I can also see splitting it something like this, just gonna have to shuffle it around until I find the sweet spot.

[deaddmwalking]

Yeah, you're right. The percentile idea is better. So, the player rolls 2d10 that is both a 2d10 attack roll, and d100 percentile to check for crits and miss. One of your dice is the tens, one is the ones. Before checking your attack roll, you see if you need to confirm a crit. A 5% crit weapon crits on 100, 99, 98, 97, and 96. If the opponent has blur, you would miss if you rolled 1-20.

Running two operations on the same dice isn't as easy as you think. Play test the heck out of it.

If you have a 10s die and a 2 die, then 6+9 isn't the same as 9+6 (even though both roll 15). Now, if one of those is a critical (or potential critical) you have to spend a non-marginal amount of brain energy distinguishing between the two results.

[DenizenKane]

Yeah, you're right. The percentile idea is better. So, the player rolls 2d10 that is both a 2d10 attack roll, and d100 percentile to check for crits and miss. One of your dice is the tens, one is the ones. Before checking your attack roll, you see if you need to confirm a crit. A 5% crit weapon crits on 100, 99, 98, 97, and 96. If the opponent has blur, you would miss if you rolled 1-20.

Running two operations on the same dice isn't as easy as you think. Play test the heck out of it.

If you have a 10s die and a 2 die, then 6+9 isn't the same as 9+6 (even though both roll 15). Now, if one of those is a critical (or potential critical) you have to spend a non-marginal amount of brain energy distinguishing between the two results.

Yes, this is a concern, but if you have 2 different colored dice, or a tens dice, it should be trivial. If you have 2 attacks you would need 4 different colored dice (or 2 different colored pairs of ones and tens d10s.), or roll them separately. If I were to release dice for this game, one of the products would be a rainbow pack of d10s with ones and tens places. And, as mentioned before you could put dots of paint or marker on your crit sides. I will be playtesting it though, my group is going to be "alpha" testing this game for our next campaign.

[deaddmwalking]

Yes, this is a concern, but if you have 2 different colored dice, or a tens dice, it should be trivial.

When you playtest it, you should include a number of people with different levels of experience.

Using 2d10 (which I favor) already involves adding two digits to get your die roll, then adding in at least one other digit for your modifier. It may have additional factors based on conditional modifiers (flanking, secondary attacks, advantage, etc).

When you accrete trivial operations, they cease to be trivial in aggregate.


Right now, your best case scenario has me rolling a d100 and determining two values. I happened to roll '42'. I'm adding the digits (6) to my attack modifier to determine if I hit, and simultaneously comparing the percentage result (42) to various other functions (critical hits, miss chance, etc). What if I also have modifiers to that result? For example, what if I had a feat that let me ignore half the concealment penalty for invisibility?

You also have a potential issue that results from performing two operations from the dice. Let's say that I have a miss chance of 20%. Clearly, if I roll a 01-20 on the percentile function, I'd miss (due to miss chance). However, a 1 or 2 on the 10s die is going to skew my die results very low anyway. You're essentially rolling 1d10+1 or 1d10+2 on any result that could be a miss. A result of 2, 3, 4, 5, 6, 7, 8, or 9 on the dice is probably already a miss, so you're not actually adding any more information density to your die roll. Assuming you could hit on a 10, 11 or 12, each of which has a 2% chance of being rolled assuming that one die is a 1 or a 2, your '20% miss chance' is really only 6% miss chance - attacks that WOULD have hit, but instead miss.

I think you're clinging too close to d20 outputs. If that's what you want, you should just use the d20.

If you're using a 2d10 RNG, you should consider taking advantage of its differences to solve problems in a different way.

[DenizenKane]

Yeah, I see what you're saying. My ideas are pretty bad sometimes.

Anyway, I'm starting to lean more towards having a flat 10% crit chance where a crit to confirm is rolling doubles. I don't think I want fumbles in this system.

Also, It saves alot of game time and gives magic users something to do if they roll for attacks, so I'll be moving away from a save model, and having firemages roll fireball attacks against a fortitude defense. Also, you can now crit on a fireball, which might cause an explosion or max dice or something.

EDIT: Actually, might make the crits rolls of 17+ because doubles is cool, but it doesnt work as well in a digital roller that outputs 2d10 results as a single number. Extending crit ranges never worked out that well anyway.

[DenizenKane]

So, been thinking more about this, and I think I'm looking at this the wrong way because I don't have a solid enough outline.

That being said, I thinking keeping the D&D theme while rethinking all the mechanics is the only way to make this game fun, and make it worth the effort of making at all.

So, for HP, I've been thinking about changing it a flat HP model with a Hit Roll vs AC, and Damage Roll vs Soak.

Hit = 2d10 + Agility
Armor Class = 10 + Agility
Soak = 10 + Strength + Armor + Level
Damage = 2d10 + Strength + Weapon + Level

The standard deviation of 2d10 is 4, so I think 10, 14, 18, 22, 26 might be good target numbers for damage. Where 10 (+0) gives a light wound, 14 (+4) is medium, 18 (+8) is serious, and 22 (+12) is deadly, 26 (+16) is extra deadly.

[deaddmwalking]

That being said, I thinking keeping the D&D theme while rethinking all the mechanics is the only way to make this game fun, and make it worth the effort of making at all.

Hit = 2d10 + Agility

In our Heartbreaker, we originally went with Agility for attack with all melee weapons. Agility was something of an uber-stat. If it contributes to your ability to hit and your ability to avoid being hit, it's pretty compelling to max it out. We did have max agility limits with armor, but there was a pretty big incentive for every melee character to go full gladiator and wear nothing but body oil.

Currently, we use Strength for attack rolls with 2-handed weapons. We use Agility for light weapons. For one-handed weapons, you choose. When using light weapons, in situations where a rogue could get a sneak attack anyone adds agility to damage.

This seems to have had the desired effect where character builds tend to be less 'samey' than before we made these changes.

[DenizenKane]

I'm thinking about getting rid of stats altogether. About the only thing that stats do other than RNG breakage is give you some scores to eat at for ability damage and a strength score for carrying capacity, and those both can be handled other ways. I think your modifiers should be all be tied to class, equipment, and skills.

[deaddmwalking]

I'm thinking about getting rid of stats altogether. About the only thing that stats do other than RNG breakage is give you some scores to eat at for ability damage and a strength score for carrying capacity, and those both can be handled other ways. I think your modifiers should be all be tied to class, equipment, and skills.

That's certainly one way to do it, but there is a reason why stats remain popular.

Take River Tam from Firefly and, I don't know, Conan as played by Arnold Schwarzenegger. From a class/equipment/skills perspective, they're going to end up looking very similar. They both can kill people with a deadly weapon.

But the person playing a character based on River wants a way to distinguish their character from the muscle-bound bruiser.

When the system allows it, you constantly see 'STR fighters' and 'DEX fighters'.

If you create a way for those characters to exist WITHOUT the abilities, that can work, but it is definitely HARDER.

The moment a Warrior with a greatsword is ALWAYS better than a Chakram you're going to lose the Xena crowd.

[erik]

Just have a Fight stat and you include fast light fighters and heavy fighters.

[deaddmwalking]

Just have a Fight stat and you include fast light fighters and heavy fighters.

But if you have a 'fight stat', what goes into it that's different between the two if not an attribute?

[erik]

Just have a Fight stat and you include fast light fighters and heavy fighters.

But if you have a 'fight stat', what goes into it that's different between the two if not an attribute?

Other than fluff? Only stuff that you care about. If you care about carrying capacity or stealth or speed then those stats may be different. I like having stats that are closer to skills in that they are directly applied. I know dnd has crap like dex checks but those almost always suck and aren’t used. Reason being if you want to have multiple modifiers then that attribute has to be pretty inconsequential on its own. So you get stuff like halflings beating giants at arm wrestling.

[Username17]

In abstract, you definitely could handle everything on the level of skills. You could have a character sheet that simply told you what your character's modifiers were for punching dudes or solving astronomical puzzles. The actual actions your character takes in the game are the modifiers that matter, and if your game has few enough categories of die roll you'll actually be called upon to roll that it can fit them all on a piece of paper the end modifiers can be all there is. It's even easier for the player with the character sheet because they don't have to add things before rolls and there aren't useless numbers on their character sheet that represent quantities that have no direct relevance.

But that doesn't mean that there isn't a cost to doing things like that. The most obvious cost is that you have to define all the tasks that could be done and write them out ahead of time. That's trivial in a computer game or board game, but it's a slightly harder prospect in an open ended RPG where player characters might plausibly end up time traveling or doing a genre crossover with a western or some shit. But perhaps the more salient problem is that it's genuinely difficult to describe what characters do in such a system. That is, a character might be good at Medicine and Computers and Repair but you actually have to list all those things when describing your character to other players. That's a pain in the ass and also not very informative since even then you don't give away what your character's secondary and passable avenues of contribution might be.

That's where things like Abilities and Character Classes come in. By describing a character as "smart" or "a techie" or whatever you can get some information across to the other players that is packaged in a manner the other players can digest and interpret and most importantly extrapolate from.

If you're going to have Warriors, it's potentially a nice thing to be able to differentiate between different kinds. Especially if it would be plausible that more than one player would be playing one at the same time. And thus having some kind of additional qualifier you can put on "Warriors" is a good thing. Stats and themes and kits and shit are good for that.

-Username17

[DenizenKane]

So does this work for a fixed HP system?

HP = 10
Attack = 2d10 + Mods
Defense = 11 + Mods
Damage = 2d10 + Mods
Toughness = 7 + Mods
Beating toughness by 1+ gives 1 damage, 5+ gives 3, 9+ gives 6, and 13+ gives 10 damage.