Sunday, December 04, 2005

Cold Iron Task Resolution

I worked up this as an introduction for my players, and thought I'd post it here also:

Cold Iron, like many RPGs, is based on a task resolution system. The player will declare some task they want to attempt (I try and hit the troll with my sword). The character will have some ability with this task (for attack, the ability is hit, often abbreviated to H). There will be some difficulty of the task. Some tasks have a static difficulty, others, like hitting trolls with big pointy things, are opposed checks, the target will resist with some ability (the troll might defend with a parry, often abbreviated as D, or a dodge, often abbreviated as Db). All check use the same randomizer. Some systems use a single die and add (d20+ability), others roll dice against the ability (d100 <= skill).

Cold Iron has a clever chart that utilizes the normal distribution to generate a modifier (often called a chance adjustment). The probabilities of getting particular modifiers follow the bell curve of the normal distribution. The clever trick is in how the probabilities are generated.

Probabilities are always a number between 0 and 1 (when expressed as percentiles, the number is multiplied by 100). Gamers have long used a pair of d10s to generate percentile values between 1 and 100 (sometimes 0 and 99). One die is labeled the 10s digit, and the other the 1s digit, and the pair is rolled and read as a two digit number (00-99, where 00 is usually read as 100). The normal distribution however requires infinite precision, more than two digits. So the concept of rolling two digits is just extended to rolling as many digits as are necessary. The way the probabilities are arranged in the normal distribution, it's not always necessary to roll a bucket full of dice.

Here is a chart that uses the normal distribution to express the probabilities for a range of values:

.000088 -25
.00016 -24
.00028 -23
.00048 -22
.00082 -21
.0013 -20
.0022 -19
.0035 -18
.0054 -17
.0082 -16
.012 -15
.018 -14
.025 -13
.036 -12
.049 -11
.067 -10
.088 -9
.12 -8
.15 -7
.18 -6
.23 -5
.27 -4
.33 -3
.38 -2
.44 -1
.50 0
.56 1
.62 2
.67 3
.73 4
.77 5
.82 6
.85 7
.88 8
.912 9
.933 10
.951 11
.964 12
.975 13
.982 14
.988 15
.9918 16
.9946 17
.9965 18
.9978 19
.9987 20
.99918 21
.99952 22
.99972 23
.99984 24
.999912 25

The left hand column is the cumulative probability (for example, on 2d6, there is a 1 in 36 chance of getting a 2, a 2 in 36 chance of getting a 3, a 4 in 36 chance of getting a 4, up to a 6 in 36 chance of getting a 7. The chance of getting a number, N, or less is the sum of all the individual probabilities of each number less than or equal to N, this is known as the cumulative probability, so the cumulative probability of a 4 or less on 2d6 is 6 in 36 or 1 in 6). The right hand column is the modifier (chance adjustment, or CA). The chart above shows the decimal point, however, it is common practice to leave the decimal point out of chance adjustment tables.

One more bit about the probability math behind this chart, the chart is designed so that a +20/3 (+6.666667) is one standard deviation "above average").

To generate a chance adjustment using this chart, the player should roll a pair of d10s, identifying which digit is first (if it's easier for you, consider it a d100 roll - except 00 will NOT be read as 100). If you look at the chart, most of the time, the number will fall in the range from 12 to 88, which corresponds to chance adjustments of -8 to +8. If you roll between two numbers, you use the lower chance adjustment (so a 51 results in a +0 CA). If you roll in the range of 90-99 or 00-09, you will note the chart has additional digits and multiple rows. In this range, you will need to roll additional d10s to generate additional digits to distinguish between the different chance adjustments. There is a simple rule which lets you roll the dice, then look at the chart. You will see that each number in these ranges starts out with a string of 0s or a string of 9s, and after that string are
2 more digits. So basically, if you roll a 90-99, for each leading 9 you roll, you need to roll an additional digit, for a 90-98, you roll one more digit. For a 99 you roll two more (which may result in rolling even more digits).

Note that if you roll a 99 and then your subsequent pair is a 09, you do not need to roll any more d10s. Your roll is a 9909, which is a +15.

Rolling low is always bad, which is kind of fun if you roll a 00, it's probably an oh-oh kind of moment...

Once you have a chance adjustment, you add it to your ability and compare to the difficulty. If your ability equals the difficulty, you will note that you have a 50% chance of success. If you roll lots of 9s and are confident your result will be a smashing success, feel free to narrate something ("The troll slips in the mud as my axe falls on his neck, I hit him with a 35 (having rolled a +24 on an 11 attack, knowing the troll has a 20 defense).").

A really good result with an attack (and some other abilities) results in a critical success. Generally, a critical success occurs when the adjusted attack is 7 or more higher than the defense. With an attack, this will cause double damage. With attacks, it's possible to get even more than double damage (normally 9 better is triple, 11 better is quadruple, etc., however, armor does modify this).

Here are some more examples:

A fighter with an 11 attack (H, typical of a 3rd level fighter) swings at a goblin with a parry (D) of 14. The fighter rolls an 89, which is a +8, so hit net attack is 19, since this is greater than the goblins D the fighter hits. Later the fighter rolls a 999985, which is a +27, and will probably smear the goblin all over the floor! Shortly thereafter, he rolls a 00045 (-23) which will cause him to fumble. The fighter needs a +3 (67) or better to hit the goblin.

The chart seems daunting at first, and there is some fancy math behind it, but after some play, most players find it easy to use, and you don't need to understand the fancy math. Many players even end up memorizing some of the numbers that come up the most, and mean the most. Normally, D is higher than H, so negative chance adjustments often don't hit. So memorizing 50, 56, 62, 67, 73, 77, 82, 85, and 88 will suffice for a large percentage of rolls.

Another thing is that since the difference between a hit and a critical is 7, you can often look at the dice and see a 60 something, and you know you hit with a +0 CA and crit with a +5 CA, so it doesn't matter if you got a +1, +2, or +3. You hit. Of course the situation could have changed, so the GM should pay attention to the rolls and may ask the player to figure it out (because now a +3 chance adjustment might score that character a crit).

For those interested in exploring the math a bit, the following Excel formula can be used to generate the chart:

=NORMDIST(chance adjustment,0,20/3,TRUE)

The first parameter is the chance adjustment you desire the value for, notice the 20/3 standard deviation is the third parameter (the second parameter indicates the average on the chart is +1, while the fourth parameter indicates cumulative probabilities should be used). I have an Excel sheet on my website that shows how the table can be generated.



Bankuei said...

Hi Frank,

Questions questions questions!

1) Who gets to decide "how much" a success or failure covers- for example, if you're sneaking into the castle, is it one roll for the whole affair (perhaps contested by opposing checks), or a roll each time?

2) Who decides the outcome? Whether failure means oops you've been caught in a trap of 20 guards or a serving maid stumbles upon you?

3) Do all attributes/stats/skills use this chart? For example, is a Strength vs. Strength test handled the same way as a Dancing contest?

4) Is there a general resistance table ("A difficult task must beat X to succeed")?

5) Who decides "how much ground" a roll covers? For example, if you're sneaking into a castle, is it just one roll, one roll vs. many opposing checks, or a fresh roll every time?

6) Who decides what the outcome of failure/success is? For example, if you fail that sneak check, is the GM given full leeway to make it anything from "You're caught in a trap by 20 guards with crossbows" to "A serving maid stumbles upon you"?

Are these stakes established up front at all, do the players get any input, or is it classic, "GM says all" type setup?

7) Does the answer for #6 also apply to combat? Most games nail combat down specifically, and get real floaty with all other conflict rolls.

8) Are there modifiers based on choices the players can make? Are any modifiers based on something other than direct fictional causality? (For example, "I love her = +2 bonus to do things to protect her and show her how I feel" etc.) Are there anything like hero points or such the player can use to modify their odds?

9) Do rolls directly influence any kind of reward system or character growth? For example, in both Call of Cthulhu and Burning Wheel, skills get better directly from usage- does something similar apply here? Or is it like GURPS where the GM hands out points and the players buy up abilities? Or maybe like D&D, with set growth patterns?

Frank said...

Ahh, excellent questions, which will also point out why I feel there is a lot of work to make a complete game...

Mostly it boils down to GM fiat. Use of the resolution table outside of combat is incredibly wishy washy. Which has caused no end of trouble.

In combat things are very specific. Opponents have offsensive and defensive ratings, and results are very specific. Various tactics and situations provide modifiers (and follow some meta-rules so it's pretty easy to come up with modifiers for new circumstances).

Mechanical reward is purely a GM fiat. Character progression is more like D&D than like GURPS.

I have been applying some Forge learning to non-combat resolution, and try and keep to one roll per situation (no more make tracking rolls until you fail). But I haven't done anything to come up with specific target DCs, or anything about how the rolls could be modified with player tactical/strategic choices.


Frank said...

To add a bit more to that response...

I think the way the game was played in the past, pretty much, combat was unavoidable. With an Alertness attribute, there was some basis to get more or less warning. As I recall, in the other games I played in, there was little opportunity for PCs to sneak about. I added a bunch of skills in back then, but really had no thoughts on how to actually use them (it is worth noting that my heyday of running Cold Iron was 1983-1989, I had a little exposure to GURPS, had done some Fantasy Hero, and had played RuneQuest a fair bit).

So assuming players could accept combat as a given (and could buy into the amount of warning, especially at night), the system worked well because combat is definitely not wishy washy.

Certainly my current thinking is that non-combat stuff has to be just as non-wishy washy. I think it also needs at least a minimal amount of informed choice (preferably more than just accept the odds or not).

In general, I don't feel like I got that much more support for non-combat from D20. Sure, some skills have a set of standard DCs, but they didn't always seem to work well, so honestly I ended up with old style wishy washy resolution.

One thing that would definitely be nice to provide solid mechanics for is a degree of success. Degree of success certainly applies to combat (and it used to apply to a few spells whose duration depended on how bad you failed your save by - but those spells became fixed duration, not quite sure why, oh, some missle spells are defined as having a regular to hit and are capable of criting, so degree of success applies to them). There are nice situational choices for spell success. Basically in Cold Iron, you always have to make a concentration check to cast a spell to use an analogous D&D term. The spell success roll is modified depending on how much you want to pay attention to your surroundings (-8 if you're being grappled, -6 if you want to get full defense against melee/missile, -3 for a -4 to melee defenses, +0 for a -8 to melee defenses, -2 if you also want to detect magic during casting, and more).

There are a variety of non-combat spells, many which end up being kind of wishy washy.


Bankuei said...

Hi Frank,

So, with what you've shown and replied so far, it sounds very much like most other games out there GM fiat + flimsy task resolution + detailed combat mechanics.

What has endeared you to this system, or what parts do you see as particular strengths that it shows that don't show up in other games?

Frank said...

Good point about it really not being all that different than lots of other systems out there...

What I like about it:

1) The biggest thing I like about it is that it really seems to have a good balance between the spell casters and the fighters. I have long been frustrated by the dominance of spell casters in D&D.

2) It has a very workable spell point system. It also balances very well for one big encounter between rest periods, but it can also handle multiple smaller encounters without feeling like the PCs can shrug off encounters (as opposed to things I see in D&D where if you don't push the PCs really hard, the mages can just dump with their best spells and take out encounters - also it doesn't depend on 3-5 encounters per rest period that seems built into D&D 3e - with no system support to encourage players to not rest too often).

3) I'll admit that the use of the normal distribution is a fascination and it may not be a mechanic that rocks the world from a "what can it do that other mechanics don't do"

4) I like the way treasure economics work with most equipment being charged items and potions. I also like how the magic items are pretty much all things that mechanically cast spells from the system. Other than potions, magic items use manna supplied by the user (all of this combines to eliminate most of the issues that arise with D&D 3e's magic item system where by the rules you can make an item for 2000 gp that does as many cure light wounds spells per day as you desire).

5) A lot of these things add up to what makes me like the system overall - for what it is, it works for me without lots of pain. Sure, it doesn't do non-combat very well (but then most of my games are 90% combat anyway).

My desire to publish it is not so much to get lots of people running Cold Iron games, but to have a solid game manual that I can share with my players. If some folks are inspired to play the game for themselves, then that's cool too (and to enable that, I am willing and interested in making it a complete enough game that someone who had never played Cold Iron before could pick up the rules and run a game [and I think that would benefit my players also]).

Of course another benefit of having something others could actually understand is that when I talk about Cold Iron, there would be something I could point to that they could read about the system (and again, I'm willing and interested in making a reasonable length introduction because again, that would help my players as well as having something some random forum reader might be willing to read).

So in one sense, I really could continue the way I have been, making the rules available to my players, and not worry too much about the copyright problems (I feel like I do have implicit permission to share the rules with my players - Mark sent me updated rules after all when I asked for what he had with intent to run a game).

Another interest I do have though, and where I would like some help, is in improving the non-combat stuff. Sure, maybe it would be better to do that kind of thing for D&D where potentially thousands of folks would use the outcome, but I want something for me and my gaming.


Bankuei said...

Ok, cool. How about a post giving us an example and overview of the item economy, and then a post doing the same for the spell point system.

Also, with regards to probability curves in games, you might want to take a look at the very awesome Symmetry idea by Walt Freitag.

Though I'm sure the Cold Iron's table works great, having 51 entries appears a bit daunting- stuff like Symmetry or games that use dice pools or exploding dice mechanics to utilize the curve in play without necessarily exposing the players to the math behind it tend to appeal to me more.

Frank said...

The table can be a bit daunting, though with some practice, I think it can be just as fast as rolling a dice pool.

That symetry system is neat, though it doesn't have a degree of success which is definitely used in Cold Iron (but of course a dice pool system could replace that - and one could use Burning Wheel style exploding dice pools to get totally open ended results [though they are only open ended in one direction]).

One of my players suggested an interesting alternative. Roll a white d10 and a black d10. Subtract the black from the white. Treat it as a 0-9, not a 1-10. Doubles always result in a +0. A 9 is exploding (but a double 9 is always a +0 and does not explode). By using 0-9, there is no discontinuity. It comes pretty close to the Cold Iron chart near the center, but extreme rolls are more likely (which would have to be accounted for in the crit multipliers - otherwise it might be way too likely to be able to be taken out in one shot).

What I have found in practice is that many people can memorize a decent portion of the chart (and those that can't memorize it can be helped by those who do memorize it). Also, since combat is simultaneous with initial declarations, there's really no reason a player can't start rolling their dice as soon as declarations are done.

What it comes down to is that I'm wary of changing the normal distribution chart. In play it has proven to work well (though it causes a bit of fragility at low level, but then D&D is fragile at low level also). Once the characters get a few levels under their belt, it occaisionally means a PC goes down fast (which adds an interesting challenge to the battle), and occaisionally a monster goes down fast, which of course is lots of fun. The negative hit point system means that very rarely is the PC unhealable. It's probably no worse than D&D's save or die spells.

Besides, there are other places in the game where the math is worse...

(As one of my players noted - there's a danger in letting engineers write game systems...).


Bankuei said...

Yeah, I've tweaked all kinds of game systems where the math makes perfect sense to me, but no one else gets it. I'm just saying that if you're going to take a new tack, you might want to get something prettier to get the same effect.

TORG uses a chart with D20's that explode on 10's and 20's to create a similar effect, and Feng Shui uses the +die/-die option, both of which create a general bell curve.

In honesty, though, you're probably best off asking yourself how granular you need everything vs. how much that chart is likely to scare people off. I mean, I have a hard time convincing people that Riddle of Steel isn't really all that complicated, because all they end up seeing is the combat charts in the back.

Frank said...

So far I've found the chart doesn't scare people off that badly. But yea, certainly if I were to go for a similar design from scratch, I'd want to revisit the chart idea.

One thing I'd like to do in simplification is get the chart onto the character sheet, even if it had to be an abreviated one.


Bankuei said...

Another idea, I found works rather well, was from some homebrew game someone did on the net- they used % dice and a D8.

The idea was that the D8 worked either as a bonus die or a penalty die. If it was a penalty die, you had to make the % roll under your skill AND make the D8 roll over a number the GM declared. So if your skill was 73% and your Penalty of 4, then you had to roll under the 73, and over the 4 to make it. Fail either and you failed the task. If it was a Bonus die, then you had to only make one roll OR the other to succeed.

This allowed you to make modifiers on the base skill, in increments of 12.5% (D8), without actually doing the math.

With a bit of math wonkery behind the scenes, I bet you could take a mixed die approach like this, and get a similar curve to what you've got, minus the chart. It'd be a more work on the design side, but would be extremely more people friendly.

Rob Muadib said...


Hey, found pointer to your resolution system from your power 19 post. And, woah, my system uses a very similar Dice Modifier system(DM, usually specified as an Action Modifier/Result Modifier system) (you call it CA right?). Extremely similar in fact. You can find a write up of it at my blog Wild Musings.

As for the chart being too difficult, I Don't think so, but then I may just be pleasing my inner engineer. I managed to fit a cut down version of my chart on the draft version of the character sheet PDF I put together, you could probably do something similar. (though admittedly I was only able to fit the 40ish row table on there, but it's good for 98 out of a 100 rolls, so I'll live with it.)

I like the way you have done your "exploding" end rolls for the over/under rolls, I might have to steal it:) I was using a system where if you rolled a 100, then you rolled another d10 to get your additional modifier, but if you got another 10, then you roll another die to see if you got a 10 on that, then you roll another d10 and add. Your system seems a bit simpler, once nicely adjusted in the chart. (You'd just put the Over/Under Roll numbers in there, would be simpler I guess.)

As for using the chart, in a lot of ways a simple percentile, or in this case d100 roll is easier to use because it converts directly to percentages, thus making it easy for the GM/Players to use as well, IMO.

As for my design, I also utilize a Log Score/Value chart to convert between Trait Scores and Value measures (range, area, speed, volume, damage, etc.). Similar to the one in TORG, which was derived from system in DC Heroes. (Mine is 10 points to a factor of 10 compared to 5 points to a factor of 10 with Torg/Masterbook.)

As for liking the numbers, I do too, there is a great beauty of combining the log progression and a Bell curvish/Normal distribution, it appeals to my inner Engineering major (Never did get my degree, switched to writing.). Don't let all artsy narrativists dude dissuade you from staying crunchy in milk. It has it's appeal too.



Frank said...

Interesting, your system seems a bit more complex, but maybe it isn't really. You might want to try and simplify your wording (one thought I have is to keep the explanation of the logic behind the table in an appendix).

If you do borrow the normal distribution chart, just credit Mark Christiansen who came up with the idea.