mathematical flaw in the D% system


Rules Questions


i just came to a terrible realization when combing through rules on concealment and other things that use a D% to determine hit/miss.

i noticed that just about every D% roll in the came (at least that i can find so far) is in an increment of 10. normally this isn't a bad thing, but when you figure the fact that the most common way a player or GM rolls for D% (out of 100) is with two D10's you notice that it suddenly your 20/100 is really a 2/10, which, while making the roll much simpler, also eliminates the need for the 2nd dice entirely.

i cant find a single instance where a D% roll goes up or down by a single number or by 5, or anything like that so as to create a roll that is dependent on both dice.

while not exactly game breaking, it does beg the question: why bother ever putting the D% into the rules instead of just using a single D10? would that not be simpler?

Sovereign Court

I'm almost certain that some kind of combination of obscure splat or racial trait, feat or spell ends up modifying a miss chance to a multiple of 5.

Shadow Lodge

A lot of people use the d10 for miss chance. Its not uncommon. Heck, I even use a d20 when the % goes up by 5, and on 25% stuff I use a d4. Nothing requires you use the D% at all.

Grand Lodge RPG Superstar 2012 Top 32

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Augury and divination.

Silver Crusade

I have a vague recollection that it was stated that 3rd ed uses a d20 when modifiers are expected, and a d% when no modifiers are expected.

Of course, that unblemished d% may have been diluted over the years...


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How is this a mathematical flaw? The extra die may be superfluous but it is not a flaw.


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A lot of tables work off d% and have small enough increments to justify it, from random loot to Teleport attempts.


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Shimesen wrote:

i just came to a terrible realization when combing through rules on concealment and other things that use a D% to determine hit/miss.

i noticed that just about every D% roll in the came (at least that i can find so far) is in an increment of 10. normally this isn't a bad thing, but when you figure the fact that the most common way a player or GM rolls for D% (out of 100) is with two D10's you notice that it suddenly your 20/100 is really a 2/10, which, while making the roll much simpler, also eliminates the need for the 2nd dice entirely.

i cant find a single instance where a D% roll goes up or down by a single number or by 5, or anything like that so as to create a roll that is dependent on both dice.

while not exactly game breaking, it does beg the question: why bother ever putting the D% into the rules instead of just using a single D10? would that not be simpler?

This has nothing to do with question begging. Sorry, it's a pet peeve that so many people don't really understand what question begging is and continuously use the term wrong. What you meant to say is "this raises the question."

Grand Lodge

Pathfinder Starfinder Roleplaying Game Subscriber

Given that there are variations in how different abilities use the percentile dice and there are things that occaisonally break the nice 5 or 10 percent multiplier, it's helpful to keep it consistent by just using one die type for percentile rolls.


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Different tables will have different simplifications to the overly complicated d% system.

For example, we simply roll an ordered 4d4 and interpret the result as a base four number (0-127 in base ten, 100 to 127 -> reroll). The hardest part is remembering which d4 goes first, second, etc., so we default to a ROY G BIV convention. I guess just dropping the second d10 for concealment chance probably could be workable as well.


Pathfinder Adventure Path Subscriber; Starfinder Charter Superscriber

What about Teleport?

Familiarity On Target Off Target Similar Area Mishap
Very familiar 01–97 98–99 100 —
Studied carefully 01–94 95–97 98–99 100
Seen casually 01–88 89–94 95–98 99–100
Viewed once 01–76 77–88 89–96 97–100
False destination — — 81–92 93–100

The percentile dice do not have any mathematical flaw in them that I can determine. So this thread is for what exactly??

Edit: The chart obviously did not format the way I have it in my edit screen, but you get the picture. Lot's on non-ten increments there!


Shimesen wrote:


while not exactly game breaking, it does beg the question: why bother ever putting the D% into the rules instead of just using a single D10? would that not be simpler?

I have a 5 in 10 chance of beating a 5 when rolling a d10.

I have a 50% chance of beating 50% when rolling d%. That means I could roll anything between a 01, though 45, up to 49, and 50 to beat.

Those two things are not the same.

I assume you've been doing fractions in school and have division on the brain, or something. Makes you think you can simplify odds in the same way. But actually, it's more complicated than that.


OK, I guess charts such as look and teleport are a thing, and actually need a D%. I completely forgot about them, to be honest. There's also random loot and magic item tables, but aside from these tables, which it make sense to use it on, other rules such as concealment don't need to use the same dice. Its an over complication of the math unless someone knows of some feat/ability/trait/etc that increases these kinds of values my increments of less than 5.

Shadow Lodge

Using the d% system for Concealment and many other things is actually a simplification, because it's really easy to say that it's a 50% chance and roll a d%. It also means that a lot of tables can be standardized and are easily adaptable when other factors not previously considered have to be added in.

Example: Confusion table could use a d4, but the GM might rule that one effect over another is more likely depending on environmental circumstances; it's easy to change the percentage roll, not easy to change the die type entirely.

Other things that use d% rolls in smaller increments: disease chances in some zones, wandering monster tables, random encounter percentages, Contact Other Plane, Plane Shift (distance 5-500 miles from target), Reincarnate, Spell Turning, Weather tables, random charges for magic items like wands, Rod of Wonder and all manner of other magic items. I ignored things previously mentioned.


Demon/devil summonings are often X5% when they do not have a 50% chance of success.


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Shimesen wrote:
OK, I guess charts such as look and teleport are a thing, and actually need a D%. I completely forgot about them, to be honest. There's also random loot and magic item tables, but aside from these tables, which it make sense to use it on, other rules such as concealment don't need to use the same dice. Its an over complication of the math unless someone knows of some feat/ability/trait/etc that increases these kinds of values my increments of less than 5.

When I GM, I assign concealment % on the fly for the rough % of the 5ft cube the target actually occupies.

An invisible toad has a much smaller % to hit randomly than an invisible squeezing ogre.

I know that isn't strict RAW, but is certainly permissible to adjust the % miss chance.

Quote:

Varying Degrees of Concealment

Certain situations may provide more or less than typical concealment, and modify the miss chance accordingly.


Reincarnate (spell) uses the D% dice:

Quote:


01______Bugbear.
02-13___Dwarf
14-25___Elf
26______Gnoll
27-38___Gnome
39-42___Goblin (Advanced Race Guide Goblin)
43-52___Half-elf
53-62___Half-orc
63-74___Halfling
75-89___Human
90-93___Kobold (Advanced Race Guide Kobold)
94______Lizardfolk
95-98___Orc (Advanced Race Guide Orc)
99______Troglodyte
100_____Other (GM's choice)


If you don't use a d100 you're doing it wrong... People look at me funny when I pull it out and insist on using it, but I still say it's one of the best dice investments I ever made.


Am I The Only One? wrote:
Shimesen wrote:


while not exactly game breaking, it does beg the question: why bother ever putting the D% into the rules instead of just using a single D10? would that not be simpler?

I have a 5 in 10 chance of beating a 5 when rolling a d10.

I have a 50% chance of beating 50% when rolling d%. That means I could roll anything between a 01, though 45, up to 49, and 50 to beat.

Those two things are not the same.

I assume you've been doing fractions in school and have division on the brain, or something. Makes you think you can simplify odds in the same way. But actually, it's more complicated than that.

A 5 in 10 chance is still 50%. Functionally, there is no difference.


Paulicus wrote:
Am I The Only One? wrote:
Shimesen wrote:


while not exactly game breaking, it does beg the question: why bother ever putting the D% into the rules instead of just using a single D10? would that not be simpler?

I have a 5 in 10 chance of beating a 5 when rolling a d10.

I have a 50% chance of beating 50% when rolling d%. That means I could roll anything between a 01, though 45, up to 49, and 50 to beat.

Those two things are not the same.

I assume you've been doing fractions in school and have division on the brain, or something. Makes you think you can simplify odds in the same way. But actually, it's more complicated than that.

A 5 in 10 chance is still 50%. Functionally, there is no difference.

Yeah I'm not seeing the issue here. 1-50, 51-00 is the same as 1-5, 6-10. Maybe he means it has something to do with dice not being entirely accurate and having the percent roll somehow affects that? I dunno.


Hi there, you must be new.
I can tell because you said you've never seen a % chart with anything other than even 10% increments, where there are dozens just in the core. Random treasure, events in the Kingdom Building rules, Teleport, Reincarnate, random encounter tables, and so forth.

There's nothing wrong with being new, and I welcome you to the hobby.

Grand Lodge

Flesh Golems go berserk on a cumulative 1% chance. Not sure if anything else really uses incremental percentages.


FLite wrote:
Flesh Golems go berserk on a cumulative 1% chance. Not sure if anything else really uses incremental percentages.

Clay golems, possibly my favorite golem ever.

Shadow Lodge

That is not the d% SYSTEM, that is a d% ROLL.

It's still a part of the d20 system.


chaoseffect wrote:
If you don't use a d100 you're doing it wrong... People look at me funny when I pull it out and insist on using it, but I still say it's one of the best dice investments I ever made.

We used one of those once. I think it is still rolling...


Durngrun Stonebreaker wrote:
chaoseffect wrote:
If you don't use a d100 you're doing it wrong... People look at me funny when I pull it out and insist on using it, but I still say it's one of the best dice investments I ever made.
We used one of those once. I think it is still rolling...

And if it ever does stop you won't have any idea what it landed on. But that's part of the charm. Makes everything hard mode!


I know a Mathematician that has "lucky d10s" and will argue all day that there is a difference between rolling his % d10s and anything else.

Yes they are mathematically the same but some people still like rolling the 2 d10s for % rolls

My GM has us roll % for a lot of things...I remember trying to find an Assassin's Dagger once...he had me roll % twice and had me call low or high...I called low the first roll and got a 2...high the second time and got a 98...he was a little perturbed since my chances were suppose to be 2%...best roll of my career lol


Drakkiel wrote:

I know a Mathematician that has "lucky d10s" and will argue all day that there is a difference between rolling his % d10s and anything else.

Yes they are mathematically the same but some people still like rolling the 2 d10s for % rolls

You mathematician is not wrong. Dice are not perfect and thus some are more likely to land on the 10 side then on the 1 side. An example would be if the die edges of the 1 side are smoother and thus make it more likely to keep rolling and if the edges of the 10 side are sharper and thus more likely to stop the die from rolling.

So it is pretty likely that due to small (or big) flaws in the die, there indeed is a difference between rolling it and any other die.


chaoseffect wrote:
Durngrun Stonebreaker wrote:
chaoseffect wrote:
If you don't use a d100 you're doing it wrong... People look at me funny when I pull it out and insist on using it, but I still say it's one of the best dice investments I ever made.
We used one of those once. I think it is still rolling...
And if it ever does stop you won't have any idea what it landed on. But that's part of the charm. Makes everything hard mode!

I got a ban on using my d100 because my GM grew tired of waiting for it to stop :(

Scarab Sages

I thought this was a thread about Runequest, or Call of Cthulhu, both of which use a d% resolution system.

To answer the original post, some abilities allow a creature to modify the base %age concelament, so a 50% would become a 25%.

That said, whenever a modified chance is a flat increment of 10%, we will usually roll one d10, for speed.

And if someone is finding that one of their d10 is giving skewed results, it should be dealt with like any other loaded die; smashed into dust on the pavement.

Spoiler:
...or kept for use with another group who hasn't spotted it yet. You know who you are.


Many dice can be heated, which causes them to seep lightly. The number on the bottom typically then becomes the largest/heaviest face of the die and the opposing face to become ever so slightly curved... causing the bottom face to turn up the least often, and causing the opposite face to turn up the most frequently.

This also happens over very long periods of time naturally. So... store your dice with your desired number facing up >.>


Snorter wrote:

I thought this was a thread about Runequest, or Call of Cthulhu, both of which use a d% resolution system.

To answer the original post, some abilities allow a creature to modify the base %age concelament, so a 50% would become a 25%.

That said, whenever a modified chance is a flat increment of 10%, we will usually roll one d10, for speed.

And if someone is finding that one of their d10 is giving skewed results, it should be dealt with like any other loaded die; smashed into dust on the pavement.

** spoiler omitted **

Snorts - I've PMed you. Twice now :-)

Scarab Sages

Got it. It's not a problem, but I haven't been able to compose a proper reply, as I'm playing catch-up after us puking for a few days, and I need to get on with some editing asap.


Remy Balster wrote:

Many dice can be heated, which causes them to seep lightly. The number on the bottom typically then becomes the largest/heaviest face of the die and the opposing face to become ever so slightly curved... causing the bottom face to turn up the least often, and causing the opposite face to turn up the most frequently.

This also happens over very long periods of time naturally. So... store your dice with your desired number facing up >.>

I hear tale that microwaves work well for this. :D


BigDTBone wrote:
Remy Balster wrote:

Many dice can be heated, which causes them to seep lightly. The number on the bottom typically then becomes the largest/heaviest face of the die and the opposing face to become ever so slightly curved... causing the bottom face to turn up the least often, and causing the opposite face to turn up the most frequently.

This also happens over very long periods of time naturally. So... store your dice with your desired number facing up >.>

I hear tale that microwaves work well for this. :D

Nothing short of microwaving or heating them in a regular oven will have any noticable effect on the dice. We actually tried the oven heating thing and rolled ALOT of times to see if there was any statistical change. There wasn't. Not saying that heating them up just right wont create a small change, but keep your expectations low... And also: Heating dice is at your own peril. You may damage dice and/or oven.

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