EDIT: Hmm, does anyone else still see the Code section with the spoiler closed?

For those interested, hopefully this can stick around until we have an actual system to use it with...assuming that in SR4 the 6's "explode" indefinately (i hope they do).

I wrote some code to empirically determining the probabilities of each number of successes across a range of dice rolled. I haven't done the theoritical formulas yet, but when someone does these numbers can be used as a validation check. The code, slapped together and poorly commented, was written in VBA. Check the spoiler if you want to read it to confirm my algorithms:

CODE

' global variable, because i'm lazy Dim iCountRerolls As Integer Function RollItAll() Dim i As Integer    ' test the results from 1 die through 12 die    For i = 1 To 12        ' 1 million rolls        Call MultiRollExplodingSixes_TN5(1000000, i)    Next i End Function Function MultiRollExplodingSixes_TN5(iRolls As Long, iNumberOfDice As Integer) As Double Dim i As Long Dim iTotalSuccesses As Long Dim iTotalRerolls As Long Dim iMaxSuccesses As Integer ' hopefully 100 is big enough for the array, otherwise it will resize Dim aSuccessDistribution(0 To 100) As Long    For i = 1 To iRolls        iSuccesses = RollExplodingSixes_TN5(iNumberOfDice)        iTotalSuccesses = iTotalSuccesses + iSuccesses        If iMaxSuccesses < iSuccesses Then            If iSuccesses > 100 Then                MsgBox "More than 100 successes in a single roll, truncating to 100 successes."                iSuccesses = 100            End If            iMaxSuccesses = iSuccesses        End If        aSuccessDistribution(iSuccesses) = aSuccessDistribution(iSuccesses) + 1        iTotalRerolls = iTotalRerolls + iCountRerolls    Next i        ' header for number of dice    Debug.Print "Dice Rolled", iNumberOfDice    Debug.Print ""    Debug.Print "Successes", "% of Rolls"            ' distribution of # of successes, as fraction of total rolls    For i = 0 To iMaxSuccesses        Debug.Print i, 100 * (aSuccessDistribution(i) / iRolls)    Next i    'average number of success per roll    Debug.Print "Average # successes", (iTotalSuccesses / iRolls)    'average number of times dice picked up for reroll    Debug.Print "Average # of rerolls occurs per initial roll", (iTotalRerolls / iRolls)        Debug.Print "--------------------"            ' also return the average    MultiRollExplodingSixes_TN5 = iTotalSuccesses / iRolls End Function Function RollExplodingSixes_TN5(iNumberOfDice As Integer) As Integer    iCountRerolls = 0    RollExplodingSixes_TN5 = CountSuccesses(iNumberOfDice) End Function Function CountSuccesses(iNumberOfDice As Integer) As Integer Dim i As Integer Dim iSuccesses As Integer Dim iExploding As Integer Dim iRoll As Integer    For i = 1 To iNumberOfDice        iRoll = Int(Rnd * 6)        If iRoll > 3 Then            iSuccesses = iSuccesses + 1            If iRoll > 4 Then                iExploding = iExploding + 1            End If        End If    Next i        If iExploding > 0 Then        iCountRerolls = iCountRerolls + 1        iSuccesses = iSuccesses + CountSuccesses(iExploding)    End If    CountSuccesses = iSuccesses End Function

You kick it off by entering "=RollItAll()" in a cell in Excel (the code should likely work in Word too, or VB itself). The results are output, via the Debug object, to the Immediate window.

I also included an count of number of times the player will have to pick out the 6's and roll the smaller subset again. I didn't break it down, just gave it as an average along with the average number of successes.

The next post in this thread contains the outpt from a sample run. I ran the code using 1,000,000 rolls for each of the dice "pool" sizes. I don't have a T table handy, but I'm guessing that 1 million rolls should at the very least get the deviation from theoretcial values down to +/- 0.1% on each of the "% of Rolls" values.

You missed the paper I linked to, didn't you? The one titled Fixed Target Number Dice Mechanics? The discussion (and link) is here.

And you also apparently missed the tables I posted here, although your tables go a little further out.

Also, GunnerJ already posted C code to empirically determine the distribution here.

Not that your version is bad or wrong or anything--it's just not as novel as you apparently thought.

Thanks for the links. I must have missed the 4 day or so window those posts appeared in and slid away. Actually, looking at the date it was a combination of a big pile of backlogged paperwork and the 3 day trip to my Grandmother's funeral on Apr 9th that did it.

I didn't really think it so much novel. After all it's based loosely on some stuff i did for SR3 Open Tests (to prove my theoretical formulas for Open Tests) to show exactly what it was that so many people had a gut feeling for, that SR3 Open Tests were FUBAR.

I didn't expect anyone to have posted that kind of detail here given some of the comments about probabilities here. If you look at those curves (ok, visualize the curves from the data) compared to the SR3 curves you get from modifying TNs a lot of comments i've seen about the downsides to fixed TN doesn't make much sense. Especially with the exploding dice (which smooths things out). I guess i should have known better given how many times people have posted that SR4 means not needing a deck to surf the Matrix. *shrug*

An example is with 2 dice you have a 1 in 20 chance of having at least 3 successes, one more than the dice you start with. You don't have to go that far up in TNs to drop off to approximately 5% chance of a single success, even with a handful of dice.

P.S. What would have been nice if the guy that did that paper had working model, not unlik that web dice calculator for SR3.

You have a 5% chance of success at TN 13 or TN14 with two dice. A little more than 5% at TN13, a little less at TN 14. That's a pretty long way up, no?

(And yes, open tests are screwy. I didn't like them when they were introduced in SR3, and I'm happy they're gone in SR4.)

What the hell kind of argument is "LOL?"

Like I said on another thread. It's like Gomer Pyle laughing at Einstein.

[quote]Plus as i said before, a concern about a given the situation should lead you to look to where the system could avoid the situation. Not assume that it will always end up there.[\quote]Sure, but since we don't get to write the rules, we don't have much direct say over whether the system can avoid situations like that. In terms of providing feedback to the people who are writing the rules, I don't think there's a huge difference from saying "If we have to make a lot of tests with 2 dice things will be really bad!" and saying "Oh no, we'll have to make lots of tests with 2 dice, it will be really bad!" Either way, the concern is voiced, and if the concern has been addressed, the developers will know that the concern will be allayed, and then can decide whether they want to say so now or not.

Given the "attribute + skill + modifiers" thing, I can imagine negative modifiers quite easily that would make more skilled people have only one or two dice. In many cases, that probably won't produce the behavior you want out of the system.

For example, even with exploding dice, although especially so without, I don't think SR4 would even be as good as SR3 at playing children, who tend to have low physical stats (save quickness, perhaps) and who haven't had time to build up much skill.

[quote]However variable TNs don't actually give that smooth a transition for opposed tests[/quote]No, they don't. Variable TNs are better at making modest differences have a large impact. If you had dice bonuses/penalties in SR3, then you could smooth things out if you wished; with a fixed TN system, however, there's not a good mechanic for making small differences have a large impact.

[quote]An example of what i was talking about changing from just Skill dice to Attribute dice + Skill dice, which is what is planned. Another example is increasing die with modifiers.[/quote]But this reduces the impact of single-point differences in skill even more. If you have a good attribute--six, let's say--raising your skill from 1 to 6 only gives you 70% more dice to roll. If it's relatively cheap to raise skills, and they can go well above 6, then skill can eventually become really important. But at least for starting runners, where everything is in the 1-6 range, there isn't room for someone to be really impressive on the basis of their skill alone. Is this good or bad? For starting characters, I'm not sure. For a long-term campaign, especially with powerful, scary opposition, such limits could be very problematic.

[quote] would be down right shocked if a good portion of 'ware didn't increase the number of attribute dice, if not the attribute itself, past 6[/quote]Sure--but I'd rather have a system that works well without cyberware, magic, etc., and then add those on. Otherwise, the system's sweet spot might be in modeling the differences between unaugmented and augmented people, but not so much between different unaugmented people.

[quote] It's also going to be curious what happens with Edge, how that can be used both inside and outside combat. If it refreshes each reroll of init and if you can use all of Edge for a given outside-of-combat project that would represent a good potential source of dice.[/quote]Given that parallels have been repeatedly drawn between Edge and karma pool, and given that we've be explicitly told that combat pool and the like are gone, I'd be really surprised if Edge functioned in the way that you describe.

[quote]As far as the potential of negative modifiers removing dice, on opposed rolls a lot of negative modifiers can be defined as positive modifiers for the opponent, and therefore could be assigned that way.[/quote]That would help a lot. I hope they do that. But there's still the problem of all the non-opposed tests--unless you make everything an opposed test. ("This car doesn't want me to fix it!")

[QUOTE=Ellery,May 7 2005, 02:30 PM] [quote]Plus as i said before, a concern about a given the situation should lead you to look to where the system could avoid the situation. Not assume that it will always end up there.[\quote]
Sure, but since we don't get to write the rules, we don't have much direct say over whether the system can avoid situations like that. In terms of providing feedback to the people who are writing the rules, I don't think there's a huge difference from saying "If we have to make a lot of tests with 2 dice things will be really bad!" and saying "Oh no, we'll have to make lots of tests with 2 dice, it will be really bad!" Either way, the concern is voiced, and if the concern has been addressed, the developers will know that the concern will be allayed, and then can decide whether they want to say so now or not. [/QUOTE]
You are coming across as it can't be done. That fixed TN just can't work. That's not constructive critism. That flat out CAN'T DO pessimism.


[QUOTE]Given the "attribute + skill + modifiers" thing, I can imagine negative modifiers quite easily that would make more skilled people have only one or two dice.  In many cases, that probably won't produce the behavior you want out of the system.

For example, even with exploding dice, although especially so without, I don't think SR4 would even be as good as SR3 at playing children, who tend to have low physical stats (save quickness, perhaps) and who haven't had time to build up much skill.[/QUOTE]

???? Yes, well SR3, and likely SR4, isn't particularly good for playing elephants either.

SR3's mechanics aren't particularly good for undeveloped characters, children or not, either. You are really reaching here. Skill 1 is asking for flubs. But these are the types of character that, once a difficult task pops up SHOULD be in deep dog doodie.

[QUOTE][QUOTE]However variable TNs don't actually give that smooth a transition for opposed tests[/QUOTE]No, they don't. Variable TNs are better at making modest differences have a large impact. If you had dice bonuses/penalties in SR3, then you could smooth things out if you wished; with a fixed TN system, however, there's not a good mechanic for making small differences have a large impact.[/QUOTE]

WTF???? First you are worried about SR4 not having steep enough, now it can't be steep enough even with Success penalties?

In the end Ellery, if you want some sort of custom bending each and every place you end up with the same mess that is SR3. Several dice systems all mixed together. I'll take playable approximation over that pile any day.

Don't have time for the rest of this.....

Hm, the quote feature appears to be broken, so I won't use it.

Anyway, I do actually spend a fair bit of time playing characters of widely different power levels with SR3, and it works out okay. The trick at lower powers is to make judicious use of pool (e.g. combat pool) and to not get into situations where the TN is too high. Since SR4 had a chance to make this better, I'm less than pleased that they've switched to a system where it will be very difficult not to make it worse. I'm not reaching--I play characters like this (esp. as a GM). I also play very powerful characters.

Also, given the past track record, I think people are justified in coming across as pessimistic. I assume the developers are mature enough to integrate a pessimistic viewpoint into their plans without feeling all pouty and hurt and ignoring the comment completely because the poster was a big meanie.

What I dislike about the fixed TN system is a one-size-fits-all mechanic that isn't a very stretchy mechanic. It's like one size fits all socks made out of woven nylon. If you have only two options--increase threshold, or alter the number of dice--there isn't much you can do to alter the the fit. So if you tune the system for, say, people who throw 8 dice, you might decide you need to increase a threshold from 2 to 3 for one test, and subtract 4 dice for another test. But when you switch to someone who throws 4 dice, or who throws 16 dice, the size of those penalties become much larger or smaller than you tuned for the 8-die person.

With opposed tests, and a fixed TN of 5, the mechanic gives a smooth variation if you have reasonable numbers of dice (6ish or more). The problem is that this is the only thing it can do. In SR3 you can have a smooth variation if you have an opposed test against a fixed target number, and a much steeper variation if the target number is the opponent's stat. One can compensate for this in game design--besides, maybe it's too complicated to have two different types of opposed tests depending on whether the difference is supposed to be steep or not. But if you're going with a system that is forced to be smooth, then you firstly need to ensure that you always start with enough dice (because it gets very spastic with too few dice), and secondly you need to allow for large variations in the number of dice if you want to differentiate people on the basis of their ability.

I don't see good evidence that they've structured the game this way. People who are decent at something will have attributes of 4-6, most likely, and skills of 4-6. A range of 8-12 dice doesn't leave much room for meaningful statistical differentiation. So the real question is: how much higher than that can we go, in a fair head-to-head test? The SR3 limits of attribute 11 (with edges) and unlimited skill (although more than 12 gets fiendishly expensive) probably give enough room; 23 dice is a lot more than 8.

But now there's a problem: this 23-die person isn't going to even notice the penalties that make a task impossible for the 8-die person. So now the non-opposed test penalties are all messed up. What to do?

If one had better ways for adjusting penalties, the 23-die person would just get a heavier penalty, so they'd notice when it was dark and the opponent was in melee behind cover. But without that, you probably don't want people rolling 23 dice, or your bonus/penalty system will break.

So you have to use fewer dice--but that means that in most cases, the very best and the pretty good aren't really that different from each other in a head-to-head test.

I suppose that one way out is to have head-to-head tests be compared as (skill or attribute) + (successes on test) rather than just plain successes. That gives more opportunity for distinction, although it probably makes most tests too sure of a thing if you have 2 or 3 skill higher than your opponent. And this still wouldn't fix the impression that the very best weren't much better than the simply okay when it came to doing something that wasn't opposed (like treating a wound, presumably). Although you could presumably invent yet another mechanic for that...but pretty soon, you'd be worse off than with SR3.

If dodging is still around, and it uses the attribute + skill mechanic, why can't they get 23 dice on a dodge test?

Also, 23 dice is quite a handful. I'd expect for that reason alone that they'd try to use fewer dice, possibly without realizing that this means that there are no outstanding masters of anything in the world (without a special extra mechanic to distinguish such people).

If they don't add dice, then what do all the improved XYZ abilities do? Do they just vanish? They obviously can't change the TN.

Sure, they could vanish. They were always pretty bland. +X dice to a skill? Blah.

That's so not funny.