16 replies to this topic

[papabees]

see this thread:

http://www.reapermin...xed-armor-stat/

Ok here's the gist. In the Old CAV1 rules attacks were determine by comparing an attack modifier (+0 to +8) plus a d10 roll vs. an Armor modifier (+0 to +4) plus a d10 roll. When there are multiple weapons this is a little unwieldy because you have to make sure you are comparing proper die results with each other.

Sooo, what I want is some to advise me on how to determine a fixed number I could use in place of the defense roll (the d10) that would give close to the same results. I was thinking "6" but I could be way off.

This is how I came up with six. Assuming the defender wins a tie; d10 vs. d10, defender win % would be:
10 100%
9 90%
8 80%
etc, you get the idea.

Add up the percentages and divide by 10 rolls and you get 55% so I went with an assumed fixed defense of "6". Am I way off?

[Silas Coggeshall]

lol Your talkin gibberish. LOL xD I'm sorry, but I'm not the best person to answer this. lol

[papabees]

So you just decided to reply and mock me

[Silas Coggeshall]

Not exactly. lol I just couldn't keep up with what you were saying. lol

[MonkeySloth]

are you just looking for a replacment of the adverage of what someone would roll on a d10? If so you would be correct in that a 6 is the adverage rolled on a D10.

[papabees]

Pretty much. I just didn't know if that roll opposing another d10 roll did weird things to the math.

[Doug Sundseth]

Median for d10 is indeed 5.5. I'll note that using a fixed defense will result in clipping the ends of the bell curve of results.

When comparing dice, you can get differences between +9 and -9 for the attacker (then adding the attack and defense factors, of course). With a fixed defense die roll of 6, you will be limited to a range of -5 to +4. Among other things, this means that in some circumstances the attacker will be unable to miss.

[papabees]

So Doug, The damage chart actually requires the attacker to beat the defender's defense by four or more before any actual damage is done (kinda weird but that's what is is), that being the case I'm not quite as worried about the Bell Curve being shortened. I think it may be time for some empirical (sp?) evidence.

[Foxden Racing]

Let me look over this again tonight, once I'm home and have access to my tools. I'm trying to make a pen-and-paper game in my spare time, have learned a lot about the math of polyhedrons.

[papabees]

Let me look over this again tonight, once I'm home and have access to my tools. I'm trying to make a pen-and-paper game in my spare time, have learned a lot about the math of polyhedrons.

Did you get a chance to take a look at this?

[vejlin]

I'd say that the biggest difference between the opposed roll (rolling two dice) and rolling against a fixed defense (rolling one die) is that you go from something that is a nice approximation of a normal distribution (a "bell curve") to something that is uniformly distributed (a flat line). No amount of fiddling with modifiers will get you out of this problem really, you just can't model the old two dice system with a single die. You can keep the bell curve against a fixed defense by having the attacker roll two dice though. Even though you would be rolling the same number of dice, I imagine it would be a lot faster for a single person to roll two dice, added the scores and add modifiers vs a fixed number, over having two people roll, add modifiers and then compare numbers.

If you are interested in this sort of thing I highly recommend Troll (by one of my old professors): http://www.diku.dk/~torbenm/Troll/ it is awesome for looking at how different dice systems work, providing you with a distribution of results. It can even handle open ended systems (like the systems that have "exploding" dice)

Edited by vejlin, 09 July 2012 - 11:25 AM.

[Foxden Racing]

I'm so sorry, it completely slipped my mind. Sending myself a reminder now.

[papabees]

@ Foxden no sweat.

@vejlin - So if I used 2d6 for attack rolls do you think i would get a equivalent bell curve?

[Foxden Racing]

I've been thinking about this, and the bell curve wouldn't apply in this situation. You're not summing the two or more die, which is where the curve comes from. On 2D6, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1 all produce a 7, whereas only 1/1 or 6/6 will produce a 2 or a 12, respectively.

Either a 5 or a 6 would work, depending on who you want to have the slight statistical advantage. Given that it's already ties-to-the-defender, I'd say 5 [otherwise, on even modifiers the attacker would need a 7 or better to hit], but that's something to tweak after some play-testing.

However, forgive my ignorance as there's no CAV or Warlord groups local...if the issue is matching die for die when rolling, would you be better off keeping what's there now, and having one of the players make a single roll? It would be easier to have the defender roll, add their Armor Value, and then have that as a fixed target number for the attacker for the rest of the round.

You could also roll one at a time, lining them up, and then doing the comparison after all rolls are made...but that requires a decent pile of dice.

The advantage to a single roll for one player it is that gameplay gets a lot smoother with a minimal change to the rules. The downside is that there's less room for variance; if only one player is rolling, but you're you're making 10 attacks per turn, as things sit now statistically one of those times both the attacker and the defender will roll a 1. With a single-roll setup, statistically that 1 for the defender will come up one in every 10 turns...meaning some turns may be complete washes, and others could be utterly devastating, whereas right now the attacker has to be red hot (or the defender has to be ice cold) for an all-or-nothing turn.

For ease of play, it'd work better...but for feeling like a heated battle, with glancing blows and lucky hits and the like, as it sits is preferable.

If I think of anything else, I'll drop a line.

[vejlin]

Sorry, but rolling two dice, adding modifiers and comparing them is equivalent to rolling two dice, adding the scores and adding modifiers and then comparing with a constant value. So Yes you do get the bell curve with the opposed roll.

As for a 2d6 system compared with a 2d10 system both have the bell curve the 2d10 just has a better resolution because two d10 gives you 100 outcomes while two d6 gives you 36 outcomes. For most purposes I am guessing 2d6 Will be sufficient. As for grouping dice in twos you can use colored dice as is done in Gruntz where I think it works really well.

Edited by vejlin, 28 July 2012 - 08:33 AM.