Quote from: WillInNewHaven;1113799A couple of kids who didn't finish high school learn how to figure (D4 + N) squared really quickly when it is how you calculate Lightning Bolt damage and their characters are casting the spell. Not only that, but "N" is a power of three mana and they figure that out quickly too. One of the other players, he finished high-school but is not a math student, figured out that N to the 0 power is one so he cast (D4) squared lightning bolts for one point each when short of power.

My friends and I had similar experiences, starting out with GURPS 3rd at 11 or 12 and eventually transitioning into learning + conceptualizing the Vehicles material...

Quote from: Bren;1113803So if I cast 1 mana, N=0. If I cast 3 mana N=1. If I cast 9 mana, N =2. Is that correct?

Then you roll 1D4 add N and square the result. So if the die roll was 2, damage would be 4 pts, 9 pts, 16 pts when casting 1, 3, and 9 mana points, respectively, right? While less nerdy than the table in construction, that's more nerdy in practice.

What happens if you cast mana that is NOT exactly equal to a power of 3?

It may be more nerdy but it does not require a table and "no tables on the table" is a Glory Road Roleplay feature.
The caster chooses how much mana to use and knows that using 8 points does no more damage than using 3 points. The only time you would add mana that doesn't give more damage is if you thought someone might hit you with a Counterspell. Say, you had fifty MP left and were going to do one last  Lightning Bolt before grabbing your spear (or running away) You might use all fifty because
a: then a 27 point Counterspell won't hurt your spell
b: 23 MP won't help you if you are dead.

Quote from: Antiquation!;1113805My friends and I had similar experiences, starting out with GURPS 3rd at 11 or 12 and eventually transitioning into learning + conceptualizing the Vehicles material...

I remember thinking I could handle any game math until T:TNE's Fire, Fusion, and Steel hit me in my junior year. It burned me.

Quote from: WillInNewHaven;1113808It may be more nerdy but it does not require a table.

True.

QuoteThe caster chooses how much mana to use and knows that using 8 points does no more damage than using 3 points. The only time you would add mana that doesn't give more damage is if you thought someone might hit you with a Counterspell. Say, you had fifty MP left and were going to do one last  Lightning Bolt before grabbing your spear (or running away) You might use all fifty because
a: then a 27 point Counterspell won't hurt your spell
b: 23 MP won't help you if you are dead.

Nice. I'd enjoy rolling a handful of dice more than doing the calculation. (In part because of the kinesthetics and the noise.) But that seems like a good system: flexible, with a range of results, and not too burdensome a calculation which could be a table for the arithmetically challenged and would be a calculation in my head as the GM. Runequest has something similar. Casters could add Magic Points (effectively mana) to a spell. Usually that was done so the spell could knock down or blow past any existing countermagic on the target.

Quote from: Brad;1113793I'm an engineer and played D&D in grad school with a bunch of dudes, three of which were engineers. There is no way we would have used such a system...pretty sure you mean "math nerds".

Maybe we were all math nerds... But the designer, myself, and at least one of the other regular GMs were definitely all engineers...

The thing is though, as a player of the game you actually rarely have to engage any more math than addition and subtraction, everything else is worked out by the designer or the GM. When magic users needed to know how much mana they had, I was usually the one to punch things into the calculator if the simple "double your mana after X time" wasn't enough. And you had to be well into the game before you had to deal with the capacitor charging formula, and I don't know if anyone actually had to deal with the leaky bucket formula. Those two formulas relate to a mana storage focus that 5th level magic users got (they highest level magic user I recall from my games was 6th level). The focus is a leaky bucket, so to fill it up, you use the same formula as used for charging a capacitor (or you just know you've had enough time and there's a simple formula that tells you how much mana is stored in it). If for some reason you use up your own mana before emptying the focus, then you need to use a different formula to determine how fast it loses mana.

But, hey, before I got involved in Cold Iron, I was deriving multiple integration for myself while trying to figure out a "correct" formula for determining how an AD&D fireball spread... Yea, seriously, I needed multiple integration before we got to it in calculus class. By the time we got to it, I thought to myself, "oh, that's what it's called" and dozed off during the classes because it already made perfect sense to me (I had started knowing integration gave you the area under a curve, ok, yep, that works right for a circle, ok, now doing another integration step should give you the volume of a sphere, yep, checks out, cool, now what happens when you set the fireball off in a large enough (but not tall enough) room? What if the center is on the floor or ceiling not halfway between?

Maybe I'm a math nerd as well as an engineer...

But hey, I just showed how you need calculus to properly play AD&D! And more complex calculus than used to produce the normal distribution chart for Cold Iron at that...

Quote from: Bren;1113801Thanks. It's occasionally fun to discuss die rolling at a somewhat deeper level than, "Use the blue D20, it usually rolls high."

I'd say that's both good and bad. It makes lookup easier, which is good.

However, the Cold Iron (CI) mechanics are designed to have a two-sided opened ended, symmetric range centered on the mean, which is something that roll again systems don't do. (They are only open ended on the high side and hence they aren't completely symmetric either.) You aren't using half of the CI range which means open ended at the bottom is unnecessary. And unnecessary mechanics are inelegant, and if the mechanics also add complexity they are bad.

I wanted to ask a clarifying question or two about the table and the die rolling method.

What is the number in the table (which ranges from -25 to +25) used for?

As I understand it, in CI a player starts out rolling to 2D10 (which is read as a decimal) and this 2-digit decimal place number is then compared to the table to figure out the bonus or minus.

As I read the table a roll of 45-55 = +0, 56-61 = +1, 62-66 = +2, 68-72 = +3, 73-76 = +4, 77-81 = +5, 82-84 = +6, 85-87 = +7, 88-89 = +8.

For rolls of 90+ additional dice must be rolled to determine one or more additional decimal places.
So if a 9 is rolled for the 1st D10, an additional D10 has to be rolled to figure out what the digit is in the third decimal. If a 9 is also rolled for the 2nd D10, a 4th D10 must be rolled to find the 4th decimal place, and so on.

Did I get that correct?

If so, there's another issue. The probabilities that I calculate appear to be symmetric, but they don't follow the strictly increasing towards the mean from the left and strictly decreasing from the mean towards the right that we see in a normal distribution. Here's the probabilities I calculated for the two digit outcomes that don't require a third (or more) digit.

-7   3%
-6   3%
-5   5%
-4   4%
-3   6%
-2   5%
-1   6%
0   12%
1   6%
2   5%
3   6%
4   4%
5   5%
6   3%
7   3%

Is this correct or am I missing something?

So a couple things.

First, the table doesn't center +0 on the peak, If you roll a 0.50 or higher you get at least a +0, so +0 is 0.50 to 0.55. A roll of 0.44 to 0.49 is a -1. So yea, you're right it isn't precisely symmetrical. Someone really thinking about that would make +0 be 0.47 to 0.53, and work out from there (it should be easy to make Excel give you such a chart). But then if OCV == DCV you would actually have a 53% chance of success, so maybe the apparent asymmetry of the Cold Iron chart is actually not so. +0 being 0.50 to 0.55 is actually the same sort of symmetry as if you took OCV + 3d6 - 11 >= DCV.

Second, you take the +0 or +1 or whatever (the chance adjustment or CA), add it to your attack rating and if (just borrowing Hero terminology for simplicity)  OCV + CA >= DCV you hit.

If OCV + CA >= DCV + 7 you crit for double damage. Assuming a sword and no armor, OCV + CA >= DCV + 9 is a crit for triple damage, Margin of success of 11-12 is x4 damage, etc.

Armor has a critical protection factor, that originally came in before double damage, but later was changed to come into play after double damage. Plate has 3 crit pro, so triple damage against plate required OCV + CA >= DCV + 10.

Now the negative side of the chart comes into play in two ways:

First, if you roll horribly, an automatic miss or fumble occurs (OCV + CA < -5 is an automatic miss, a net -10 is drop weapon, with various other results sprinkled in all the way down to -16. One nice thing about the system, once you have some levels under your belt, fumbles become really rare.

Second, if your opponent has a really low defense, and you have a really good offense it's not hard to get into the range where a OCV - 10 still hits. And yep, you with your OCV of 20, if you roll off the chart (I have a handy chart that goes from -40 to +40), you could drop your weapon or worse. I have seen perhaps a few (one for sure) roll that was above +25. I don't remember any spectacularly low rolls, but the nature of the game means that some of them may not have mattered. If you have an OCV of 10 and roll off the bottom of the -25 chart, it doesn't matter what you actually rolled, you got the worst possible fumble already.

Quote from: HappyDaze;1113812I remember thinking I could handle any game math until T:TNE's Fire, Fusion, and Steel hit me in my junior year. It burned me.

I haven't read it, though I've heard its reputation. Maybe I should give it a look and see if my math skills have aged as poorly as I suspect they have. :cool:

Quote from: Bren;1113726That's wrong. Chits have always been available and were in use for some games.

According to at least two of the original players the damage was d6 because that is what they had on hand. Gary apparently experimented with variations before the polyhedrals caught on and they settled on whats now the more familiar die uses that I believe first showed up as a variant in Greyhawk? You see that even into BX D&D where the basic part uses d6 and the expert introduces very similar polyhedral die for damage.

According to at least two of those players the chit system was not popular and they ditched it ASAP. Pretty sure Gronan commented on that in a thread here on polyhedrals a year or three ago but I cant find it. Should be the same thread we discussed the origins of the polyhedrals. (They were not dice. They were a set for schools to teach... polyhedrals.)

Back on topic. Whatever that was.

One small irk is games that use polyhedrals just to be using polyhedrals when going with just one, or at least fewer, type would have better suited the system.

Quote from: ffilz;1113816First, the table doesn't center +0 on the peak, If you roll a 0.50 or higher you get at least a +0, so +0 is 0.50 to 0.55. A roll of 0.44 to 0.49 is a -1. So yea, you're right it isn't precisely symmetrical.

Thanks for the clarification. I've recalculated the probabilities and I see now that the CA probability distribution is centered where CA = -0.5; here are the probabilities with the two digit outcomes that don't require a third (or more) digit in bold.

Spoiler

CA   P(CA)
-25   0.01%
-24   0.01%
-23   0.02%
-22   0.03%
-21   0.05%
-20   0.09%
-19   0.13%
-18   0.19%
-17   0.28%
-16   0.38%
-15   0.60%
-14   0.70%
-13   1.10%
-12   1.30%
-11   1.80%
-10   2.10%
-9   3.20%
-8   3.00%
-7   3.00%
-6   5.00%
-5   4.00%
-4   6.00%
-3   5.00%
-2   6.00%
-1   6.00%
0   6.00%
1   6.00%
2   5.00%
3   6.00%
4   4.00%
5   5.00%
6   3.00%
7   3.00%
8   3.20%
9   2.10%
10   1.80%
11   1.30%
12   1.10%
13   0.70%
14   0.60%
15   0.38%
16   0.28%
17   0.19%
18   0.13%
19   0.09%
20   0.05%
21   0.03%
22   0.02%
23   0.01%
24   0.01%

The graph is symmetrical about a CA of -0.5. But it doesn't look like a normal distribution. There are flat spot in the middle with several peaks, dips, and rises on either side. It may be easier to see in this graph of the probabilities for CA between -25 and 24.

QuoteSecond, you take the +0 or +1 or whatever (the chance adjustment or CA), add it to your attack rating and if (just borrowing Hero terminology for simplicity)  OCV + CA >= DCV you hit.

If OCV + CA >= DCV + 7 you crit for double damage. Assuming a sword and no armor, OCV + CA >= DCV + 9 is a crit for triple damage, Margin of success of 11-12 is x4 damage, etc.

Thanks. I'm familiar enough with HERO that this gives me a better  understanding of how the Combat Adjustment is used. It's certainly an interesting approach.

Quote from: Omega;1113821According to at least two of the original players the damage was d6 because that is what they had on hand.

Yes, everybody has d6's from board games like Monopoly, Yahtzee, Risk, and many others.

And of course chits weren't popular. Their fiddly, awkward, sometimes hard to pick up, and the chits are easy to misplace. But they were in use in that period. I had mid 1970s board games that used chits.

D&D probably would not have been nearly as popular in the 1970s if TSR had not included dice with the first boxed set. They weren't great dice, but they worked...at least for a while. The plastic is pretty soft. I still have them, but after 45 years there's not much corner or edge left on the D20. And the pink d6 was always kind of ugly. But the D4 still works both as die and caltrop.

QuoteOne small irk is games that use polyhedrals just to be using polyhedrals when going with just one, or at least fewer, type would have better suited the system.

I don't appreciate companies that invent mechanics just so they can sell me funny dice.

Quote from: Bren;1113839I don't appreciate companies that invent mechanics just so they can sell me funny dice.

That is worse then every weapon rolling the same die.  Having a bunch of dice that end up rolling triangle.

Quote from: Bren;1113838Thanks for the clarification. I've recalculated the probabilities and I see now that the CA probability distribution is centered where CA = -0.5; here are the probabilities with the two digit outcomes that don't require a third (or more) digit in bold.

Spoiler

CA   P(CA)
-25   0.01%
-24   0.01%
-23   0.02%
-22   0.03%
-21   0.05%
-20   0.09%
-19   0.13%
-18   0.19%
-17   0.28%
-16   0.38%
-15   0.60%
-14   0.70%
-13   1.10%
-12   1.30%
-11   1.80%
-10   2.10%
-9   3.20%
-8   3.00%
-7   3.00%
-6   5.00%
-5   4.00%
-4   6.00%
-3   5.00%
-2   6.00%
-1   6.00%
0   6.00%
1   6.00%
2   5.00%
3   6.00%
4   4.00%
5   5.00%
6   3.00%
7   3.00%
8   3.20%
9   2.10%
10   1.80%
11   1.30%
12   1.10%
13   0.70%
14   0.60%
15   0.38%
16   0.28%
17   0.19%
18   0.13%
19   0.09%
20   0.05%
21   0.03%
22   0.02%
23   0.01%
24   0.01%

The graph is symmetrical about a CA of -0.5. But it doesn't look like a normal distribution. There are flat spot in the middle with several peaks, dips, and rises on either side. It may be easier to see in this graph of the probabilities for CA between -25 and 24.

Thanks. I'm familiar enough with HERO that this gives me a better  understanding of how the Combat Adjustment is used. It's certainly an interesting approach.

The funny bumps are due to rounding. The numbers from the Excel formula are:

0.499999999781721
0.559617711501766
0.617911357472630
0.673644758774862
0.725746935061448
0.773372720270208
0.815939908268087
0.853140919152560
0.884930268282292

When rounded to two digits, those match the original Cold Iron chart. The Excel chart (on the plus side) which I did out to +50 shows the following mismatches from the original chart:
+9 Excel has .911 while Cold Iron has .912
+13 Excel has .974 while Cold Iron has .975
+31 Excel has 9999983   while Cold Iron has .9999984

My Excel sheet also shows the delta between each step:
5.961771172004490
5.829364597086430
5.573340130223170
5.210217628658590
4.762578520876060
4.256718799787910
3.720101088447280
3.178934912973240

Which you can see has the expected properties. A more elegantly shaped curve might be had by taking the deltas and rounding them (and then correcting if the cumulative probability get's ahead for more than one or two steps).

Another solution would be to bite the bullet and roll at least 3 dice, though I'm not sure that accuracy is necessary for a game.

Quote from: ffilz;1113845The funny bumps are due to rounding. The numbers from the Excel formula are:

0.499999999781721
0.559617711501766
0.617911357472630
0.673644758774862
0.725746935061448
0.773372720270208
0.815939908268087
0.853140919152560
0.884930268282292

When rounded to two digits, those match the original Cold Iron chart. The Excel chart (on the plus side) which I did out to +50 shows the following mismatches from the original chart:
+9 Excel has .911 while Cold Iron has .912
+13 Excel has .974 while Cold Iron has .975
+31 Excel has 9999983   while Cold Iron has .9999984

My Excel sheet also shows the delta between each step:
5.961771172004490
5.829364597086430
5.573340130223170
5.210217628658590
4.762578520876060
4.256718799787910
3.720101088447280
3.178934912973240

Which you can see has the expected properties. A more elegantly shaped curve might be had by taking the deltas and rounding them (and then correcting if the cumulative probability get's ahead for more than one or two steps).

Another solution would be to bite the bullet and roll at least 3 dice, though I'm not sure that accuracy is necessary for a game.

Oh, and on the Hero front, I actually have a chart that replaces the 3d6 of Hero with a chance adjustment... (and we call it chance adjustment not combat adjustment since it's also used for other resolution).

But the system is more than just the dice mechanism (as any system is), the magic system, the details of the combat system, and how they interact combined with how magic items work makes for an interesting system with tactical and strategic choices. It can then be layered with non-combat procedures to make for interesting over all play. I'm contemplating using the system (with some non-combat procedures cribbed from other games) to run a West Marches inspired "leveled" wilderness with exploration.

And we've strayed far from the topic... :-) (though I'm sure plenty would find the whole idea of Cold Iron objectionable so there you go...).

Quote from: ffilz;1113845The funny bumps are due to rounding. The numbers from the Excel formula are:

Yeah, that checks. The error due to rounding is fairly significant though.

QuoteWhen rounded to two digits, those match the original Cold Iron chart. The Excel chart (on the plus side) which I did out to +50 shows the following mismatches from the original chart:
+9 Excel has .911 while Cold Iron has .912

CA = +9 and CA = -10 are the locations at which the rounding errors no longer have a significant effect on P(CA) from the chart.

QuoteMy Excel sheet also shows the delta between each step:

Which you can see has the expected properties.

Yes. Your Excel numbers have one more digit of precision that the numbers in the chart, but essentially those are the same as deltas I get from the chart.

QuoteAnother solution would be to bite the bullet and roll at least 3 dice, though I'm not sure that accuracy is necessary for a game.

I think if one is going to go to the effort of calculating a CA, one should avoid spikes in the graph of the probabilities. Having a higher probability to roll a more extreme CA than a less extreme CA would bother me.

   If for some CA=N where N>0, the P(N+1) > P(N) is true or for some CA=K where K<0, the P(K) < P(K-1)

In the chart that statement is true when N = 2, 4, and 7 and when K = -4, -6, and -9.

On the other hand, at the point where I always need to roll three D10 dice to get probabilities in the tenths of a percentage, I start to wonder if it would be better to use a different method of handling the whole thing that doesn't need a chart or routinely need an extra die.

Of course it could be that I'm overly fond of opposed rolls in combat and the simplicity of rolling and computing fumbles, misses, hits, better hits, and still better hits in Runequest.

Quote from: Bren;1113915Yeah, that checks. The error due to rounding is fairly significant though.

CA = +9 and CA = -10 are the locations at which the rounding errors no longer have a significant effect on P(CA) from the chart.


Yes. Your Excel numbers have one more digit of precision that the numbers in the chart, but essentially those are the same as deltas I get from the chart.

I think if one is going to go to the effort of calculating a CA, one should avoid spikes in the graph of the probabilities. Having a higher probability to roll a more extreme CA than a less extreme CA would bother me.

   If for some CA=N where N>0, the P(N+1) > P(N) is true or for some CA=K where K<0, the P(K) < P(K-1)

In the chart that statement is true when N = 2, 4, and 7 and when K = -4, -6, and -9.

On the other hand, at the point where I always need to roll three D10 dice to get probabilities in the tenths of a percentage, I start to wonder if it would be better to use a different method of handling the whole thing that doesn't need a chart or routinely need an extra die.

Of course it could be that I'm overly fond of opposed rolls in combat and the simplicity of rolling and computing fumbles, misses, hits, better hits, and still better hits in Runequest.

I certainly get your concern with the inelegant numbers on the CA chart, and certainly the table lookup does have handling time, and the math of the system does certainly have an impact. On the other hand, I've started to worry a bit less about little quirks of systems, and focus more on does the system as a whole provide for enjoyable play. Cold Iron certainly did. I'm not sure I could find a group of players today that would result in the same enjoyable game, but one can always hope. The reality is I never noticed those spikes in the probability curve, so yea, they could be fixed with a bit of careful hand tuning, but does it really matter in play. And it's not unique in RPGs, I've seen other games with odd bumps due to rounding - and this isn't a rounding error, it's a just a quirk that comes out due to the particular curve involved and how rounding interacts with it - look at store receipts sometime and see how various stores handle 3 for $1 type pricing, when do they charge $.34 for an item? Is it the 3rd or the 1st or the 2nd? Rounding the cumulative price up would have the .34 be the 2nd item (0.66666... rounding to 0.67), but some might prefer it be the 3rd and others the 1st.

Funny you should mention RQ because that's another game I love despite it's quirks. I haven't run it at levels where the "I hit" "he parries" goes on ad infinitum, so that issue that some have raised with opposed rolls hasn't bothered me. It's also interesting to note that RQ definitely was an inspiration to Cold Iron (so was The Fantasy Trip - having started playing in a TFT game, I see spells that came over to Cold Iron almost without change...).