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Posted by: hyzmarca Dec 9 2007, 03:45 AM

6=7, many people complained about it. A TN 6 is equal to a TN 7. There is no possible chance of getting less than a 1 on a die. It is important when adding up modifiers, as many has pointed out, since 6+1 is different from 7+1, which is true, and it is the best argument to support keeping 6=7. I'm not here to discuss the merits of 6=7, rather I intend to propose a novel solution to the problem for those who want it.

One proposed solution was a 1s never count system, but that only created a 7=8 problem. But what if, instead, we subtract 1 from the value of all sides of out dice, so that 1 becomes 0, 2 becomes 1, and so on, and we subtract 1 from all TNs so that the minimum TN becomes 1. This gives us a 0-5 die with average with the same probabilities on the first 5 TNs. The Rule of 6 becomes the Rule of 5. A TN of 6 (Formerly 7) is reached if one rolls a 5 (Formerly 6) and a 1 (Formerly 2), thus removing the 6=7. Shifting all values back one also means that a TN of 7 (Formerly one must roll a 5 and a 2 (Formerly 3), and so on. The 7=8 problem is avoided.

I don't know why this would be particularly useful, I just thought of it and felt like posting it.

Posted by: ShadowDragon8685 Dec 9 2007, 04:08 AM

Or you could just accept 7, and every 6th number after that one, being a "gimmie" in order to make what would be utterly brutally punishing utterly brutally punishing, but with a small bone thrown to the player.

Or just accept that 6=7, for sufficiently large values of 6.

Posted by: mfb Dec 9 2007, 04:25 AM

you can greatly reduce the 6=7 issue by, as i recall, rerolling on a 5 or greater and subtracting 1 from the reroll. so, for instance, let's say you roll a 5; that entitles you to a reroll, which comes up 6; that entitles you to a further reroll, which comes up 4. your total roll for that die is 5 +6 +4 -2 (for two rerolls) = 13.

you can reduce it even more by rerolling on 4+ and subtracting two.

Posted by: Kagetenshi Dec 9 2007, 04:27 AM

That's been proposed before—the real problem with it is that it either makes a bunch of tests significantly harder (basically everything TN 11 and greater, though you notice it on 7-10 as well), or makes you go back and redo a gigantic swath of TNs—which are substantially at nice, visually appealing points right now.

Edit: Eyeless discusses some solutions http://www.sr3r.net/forum/viewtopic.php?t=51.

~J

Posted by: mfb Dec 9 2007, 05:26 AM

that's surprising, to me. i wouldn't think the -1 per reroll would mean more, statistically, than doubling your chances of getting 6+ per die and reroll. regardless, it seems like it'd be easy enough to skew the system such that the issue is pushed off to TNs of, say, 18+, at which point it generally becomes academic.

Posted by: Kagetenshi Dec 9 2007, 05:32 AM

Whoops. No, I was talking about the reroll-6 add-5 solution. I don't remember offhand how big a chance your suggestion was.

~J

Posted by: mfb Dec 9 2007, 05:38 AM

i'm pretty sure i remember seeing charts of it, compared to charts of 6=7, and thinking "that's not too far off."

Posted by: Telion Dec 9 2007, 08:18 AM

if you really hate the 6 =7, whenever they roll a 1 following an exploding die, give them a 50% chance of going to either 6 or 7. no fancy math, and keep it simple without modifying to much of the mechanics. just delay the game for a moment.

Really I've learned to deal with it the 6 = 7 and feel it works just fine. besides those mooks have the same advantage, along with anything you throw at the players.

Posted by: Karaden Dec 9 2007, 08:56 AM

Hum hum, there is a problem with the 0-5 and -1 to all TNs though. While it is no different for TNs of 2-6, which will still have the same odds, it quickly becomes a problem as it makes higher TNs even harder to get to. Lets see an example. As rules are, a TN of 15 requires a roll of 6, then another roll of 6, followed by a roll of 3 or higher. Now, at your proposed system, the TN would change to a 14, and you would now need a roll of a 6 on the die, then another 6, followed by a 5. Obviously the test has become more difficult now, and there is no real way to fix it. If you say 'well, let's just add another -1 at some point' then you run into some TNs being adjusted to be exactly the same, which was the original problem.

Don't know about other solutions, I'd have to look at charts for the reroll on 5+ thing to know how that works out.

Posted by: Fortune Dec 9 2007, 10:49 AM

It's a feature, not a bug!

Posted by: Stahlseele Dec 9 2007, 11:24 AM

Posted by: Ryu Dec 9 2007, 12:14 PM

No complaining about chicago´s local wildlife please. The white man has done enough already to damage nature, no need to endorse people who want to nuke natures best...

--
Our prefered solution was the reroll 5+6, but only add 4 solution. The reduction in variance is also neat...

Posted by: Narse Dec 10 2007, 04:04 AM

My solution: (Take this with a giant grain of salt as I have played very little SR3)

7 does not exist. TNs of 1+6n where n is a positive integer do not exist. Thus a TN of 6 with a +1 to TN penalty becomes a TN of 8. Any TN assigned in the books that would be eliminated (I'm pretty sure that there aren't any) is reevaluated to a multiple of 6, for a result of the exact same probability. I think this is in line with the dev's thinking. If you look at the TNs for weapon range table in SR3, the TNs go 4,5,6,8 (IIRC) indicating that there shouldn't be a TN of 7. This keeps the math minimal as long as you don't have bonuses or penalties in excess of 5. I would think this wouldn't occur too often.

Posted by: mfb Dec 10 2007, 04:37 AM

that just shifts the problem one place. instead of 6=7, you end up with 7=8.

Posted by: Mercer Dec 10 2007, 04:41 AM

4, 5, 6, 9, weapon ranges. (Here nor there, although I used to use the Vision Mag rating as a reduction of the TN rather than range category, so a Extreme Range shot with a Mag3 scope was a TN6, rather than 4. Mag didn't reduce the TN under the base for the shot though, so no Mag3 at Short range-- it was still TN4.)

Posted by: Kagetenshi Dec 10 2007, 04:57 AM

4,5,8,9 for some weapons.

~J

Posted by: Mercer Dec 10 2007, 05:17 AM

I wasn't aware of a variant Long range, but I'm mildly curious. Which weapons got the 8?

And to at least pretend this isn't off-topic, the 6=7 thing never bothered me. My first group added the next result to 5 instead of 6, but after that group disbanded I never saw that houserule again. If you had a TN6 and something took it to 7, it was basically a little "Merry Christmas" moment; you could have been getting screwed harder by the system but you weren't.

@Telion: I also considered the 50-50 roll for 1's on the re-roll, but I came down on the side that the one thing SR didn't need was more rolling.

Posted by: Kagetenshi Dec 10 2007, 05:38 AM

Grenades (thrown and launched), mortars, rockets, missiles, and, curiously, target designators.

I was about to make a quip about how, while the designers obviously didn't care enough to fix 6=7, they did care enough to not give anything 7 as a fixed, unmodified TN, but the Tiffani Needler just had to come along and prove me wrong. Still, it's the only TN I can find offhand in {6n+1 : n ∈ N} that's specified as such (that is, not part of a sliding TN or the result of modifiers).

~J

Posted by: Narse Dec 10 2007, 05:59 AM

Posted by: mfb Dec 10 2007, 07:16 AM

the reason 6=7 is unwanted is that there's a skip in the progression of difficulty. you have a fixed chance of succeeding at TN 5 with X dice. that chance goes down when you roll against TN 6. it should go down again when you roll against TN 7, but it doesn't. and at TN 8, there's a big jump in difficuty. that's the issue that these fixes are attempting to resolve.

with your solution, the same problem exists, it's just bumped up by +1 TN. you have the same fixed chance of succeeding at TN 6, but if the TN is 7 (say, base TN 4 and +3 for some situational modifier), you treat it as an 8--you have to roll a 6, and then reroll a 2+, to succeed. if the TN is actually 8 (base TN 5 and a +3 modifier), you of course treat it like the 8 it is. you've got that same lack of progression, and the same big jump in difficulty.

Posted by: Kagetenshi Dec 10 2007, 07:45 AM

Actually, at TN 8 there's a very small jump in difficulty (6/36 -> 5/36), except insofar as the last "jump" was zero so it's infinitely larger than the last jump. The closer you get to a multiple of 6, the steeper the probability curve. Your other criticisms of that plan stand.

~J

Posted by: ShadowDragon8685 Dec 10 2007, 08:18 AM

Is it really that big a problem, unless you're the kind of person who worships probabilities and orgasms over statistics?

Posted by: mfb Dec 10 2007, 08:21 AM

that doesn't match my experience, or what i've come to understand from discussing TN probabilities with others. i could be misremembering, but from what i recall, succeeding at TN 8 is roughly twice as difficult as succeeding at TN 6/7.

Posted by: Kagetenshi Dec 10 2007, 08:34 AM

Nope, it's at the 5/6 or {n-1/n : 6|n} boundary that things are twice as hard. Odds on a single die go:

Posted by: mfb Dec 10 2007, 09:16 AM

psh, yeah, if you trust numbers and science.

Posted by: Kagetenshi Dec 10 2007, 09:22 AM

Transitive relations may lie to you, and the power set of multisets may deceive you, but the probability mass function is always faithful.

(Guess what I've been doing for the last sixteen hours solid!)

~J

Posted by: ShadowDragon8685 Dec 10 2007, 03:07 PM

Something from which you ought to have a long break?

Posted by: Kagetenshi Dec 10 2007, 03:13 PM

I had about an hour-long nap before the combinatorics started again, does that count?

~{J : J ∈ {dead_people}}

Posted by: Moon-Hawk Dec 10 2007, 05:11 PM

My solution was always to not care. It worked well.

Posted by: BookWyrm Dec 10 2007, 05:14 PM

Math make head hurt.

Posted by: Karaden Dec 10 2007, 06:19 PM

You know, there really -isn't- a solution to the 6=7 'problem' that doesn't involve affecting the difficulty of other TNs in some manner one way or the other, just accept it as a limitation on the very nature of using dice to make random numbers. The one solution out there would be to figure out the exact % chance of getting any particular number and having a computer generate a random number. Then you would tweek the TNs of 7, 13, 19 and the others to be a % somewhere inbetween 6 and 8. (well, 13 between 12 and 14 etc. of course.)

Actually I take back my first statement, there is a solution, and that is when you get a six, then a one, you reroll the one with needing a 4, 5, or 6. But this is just more dice rolling, does the game really need that?

Posted by: Narse Dec 11 2007, 05:00 AM

Posted by: Kagetenshi Dec 11 2007, 08:48 AM

I'm too tired to be sure, but I think your suggestion is just a slightly obfuscated version of reroll-6, add-5.

~J

Posted by: Fuchs Dec 11 2007, 09:26 AM

Posted by: Critias Dec 11 2007, 09:30 AM

Ditto. I always liked 6=7, in fact, because it gave you a little more incentive to try and work your combat options (using cover, take aim actions, stacking the right bonuses and stuff) in order to hit that "sweet spot."

Posted by: Daddy's Little Ninja Dec 11 2007, 03:29 PM

I think you are over thinking it.

As I understand it a 7 is not 'useless' because of maybe modifiers. for example sure a '7' for a target number shooting is a dead cert if you have only that, but a +2 for a smart link means you have to roll a 5 or better to hit (1 in 3 chance) but if it is a 6 normally and you have the smart link you need to only beat 4,(1 in 2 chance). Or if you are a bit further out and the target number to shoot is a 9, there is your incentive to close the range until it is only a 7. etc

Posted by: ShadowDragon8685 Dec 11 2007, 03:43 PM

I just like 6=7 because it's a little, as was said earlier, "Merry Christmas" moment.

The system's way of self-correcting for it's extremely steep difficulty. It's like saying "We're using bell-curvacious dice on a linear difficulty scale that gets logarythmically more difficult as you go higher. So as a way of giving something back, we'll just make every multiple of six just as hard as every multiple of six +1, or make every multiple of six +1 just as easy as the multiple of six. Therefor, you can eke out that little bit of extra chance without more risk than would be incurred on a six.

Posted by: mfb Dec 11 2007, 04:06 PM

Posted by: Kagetenshi Dec 11 2007, 05:51 PM

It's hard to tell, but it looks like the effective TN shift magnitude gets increased by one when going past a multiple-of-6 boundary (henceforth referred to as "the 6 boundary", even if it's 12<->13, 18<->19, etc.). What happens when going downwards, or when both positive and negative TN modifiers make it cross both ways, or when crossing due to multiplication, isn't clear and may make TN summing non-associative and non-commutative.

~J

Posted by: mfb Dec 11 2007, 10:54 PM

so if the TN is higher than 6, you add 1 to the TN; when it's higher than 12, you add 2 (or, rather, another +1 for a total of +2), and so on? that would make a lot of tests a whole lot harder. someone else will have to figure out how such a scheme would work out, as far as smooth progressions go.

Posted by: Ryu Dec 11 2007, 11:46 PM

It was uncommented, so again:

Reroll 5+6, add 4. 5 is unchanged, 6 achieved at 2/6*5/6=10/36, 7 at 2/6*4/6=8/36. Both used to be 6/36. 8 is 2/6*3/6=6/36 now. And it is smoother because it uses more balanced hit/miss propabilities for rerolling.

Posted by: Stahlseele Dec 11 2007, 11:48 PM

smooth compared to what? gravel street you're being dragged on? O.o

Posted by: mfb Dec 12 2007, 12:08 AM

Posted by: Ryu Dec 12 2007, 03:04 AM

Got that one from DS back in the day - one of the few houserule suggestions that was suggested once and accepted without discussion.

Posted by: Kagetenshi Dec 12 2007, 03:39 AM

So you do find it workable in day-to-day play? I've always sorta looked askance at it. I'll have to slap together a chart when I get the chance.

~J

Posted by: Narse Dec 12 2007, 07:39 AM

Posted by: mfb Dec 12 2007, 07:41 AM

Posted by: Kagetenshi Dec 12 2007, 08:25 AM

Under the current system: TN 8, +3 TN = TN 3, +8 TN = TN 11

Under Narse's proposed system: TN 8, +3 TN = TN 11, TN 3, +8 TN = TN (3 + 3=6) + 5 TN = TN (6+1)+4 TN = TN (6+1+1)+4 TN =TN 8+4 TN = TN 12

In other words, base TNs and modifiers stop being commutative. Never mind the probability distribution, that's a deal-breaker for me right there.

~J

Posted by: mfb Dec 12 2007, 08:31 AM

yar, that's what i meant by the progression of difficulty. probably shouldn't be using the same term to refer both to this and to the array of chances to succeed at TN X with Y dice, but whateva.

Posted by: Ryu Dec 12 2007, 12:11 PM

Posted by: Penta Dec 12 2007, 12:51 PM

This hurts my head enough to think:

Isn't Fixed TN easier just for the not having to game probabilities?

Posted by: Kagetenshi Dec 12 2007, 01:07 PM

Tried making a test with less than 1/3 chance of success by an average character recently? Before you answer "threshold", consider what that does to the probability of success of people with low skill, as well as if it's really any easier to calculate.

(The short answer is that the fixed TN system discards the utterly trivial part of probability calculation, the part that we're all doing in our heads for this discussion, but keeps the bit where it gets messy and which we're all putting off until the last possible moment. I guess it is a fix for the 6=7 bug, but, well, when you've got the ability to write the rulebooks and the ability to get paid for it most of the difficult parts of that go away.)

~J

Posted by: Ryu Dec 12 2007, 02:19 PM

You need statistics for both systems. Basically any discussion on this depends on the implementation of the system in SR.

A fixed TN/threshold system has a binominal distribution with p=0.33. That can be calculated ingame, but I would use the no-longer-needed BBB as an impromtu club on the offender. What works here is that you instantly know that less dice is bad and compare average successes with threshold. Easy to grasp != there is no math.

If you intend to improve the variable TN system, you *need* to make the whole range of skill ratings work. Variance of actual results decreases with an increasing number of dice, as it does with the equality of hit/miss chances. Being able to calculate that does little to improve low skill ratings usability. Three dice can all come up as a success at TN 12, but that deviation from the average is compensated by getting a miss more often than the average would suggest. More dice = closer to the average = better. The less dice the system is build for, the higher the chance of an absolute beginner to hit a TN that is rated ultra-hard.

Posted by: mfb Dec 12 2007, 08:09 PM

Posted by: Kagetenshi Dec 12 2007, 08:15 PM

Posted by: mfb Dec 12 2007, 08:18 PM

haha, well, you can game those too, just not with any objective guarantee of success. eg, betting red when the wheel has spun black the last few times.

Posted by: Kagetenshi Dec 12 2007, 08:44 PM

I'd draw a line between "gaming the system" and "applying magical thinking", myself, but we've reached the hair-splitting phase of this discussion I think

~J

Posted by: Cardul Dec 25 2007, 10:51 AM

Posted by: kzt Dec 25 2007, 07:17 PM

Why do people who design game systems not have the foggiest clue how the game system is going to work in actual play because they have have not the vagues idea about the probability of success or failure? I mean 1st edition was totally nuts, as the examples in the book would happen about once in 500 tries, but there the examples of typical pedestrians who have a negligible chance to notice a crowd of terrorized citizens charging at them accompanied with machine gun fire in the background.

Posted by: Kagetenshi Dec 25 2007, 08:00 PM

Unless I'm misreading the post, I suspect it's because attitudes like Cardul's are not uncommon, including among designers.

~J

Posted by: Ryu Dec 26 2007, 02:37 PM

Most people writing for our game systems happen to be writers, not game designers.

What we do here when we are not playing is not what we do in game time. Some oddities are no problem, some can be quite game-breaking. We needed to fix 6=7 (and more important 6=0,5*5) because it encourages gaming for TN mods.

I´m all for avoiding complicated systems, but here we have some very easy solutions at our disposal. The argument Cardul makes here is common, but to me sounds like "stop thinking about rules when you play". That is only possible if the thinking was done beforehand.

Posted by: Wounded Ronin Dec 29 2007, 04:18 AM

Posted by: Moon-Hawk Jan 4 2008, 09:28 PM

I just came up with this in another thread, after I finished making an ass of myself.

One way to fix the 6=7 problem is, when rolling for TN 6, and ONLY when rolling for TN6, using exploding d4's against a TN6.
Probability of TN5 on exploding d6: 33.33%
Probability of TN6 on exploding d4: 18.75%
Probability of TN7 on exploding d6: 16.67%

As TN increases, probability of success decreases monotonically (until you hit the TN12=13 problem, which is a LOT less common of a problem)

It's not pretty, but it's pretty simple.

Posted by: The Stainless Steel Rat Jan 14 2008, 07:53 PM

A little thing I put together here about 2 years ago directly addresses this issue.

http://forums.dumpshock.com/index.php?showtopic=12340

It may be a little cumbersome to some people as it requires charts on hand for reference (one chart for all target numbers 1-20 is what we use), but on the other had there's no more buckets of D6's to deal with. Every roll is a percentage roll with 2D10's (with the occasional reroll to determine the decimal of the percent rolled - rarely needed)

Posted by: Eyeless Blond Jan 18 2008, 08:06 PM

Posted by: Kagetenshi Jan 18 2008, 08:13 PM

Yeah, I remember it from there—though I guess I'd forgotten the chart (with good reason, apparently—no offense, but I nearly went blind looking at it again ).

~J

Posted by: Eyeless Blond Jan 18 2008, 08:33 PM

Yeah, sorry about that. One of these days I'll work out this whole newfangled "pictures" thing and post a "chart", for all you people who don't live and breathe numbers.