There were several threads on the old forums discussing alternate dice rules and methods for smoothing out probability curves, e.g., how to avoid an automatic 7 whenever you roll a 6. I'm writing a Java dice roller for SR and I'd like to incorporate a 'smooth' option into the program using one of these methods. However, it doesn't look like there is a general consensus of what the best approach is, and I'm no statistician. What are your thoughts?

I voted other. Our group just uses the regular rules. We have never had a problem with canon rules.

i just vote to use normal dice rules

I do this: when you roll a 1 after a 6 you roll another die. If it's a 1-3, then your original result is a 6, and if it's a 4-6, your original result is a seven. It's only one extra roll for the rare problem of rolling a 1 after a 6 against a target number of 7.

Edit: Good lord, that's unclear. Did anyone understand it the first time they read it?

Voted for Other.

Core rules. It's simple, and the fact that there is a probability hole at 7, 13, 19... has never really bothered me. It doesn't really give anyone an advantage since everyone can attain those numbers anyway. Of course, anyone looking at TN 8 will tell you that the die is just as likely to roll a 1 as any other number.

I have to agree that the cannon rules aren't too big a problem. If you go messing around with the probabilities as they are, you end up pushing the problem around instead of solving it (in most cases). If you want to change around the way a 6-7 or 12-13 is currently represented, you have to also adjust the TNs of tests to match. A 6 = 5+die system would make any TN over 6 even less likely (particularly 12 or greater). It's not been my experience that TN 7 was all that common. At least, not common enough to warrant changing the dice mechanics (if it's a 7, it's just as often an 8-10).

If it ain't broke, why fix it???

It is broken to a degree. Problem is that it's been compensated for in most cases by the numbers laid out for concealability and the like, which means shifting over to modified exploding 1d6+(1d6-1) would require all teh core numbers to be messed with. Not a bad idea, in my opinion, but likely not worth it unless you're already overhauling a lot of the game.

Is it that bad that 6 and 7 are the same? I have never really had a problem with it. Just this week end I had a character breaking into a corp. The office desk he was braking into was locked wth key locks. The GM cliamed they were super hard to pick 24 tumbler locks. TN 12, for each of the 5 drawers. It only took 8 or 9 rolls to open them all. 4 of the 5 opened on 1 roll, it was the drawer with pay in it that was the one that took multiple rolls. In our game target numbers around 10 and above are common, skills of 3 or 4 are the norm. Rolling in full view of everyone, targets are hardly missed. When we were taught SR in first edition well over 10 years ago, the guys teaching me and the current GM, said that armor was added to TN for shots. We have always played that way with all the other mods on the TN. So a human running in a dark alley at short range wearing an armored jacket, being being chased by another guy shooting with a smart link could easily reach TN of 13 or so. And that is common in our games. Suprisingly a lot of people still get wasted. End alot of other crazy Tn being hit.

On a little wierd side note, when I play certain characters I can hit amazing numbers with ease. If anyone needed a really hard to get piece of equipment they would call my character. I once got a monowhip, a suit of Mil grade armor, and a bunch of mil grade stuff. And enough successes that the guy who wanted would still be young enough to use it. That character is now retired as a fixer. Some of the old characters still call him.

I think its better to keep to the Core Rules. TN modifiers are HUGE modifiers at most levels. TN 5 vs TN 6 is half the successes with a GOOD chance of no successes.

According to the Shadowrun Probability Chart, these are your chances:

Rolling 1 Dice:
TN 2: 83.33% TN 3: 66.66% TN 4: 50% TN 5: 33.33% TN 6: 16.66%
TN 7: 16.66% TN 8: 13.88% TN 9: 11.11% TN 10: 8.33% TN 11: 5.55% TN 12: 2.77%
TN 13: 2.77% TN 14: 2.31% TN 15: 1.85% TN 16: 1.38% TN 17: 0.92% TN 18: 0.46%
TN 19: 0.46% TN 20: 0.38% TN 21: 0.3% TN 22: 0.23% TN 23: 0.15% TN 24: 0.07%

Those numbers are good enough for me.

Sphynx

OK.... let me make myself clear here... this poll is strictly for ALTERNATE DICE RULES only. That means, 'if you had to use something other than the core rules, what rules would you use?'. Sticking to the core rules is not an option in this poll.

I am not taking a poll of whether or not you use core rules. I am trying to assertain what alternate dice rules would result in [edit]a smoother probability curve than the one produced by the core rules.[/edit]

If you love the core rules, that's great, but we're not talking about core rules here - just alternate rules.

I use special d7's instead of d6's. Then if someone rolls a 7, I have them roll a d10: 1-5 no reroll, 6-8 reroll on a d6 (with no reroll if you roll a 6), 9-10 reroll on a d7. If they roll a 7 on the d7 reroll, they have to roll a d10 again but the odds change, this time 1-6 is no reroll, 7-9 is a d6, and 10 is a d7. If they get another 7, they have to roll a d20 and if the die comes up on number 3 exactly, they get to reroll again with a d7. If they get another 7 after that, I bring out a deck of cards and ask them to name a card. If they draw that card off the top of the deck, I let them reroll again, and continue that for further 7's.

This evens things in just the right way for me.

Well, uhh, dude? If this many people are posting that they don't think it's a problem worth losing sleep over... maybe that's a sign that you don't need to worry about it, y'know?

Well, I (and my players liked it) have always simply applied the rule of one to the second roll. If you needed 7 or higher and are luckey enough to roll a 6, roll that next die and add it to the roll...unless you roll a 1. Then it's a failure. Also, to increase the likelyhood (and fun, though it remains rare) of "oops's" if you get ALL 6's and then ALL 1's on the secondary dice, it's an "oops" and you fragged up bad! If you needed a 13, then you have to get all 12's followed by all 1's to get an "oops." I have yet to get an "oops" that way when it wasn't a single die rolling for the task. It also makes players think twice about trying the really hard stuff, when they should probably be running away. Of course, I'm eeeville!

My GM plays with a rule that you can get 2 successes from a single die if you roll 3x target number (also 3 succs. if you roll 9x TN etc.). For the most part it plays like canon, but 6/7 are differentiated because it's the difference between rolling 18 vs 21 to get the multiple succs.

I also didn't tell you other midigating circumstances either. Like sustaining an Ivisibiltity spell, while waiting for the guards on code red looking for me.

And you are right we don't use the +2 and higher per try. I don't know why we have never used it. I geuss we just look at it as, if you fail you just wasted the time you put into it, but you can try until you pass. Unless of course there is something that will make it impossible, like a three try alarm trip, or a encrytption that changes everytime someone fails an to access it. I don't recall to many skill check in shadowrun who say that if you fail you add +2. I know some tests say you waste half the time in the process, or if you fail, success is for ever impossible.

And yes I think gravity or the space time quntinum is messed up in our GMs house.

And I don't think SR takes repeatitive tasks into account when doing a skill check. Picking one lock will be different then another, but in theory if you pick enough locks eventually lock picking should be easier. Well it does if you continue to increase the skill, but the TN's stay the same. If skills went up and TN's went down after alot of practice then eventually picking a lock would be so easy that it would be like using a key for that lock. If the TN's stay low vs. a high skill rating that would seem right, but if you run into a decent lock, even though have a couple to practice on, the target number would still be the same and still difficult, no matter how offten you practice on it.

And now Daishi applies his Stats course to something useful...ish.

I took your three options and compared them to the the canon rules. I quickly noticed that the first two systems are statistically identical. So I dropped the second d6 method. If it seems clearer to you that way, then use it.

I calculated the probability of a success from a single die for target numbers (TN) of 2 through 36. Just to get the range. The numerical results are in the following PDF files for those interested:
Comparative Probability Table
Comparative Probability Graph
Comparative Logarithmic Probability Graph

None of the options actually produce a smooth function (see the log graph). All of them are discontinuous (or rather their slopes are, but let's not go there. I guess I just did, but forget that...) The difference is that the plateaus at multiples of 6 are removed.

For the 5+ d6-based systems, the only difference is that the plateaus are removed. The probability slope for increasing TNs remains the same. This basically means that with the 5+ system, higher TNs become that much harder to achieve. An equivalent of a +1 mod to a TN for every multiple of 5 over 6 (when using the canon system).

Using the d8 system, the plateaus are also removed. Since the probability is based on multiples of 1/7 instead of 1/6, the overal probability slope is less drastic than the +5 system. Thus, higher TNs are easier to hit than with the 5+ system. At lower TNs, however, the d8 system typically increases the probability of success. By a margin equivalent to about -.5 to -1 modifier to TNs (just guessing on this part). Easier TNs become that much easier with this system. This difference is lost as the TNs become higher, and the d8 system becomes harder on high TNs. This changeover from easier to harder occurs at about TN 12.

Despite the weirdness of the plateaus, I would stick to the canon d6 system. The alternative systems skew the current implementation of TN mods in bizarre directions. The +5 is especially annoying since it just makes the game harder. The d8 system exaggerates the current system, with lower TNs becoming easier and higher TNs just becoming harder. But if I had to choose between the two, I'd take the d8 since it's more true to the original and not as punishing as the +5 system.

Man, I'm bored...

Thanks, Daishi, for that clear, concise explanation. I appreciate the effort. Based on your analysis, I'll probably go with the D8 for the alternate 'smooth' option, and just note the caveats in the help doc.

Thanks to everyone else for an interesting discussion!

I'm the one who just voted for your first option (6s as 5s, including the first die). We never found the TNs to be too high: if they were higher than 6, that just meant the action was supposed to be challenging. The highest preset TN ever achieved under this system (over years of playing) was 24; the highest open test TN ever achieved was 36. Most TNs started between 3 and 8 based on the desired action alone, before situational modifiers. It worked well.

I've updated my graphs and tables to include the 4+ system that Random Voices suggested, so you can take a look at those. The 4+ system is more true than the 5+ system, but still not as close as the d8 system. The most noticeable difference is that since the chance of getting a second roll is double, higher TNs become easier to achieve. This is most noticeable in the TN range of 6-8, but holds true for most TNs above 5.

For a dice rolling program, I would still go with the d8 system. It holds the closest to the canon system over the widest range of TNs. If you have a pile of d6s and really want a "smoother" system, then I would suggest the 5+ system. Although higher TN do become harder, the sweet spot of the 4+ system at TN 6-8 would change the game a fair bit more. (For the way my crew plays, at least.)

But in the end, I still say stick with the current system. None of the others offers a clear improvement over it.

What the heck's the matter with mine? No extra math and no altered result probabilities. Also, it only comes into play rarely with TNs of 7, 13, or 19, and then only if you happen to roll a 1 afterward. Is there something I'm missing about it? Does it stain your clothing or cause a rash? What's the matter with it?

arg.
dice system.
arg.

the probability gulf from 5 to 6 (and every similar thereafter) is what always bothered me. more dice are next to useless compared to getting the diff from 6 to 5, except for very low dice pools. and given that NOBODY would consider using a skill at 1 (because the probabilities are ABYSMAL for less than skill 3) it never comes up in games 'round here. (let's say you had a skill at 1, and the linked attrib at 6 or 8 or freakin huge. at some point, it's better to just default than to actually use the skill. though the +4 really offsets that, i suppose. if it was only +2 it'd be a much harder decision. like knowledge skills are for Johnny Mnemonic. :P )

even with an entire karma pool thrown at rerolls, no decker will ever install that last bit of ActiveMEM that requires diff 18. (bah linear diffs. should be log-2!)
fix that, and you've got a discussion. (please? i'd like more utils!)

whitewolf's solution was to disallow MAX_ROLL diffs from normal play, which people promptly forgot. but with any success vs single die (and hence linear prob. distrib.) system, that last number will always be twice as hard as the prev. which i suppose is why D20 irritates me so much. increasing the linear scale (such as CoC's d100 system) only lowers the magnitude of the "N-1 to N eccentricity".