1D20 vs. 3D6: which simulates reality better?, A layman's analysis of the probability. Options

[Umbrage]

Disclaimer: I'm not a statistician by any stretch of the imagination, I've just got too much time on my hands this particular Sunday evening. ;-)

I got to wondering why SR uses D6's while other systems use D20's. Thinking about it, I realized that a D20 has a linear probability curve. If plotted on a graph, it's a straight, downward slope. This means, for example, that hitting a target number of 6 (or more) on a D20 is 5% less likely than hitting a 5 (or less). In fact, no matter which target number you need to hit, it's always 5% harder or easier than the next TN.

This didn't seem very realistic to me. It would make more sense if the amount of effort between a "very easy" task and a "easy" task was greater than the effort between an "hard" task and a "very hard" task (e.g., a logarithmic curve for those of you playing along at home).

However, a true logarithmic curve wouldn't be entirely accurate either. There ought be be a "sweet spot" in the middle. This would mean that most attempts at using a skill should be somewhere in the middle. Meaning, it should be more likely that a runner perform a skill "ok" versus "horrible" or "spectacular".

Anyhow... I plotted the probability curves of both a 1D20 and 3D6. The graph in question should make my point bit more clear. According to the definations that I layed out above, the 3D6 is a better representation of reality.

Between 1 and 4, the slope is very steep. This means that things rapidly get more difficult to accomplish, at first. The "sweet spot" occurs between 5 and 10. Between those ranges, the slope is almost the same as a D20. This would mean that as you enter the average zone, things don't so much harder so quickly. Finally, beyond TN 10 things start to level off a bit. It's kinda like saying "TN16, TN17... what's the difference? They're both pretty unlikely".

Anyhow... hope that helps. And if anyone who's better at math than me (not hard to do) sees a glaring mistake in my analysis, please let me know. ;-)

[Modesitt]

Short answer - d6's are platonic solids. They're also very, very common and easy to get ahold of.

Long answer -
There are basically two approaches to making numbers in RPGs that work.

1. Static number of dice, dynamic target. This is what the d20 is. It's the exact same die(or number of dice) every time, just what you want to roll changes every time. d20 is preferred for me because it's very easy to just look at targets and say "Huh. I only have a 25% change of succeeding." This idea is also used in Feng Shui RPG(You always roll 2d6 for task resolution - Sorta. It actually adds up to nothing) and some others.

2. Dynamic number of dice, static target. This is what White Wolf uses now and SR4 uses now. I don't prefer it, but it works.

There's a reason White Wolf changed, there's a reason SR4 is changing and that's because dynamic numbers of dice and dynamic targets blows. SR does some marvelous things with it, but every single one of them would be better if it wasn't just a testament to the designers creativity and actually had a good system behind it.

Fortunately, you propose a static number of dice system with shifting targets, so you're on the right track.

----
Here's the real reason I hate the d6 system SR uses WITH A PASSION.

You CANNOT 'tweak' the probabilities. With a d20, you can be pretty liberal with bonuses and penalties and not worry about throwing off the odds. But when you're dealing with a d6, you can't throw around TN modifiers for everything. Every +1 TN is a pretty big deal. So even if you wanted to, you can't implement the little details.
----

Yes, that had to do with your analysis. The reason d20 is superior to 3d6 has nothing to do with realism and everything to do with the realities of gaming. It's better for a game designer because you can stack a bunch of penalties on people and know every single time you give someone +1 to their DC, you know exactly how much an effect this has on them. You know there is now a 5% lower probability they will succeed.

With your 3d6 approach, you have absolutely no way of knowing what this particular +1 TN will do to their probability. Maybe their original TN was 4 and now it's just 5. Or maybe their orignial TN was 17. You don't know. Balance is a lot harder to achieve when you have no idea what all of your numbers add up to.

So even if I agreed with you on what was 'realistic'(And I don't, I absolutely reject the entire idea), I would still say the d20 was superior to the 3d6.

Edit: Hoping no one replies before I remove something.

[Umbrage]

[Dippy]

Well although I've only been GM'ing SR for a few months I've been a GM for about 20 years and have run many different systems in that time. My conclusion is that none of them emulate reality at all. There are just too many permutations to events that you are trying to emulate to expect any dice rolling system to work very well. The best you could do is to vary the systems in the same game, because some systems are better for some situations than others. However neither game designers, GMs nor players want such complication.

However don't forget that RPGs are not emulating reality anyway, they are emulating a dream for the purposes of giving enjoyment. And of course everyone has different needs from the game. I am aware that many people enjoy rules and detail, whereas others (such as myself) are more into the role-playing (i.e. improvised acting), and intellectual challenges.

Having played AD&D for years, I have kept with it because of its simplicity. Yes it is easy to deal with 5% probability steps, but I only ever used them as a guide anyway. This is why I have not adopted 3rd Edition so-called d20 rules. I find that there is often too much variation on a d20 roll for every circumstance.

I am still learning SR. At first I was a little worried about the system, but having used it now for a few months I quite like it. Certainly it is more difficult to judge the impact of increasing a TN by 1 in every situation, but of course the great power of the system is that a test is not just pass or fail, it has degrees of pass.

What I have been doing is avoiding setting TNs too high by risking setting them too low instead. Then I can vary the results of the test by setting a threshold, even after the dice have been rolled. Some may suggest this is cheating, but those would be rule-players. I know how to make a game enjoyable for my players, and quite often that means I prefer to decide if a PC succeeds or not. The trouble is many players expect a dice roll so sometimes you need to provide one, but steer the result the way you want.

[mmu1]

What is up with that 3d6 curve? Why the strange dips? I'm pretty sure (from playing GURPS for a while, if nothing else) that it's not supposed to look like that.

[Aku]

What does everyone think adding fractions would do for modifiers? instead of having any given situation add +-1 or 2, make "smaller" situations, where indvidually they help (so any fraction gets rounded down) but if chained together, you can get some nice modifiers? I was thinking maybe .5 or .25 points...

[toturi]

[Umbrage]

[Austere Emancipa...]

The curve is probably weird because it's made with a dumb program. Since it's apparently just 3d6 totaled vs. a TN of 3-18, it should be a "smooth" curve without any dips. Plot away on Excel:

[mmu1]

[Umbrage]

[Umbrage]

[Modesitt]

[Arethusa]

The more sides a die has, the less granular the system. D10s offer more opportunity for fine tuning and details than D6s. That's all.

[Austere Emancipa...]

[Fester]

I checked yesterday and was able to buy some non-6 siders without a SIN in about 15 minutes with my short list of contacts and Incompetence:Ettiquette flaw.

[Cynic project]

[Umbrage]

[Modesitt]

[Arethusa]

[Umbrage]

[Arethusa]

And, amazingly, that's exactly what a good GM brings to the table, considering he is basically the director of the game, if you'll pardon the analogy.

And being a game designer isn't quite so thankless when you're good at it. The people that punched out SR3 weren't.

[Modesitt]

[Arethusa]

There's obviously no getting around the simple fact that in designing an abstract representation of real life phenomena for a game, you're going to end up with a poor simulation of reality no matter how hard you try. Things will get left out, or at least be poorly simulated. (This sounds like it's heading for Bazin Artifice theory, but it only sort of is, so bear with me.)

However, I have to disagree with you; where this happens and to what degree— and, more importantly, how— is the game designer's responsibility. The six year old playing with a gun and getting a lucky hit is a small part of a larger dynamic: in this case, specifiaclly, unpredictability. As it stands now, I can be damn sure that if someone doesn't know how to use a weapon properly, he can't possibly get lucky and take me down. IN reality, anyone with a gun is a potential liability, and leaving out a dynamic of unpredictability— among many other things— dramatically alterns (and dulls) the gaming experience.

There's no arguing that abstraction is a necessary element in tabletop gaming. The difference is that well directed and designed abstraction shapes a game and the experience of it; poorly handled, clumsy abstraction deadens it.

[CoalHeart]

To tell the absolute honest truth when I very first read Shadowrun's dice rule system I thought it was addition and division, and a little subtraction.



Eg.
Sam the Main Man Machete Maniac has Edged weapons:Machete 3(5) and a combat pool of 5.
Strength 4 weapon damage Str+3 S (from being a dikoted machete)

Standard attack comes out to be. Roll 5, + 3 CP for 8 dice.
Roll 8 dice.
1 1 2 3 4 5 5 9.
Then add them up.
for a total of 30. Now divide by your target number, 3 (Reach weapon and all) for 10 successes.

Now Flim Flam The Turkish Trog Tank really doesn't want to get hit, so he counters as normal, with his own sword. but less skill.
Edged Weapons : 3, Combat pool 5

So Flim throws down his 3 dice plus 3 combat pool for a total of 6.
1 2 3 4 4 5
Add it up, for a total of 19, div by 2 (target number, from wep and natrual reach)
9 successes. Oh oh he still gets hit by 1 success.


Then you go onto figuringout damage
Sam rolls 7 dice, from his strength and the weapon.
<insert rolls>
Sum value Divide by your attack Target number, so 3. So thats how much he inflicts.

Then Flim Soaks
Rolls Body + CP + armor rating
<insert rolls>
Sum value divided by amount of dice Sam did damage with 7 in this case.

Any remainder successes left means Flim's player marks the S damage and suffers as usual



This was how we played it on our first test game of the shadowrun system. Totally and completely wrong, but it was still fun.

Oddly this way it somehow works out that no matter how badly you roll if you are skilled enough at doing something you can never fail even with all 1s. Eh...

I rather like shadowrun's current rules I'm sad to see them go over to the static side.