2 up, 2 down

[Sean Waters]

Here's an idea.

 

We have talked about the merits of a d20 system, replacing the 3d6 roll.

 

Can I suggest one interesting variant would be a 4d6 system? Now I don't anticipate widespread popularity as Hero is 3d6, but it could work well for a couple of reasons, and I'd like to get people's feedback on the concept.

 

The way I envisage it working is this: two sets of differently coloured 2d6 (say green and red, shall we?).

 

Roll all 4 dice and EITHER:

 

1. Add greens and subtract reds, OR

2. Apply the biggest result (greens positive and reds negative)*

 

to obtain a result from -10 to +10. Red and green ties always yield a result of 0.

 

Example:

 

rolling (greens first): 4,5,3,2: greens = 9 and reds = 5.

 

By the first method this would yield a result of (9-5) = 4, and by the second it would yield a result of 9, that being the highest (absolute) total.

 

OK, so why bother?

 

Well, first off it would enable us to 'zero' everything - 4d6 does have a zero/mid point that can actually be rolled, unlike 3d6, which I kinda like, and that means that we would not have to add artificial constants into our calculations to make the system work; well we would, but they would all be zero: you wouldn't need that '11' in the combat calculation, or that '9' in the skill roll. Roll, and add the result to your OCV, that will be the value you hit, for example.

 

Secondly, certainly if you use the second method, the results are likely to be quicker to interpret and more dramatic than a straight 3d6 roll, it would really be a 2d6 distribution favouring high rolls.

 

Yes it could and probably would change the dynamic of the system a bit: high DCV would be a less useful defence with method 2, as extreme results are more likely, but a more useful defence with the first method as rsults would tend towards zero far more.

 

Anyway, I thought, as we had devoted quite a lot of time to the d20 concept, one way and another, it might be interesting to debate going a slightly different way....

 

 

 

 

 

 

 

*this gives a quite different distribution to 4d6-14 - it tends towards more extreme results. If you want the distribution curve tamed, you use the same method but count the smallest not the biggest total.

[Cancer]

Re: 2 up, 2 down

 

Any RNG system where the mean is constructed to be zero can be more straightforward to apply, as long as your skill and target-number system is set up to accommodate it. 2d6 minus 2d6 gives you mean zero, variance 11 2/3 (or s.d. 3.42), and extremes of +/- 10.

 

The question is how to adjust the width of the distribution, when you want to do that. Adding pairs of up/down dice concentrates the distribution more (while allowing greater deviation from the mean); the question is how to widen it if you want that.

 

A max(2d6) minus min(2d6) -- that is, roll 2d6, subtract the lower d6 from the higher d6 -- gives you a triangular distribution with the most probable value being zero, but the average is off that. I'll have to work out what it looks like if you have two distinct pairs and then you take a max-min difference.

[Sean Waters]

Re: 2 up, 2 down

 

Any RNG system where the mean is constructed to be zero can be more straightforward to apply, as long as your skill and target-number system is set up to accommodate it. 2d6 minus 2d6 gives you mean zero, variance 11 2/3 (or s.d. 3.42), and extremes of +/- 10.

 

The question is how to adjust the width of the distribution, when you want to do that. Adding pairs of up/down dice concentrates the distribution more (while allowing greater deviation from the mean); the question is how to widen it if you want that.

 

A max(2d6) minus min(2d6) -- that is, roll 2d6, subtract the lower d6 from the higher d6 -- gives you a triangular distribution with the most probable value being zero, but the average is off that. I'll have to work out what it looks like if you have two distinct pairs and then you take a max-min difference.

 

The greater deviation from the mean is not too bad a thing IMO: at present we have a range of 15 values: this puts it up to 21 - it makes unusual results possibly without having to resort to a '3 or 18' critical/fumble rule. OTOH the concentrated distribution theoretically makes the results more predictable: it doesn't really seem to work that predictably in practice

 

I may have explained the second option poorly: the idea is that you roll the red and the green and ONLY bother with the bigger total face value i.e. if you roll RED 3,4 and GREEN 1,5, the result is MINUS 7, if you roll RED 1,3 GREEN 2, 6 the result is PLUS 8. I have no idea how the distribution on this one would look, but I'd be fascinated to know.

[EverKnight]

Re: 2 up, 2 down

 

If I understand your second option correctly it is not possible to get -2, -1, +1 or +2. Is that correct and is it what you intended? In fact the result would lean to extreme values that would seem to ignore that actual OCV and DCV values. Say OCV is larger than DCV by 2, with this method a positive result will hit and a negative result will miss. The difference between the OCV and DCV values are irrelevant unless a zero result is achieved. Compare that to a situation where OCV is lower than DCV by 2, again positive results will hit and negative results will miss. It is only with a zero result that there is a difference in the outcome.

 

If you take the lower of the two dice values then I still think that you will have a similar problem. That is large differences in OCV / DCV would be needed to have an effect on the odds of hitting.

[L. Marcus]

Re: 2 up, 2 down

 

. . . FUDGE just flashed before my eyes . . .

 

I think I like this suggestion, but it will of course add som extra time at dice rolls.

[Cancer]

Re: 2 up, 2 down

 

I may have explained the second option poorly: the idea is that you roll the red and the green and ONLY bother with the bigger total face value i.e. if you roll RED 3' date='4 and GREEN 1,5, the result is MINUS 7, if you roll RED 1,3 GREEN 2, 6 the result is PLUS 8. I have no idea how the distribution on this one would look, but I'd be fascinated to know.[/quote']

 

Assuming that if the red & green totals being the same gives you zero, then you get a symmetric distribution:

total cases = 1296

mean: 0.0

variance = 68.1203703704

sigma = 8.25669261708

-12: 35

-11: 66

-10: 90

-9: 104

-8: 105

-7: 90

-6: 50

-5: 24

-4: 9

-3: 2

0: 146

3: 2

4: 9

5: 24

6: 50

7: 90

8: 105

9: 104

10: 90

11: 66

12: 35

 

Doesn't look like it has that much use.

[Sean Waters]

Re: 2 up, 2 down

 

Thanks to both Cancer and EverKnight for their comments and pointing out that you cant get -2,-1,+1 or +2. Facinating distribution dipper too - very impressed with Cancer - I wouldn't know where to start. I don't think option 2 is a go in the light of this: tends too much towards extreme values, but I might road test option 1 to see how it goes, and bring everything down to zero offsets.

 

In fact this sort of distribution (#2) is almost a coin flip: you'll hit easily or miss badly....

[Bloodstone]

Re: 2 up, 2 down

 

::Looks at 5ER::

 

::Looks at proposed color of dice::

 

::Steals red dice and tosses a set of Black Dice at Sean::

 

There, now the system is perfect, except for the math...

[Mike W]

Re: 2 up, 2 down

 

I think that changing the dice would require you significantly alter other things in the system. Changing the usefulness of DCV changes how often people get hit - which means people have to alter their defenses to reflect that - and then attacks have to change to make sure they can still do decent damage...I think you're creating a domino effect that would result in you creating something that looked about as much like HERO as Fusion did - some vague resemblences but as many differences as similarities.

[schir1964]

Re: 2 up, 2 down

 

This is an intriguing idea Sean. Do mind posting it at GIR so I can tinker with it?

 

- Christopher Mullins

[The Souljourner]

Re: 2 up, 2 down

 

I like the idea of not needing the 11+x and 9+x numbers. I also think your option #1 is very unique and interesting. However, I think there is an easier way to do it. Make DCV a target number - your DCV is equal to 11+Dex/3. To hit, roll 3d6, add your OCV, and that's the DCV you hit.

 

For skills, roll 3d6 and add ability/5. The GM sets a difficulty for the task, where 11 is 60% sucess for joe average, 13 is 60% for a stellar natural athlete, etc.

 

What I like best about these methods is that they make rolling high a good thing, don't require subtraction (which is generally more difficult than addition), and for skills, make it a lot easier for a GM to figure out how to adjust difficulty.

 

-Nate

[mattingly]

Re: 2 up, 2 down

 

If I were to add a fourth die, I'd use it like the old "D&D Cheater" roll-ups. Roll 4 dice, use the 3 you like the best.

 

This would make successes more likely, so that most attacks would land, most activation rolls would succeed, and most skill rolls would be bunny. That migth make for an interesting style of play.

[Sean Waters]

Re: 2 up, 2 down

 

We cheated differently: you arrange the three dice as you want (6s in DnD, 1s in Hero) and wait for the GM to look away, roll three OTHER dice, for sfx, and then exclaim 'WoW!", pointing at the arranged dice and scooping the others out of sight double quick.

 

Now THAT would make an interesting syle of play, especially when it becomes obvious that you have the power to consistently roll maximum damage on 12d6.

[Cancer]

Re: 2 up, 2 down

 

BTW, for modest numbers of dice, cranking out distributions like that is pretty quick and easy. I've done that sort of exhaustive examination of probabilities before.

[Jaxom]

Re: 2 up, 2 down

 

I don't understand the fascination with changing the probability distributions in obscure ways. I've seen systems do it and in general all it does is make players unfamiliar with their odds and often leads to little corners that the developers didn't think of because they were busy thinking up a cool new way to generate a distribution without figuring out what it looked like.

 

Let's face it. Anyone who has played for a while has a feeling for what kinds of numbers 3d6 produces. Same for percentiles. So if you say you need a 5 or less, people know what that means.

 

I don't know why you feel the need to change the dice mechanism but the three reasons I can think of are that 1) you don't like remembering 11 vs 9 and doing the math, 2) you don't like the distribution of 3d6, 3) you just want something new.

 

If you're trying to accomplish option one above, then Nate's suggestion above

However, I think there is an easier way to do it. Make DCV a target number - your DCV is equal to 11+Dex/3. To hit, roll 3d6, add your OCV, and that's the DCV you hit.

 

For skills, roll 3d6 and add ability/5. The GM sets a difficulty for the task, where 11 is 60% sucess for joe average, 13 is 60% for a stellar natural athlete, etc.

is probably an easier way of doing things which would require minimal changes (if any) in the system. Mathematically you could actually use exactly what is in the system right now if you simply chose to write your DCV down as 11-DCV and then told everyone that their target number is "this number plus their OCV". Similarly, the current skill system lets you write down (once, at character creation) the targets for all your skills. The math required to find the difference between your roll and your target to determine how successful you were is no harder than the math to find the difference between two pairs of dice and of course your GM could just apply penalties by lowering your target number ("This is a really hard computer code, subtract three from your programming target number"). You had to write the skills down in the first place, write a target number (with zero modifier of course) next to each one when you do.

 

If you really just want a new distribution then you should start by deciding what kind of distribution you want and then ask what kinds of dice give you those distributions. Since I don't see that kind of logic in any of these posts, I am going to assume that nobody here is worried about the distributions except in the sense that a natural 3 or 18 is hard to get and maybe a flatter distribution would appeal to some. For the simplest flat distribution, roll one die (see the d20 proposals because 1 in 20 is much more common than 1 in 216).

 

Finally, if you are really just looking for a new experience, then I suggest that you read forums on other game systems. Ars Magica is a modified flat distribution which uses a single d10 which can "explode" exponentially. (If you roll a 1 you roll again and multiply by 2. Another 1 is another factor of 2.) There's Riddle of Steel which is pools of d10 with target numbers and counting the number of successes. Shadowrun was similar until 4th Edition (which I have not looked at yet) but which relied on pools of d6s instead. There's the diceless option of the Amber role-playing system. Savage Worlds uses a pair of dice which are linearly open-ended (roll high, roll again and sum) where you take the higher result of the two dice. Serenity is similar but you sum the two dice.

 

People in forums about those systems would be much better able to tell you what kinds of results those dice systems yield and then you could take what you learned from them to yield the kinds of results you are looking for in Hero. In all cases, they are substantially different types of distributions which means that the type of influnce the dice can exert varies. I've played all of them and by far the best distribution in my opinion is the 3d6. Ars Magica leads to the case where a player looks at you and says, "What do you mean my target number for a single d10 is 225?" Shadowrun leads to, "What do you mean I need 5 successes? I only have 4 dice!" Savage Worlds leads to juggling numbers so that your dice just track your target numbers because on a d6 it is impossible to roll a 6 or a 12 since you will automatically pick it up, reroll and add the result. This leads to the counter-intuitive logic that it is more effective to buy a d6 when looking for 8s than it is to buy a d8. (Essentially the same as buying to 13 to get the round for your skill roll ni Hero today but more readily abused.)

[Sean Waters]

Re: 2 up, 2 down

 

I like the idea of working to a zero offset, and 3d6 lacks a rollable midpoint. I think Hero players will have sufficient feel for a 4d6 distribution. One of Heros stated design intentions is the potential for spectacular success and failure - a 4d6 distribution makes this more possible whilst retaining a good level of predictability: like I said at the start I dont expect everyone to nip out and buy an extra d6, but I might give it a road test and I thought some others might be attracted to the idea.

 

Thanks for the other game references.

[prestidigitator]

Re: 2 up, 2 down

 

How about 1d6+1d3-(1d6+1d3)? That even has a standard deviation close to that of 3d6.

[The Souljourner]

Re: 2 up, 2 down

 

Jaxom, we spent a long time talking about d20 vs 3d6 and the consensus seems to be that you can't really change the distribution without drastically changing most of the basic rules of hero.

 

+1 in hero is a much bigger deal than +1 in d20. That's ok, it's built into the system. I think the main problem is the method by which you arrive at your decision of success... 11 + ocv - 3d6 is probably one of the clumsiest processes I've seen.

 

I don't think it's a big deal that there's no midpoint on 3d6. Stastistically, it exists, and the fact that by default you have a ~60% (if I remember correctly) chance to succeed isn't really a problem. Who says it should be 50%? *shrug*

 

-Nate

[Lord Mhoram]

Re: 2 up, 2 down

 

Here's an idea.

 

We have talked about the merits of a d20 system, replacing the 3d6 roll.

 

Or demerits as the case may be. I replace the d20 in my D&D games (and other d20 system games) with 3d6. I love my bell curve.

[Sean Waters]

Re: 2 up, 2 down

 

Indeedy, I prefer a bell curve too, but 4d6 has a similar shaped curve to 3d6, and equally predicatable results. Succeeding on a zero, btw, on 4d6-14, or 2up, 2 down, occurs about 55% of the time, not 50%. d20 has an entirely different distribution - a flat line - which makes it too random for my tastes in a game with fundamental mechanics like Hero. the problem with a 3d6 roll in d20 (I'd have thought) would be that you have a much tighter distribution so the likelyhood of hitting anything with an AC above a certain point becomes almost vanishingly small. Still, it is an interesting idea...

[EverKnight]

Re: 2 up, 2 down

 

Jaxom, we spent a long time talking about d20 vs 3d6 and the consensus seems to be that you can't really change the distribution without drastically changing most of the basic rules of hero.

 

+1 in hero is a much bigger deal than +1 in d20. That's ok, it's built into the system. I think the main problem is the method by which you arrive at your decision of success... 11 + ocv - 3d6 is probably one of the clumsiest processes I've seen.

 

I don't think it's a big deal that there's no midpoint on 3d6. Stastistically, it exists, and the fact that by default you have a ~60% (if I remember correctly) chance to succeed isn't really a problem. Who says it should be 50%? *shrug*

 

-Nate

 

The fact that 3d6 does not have a midpoint means you can have a 50% chance. That would be if the default was 10-, i.e. the lower eight numbers succeed and upper eight numbers fail.

 

Oh, and I too like a bell curve to my dice rolling.

[Jaxom]

Re: 2 up, 2 down

 

Jaxom, we spent a long time talking about d20 vs 3d6 and the consensus seems to be that you can't really change the distribution without drastically changing most of the basic rules of hero.

 

Oh, I agree completely. That's why I asked what Sean's purpose was in putting forth these proposals to change dice usage. I note that most people have responded that they like the bell curve but that the exceptions seem to be people who like to have a better chance of extreme results. That would specifically mean *fewer* dice, not more. Hence the suggestion of 4d6 (in any form) is going in the other direction.

 

The other point that has already been mentioned is that a distribution with a value at the mid-point specifically makes it impossible to have a 50-50 chance of something. But that's a matter of preference and flavor anyway.

[Cancer]

Re: 2 up, 2 down

 

I admit I've explored different dice distributions, both to get a better handle on what would come out of an existing system, and to see if I could find easy-to-build RNG distributions of particular shapes for my own evil purposes.

[prestidigitator]

Re: 2 up, 2 down

 

Indeedy' date=' I prefer a bell curve too, but 4d6 has a similar shaped curve to 3d6, and equally predicatable results. Succeeding on a zero, btw, on 4d6-14, or 2up, 2 down, occurs about 55% of the time, not 50%. d20 has an entirely different distribution - a flat line - which makes it too random for my tastes in a game with fundamental mechanics like Hero. the problem with a 3d6 roll in d20 (I'd have thought) would be that you have a much tighter distribution so the likelyhood of hitting anything with an AC above a certain point becomes almost vanishingly small. Still, it is an interesting idea...[/quote']

If you use 3d6 in D&D you should also divide all bonuses and penalties (including Skill Ranks and Ability Modifiers) by two. Then you actually have the Hero System almost identically, by the way. I noticed this the INSTANT 3rd edition D&D came out.

[PhilFleischmann]

Re: 2 up, 2 down

 

Your method 1, 2d6-2d6 is absolutely identical to 4d6-14. There is no real difference at all. If that's the way you want to go, you don't even need to get dice of two different colors, just subtract 14.

 

The problem IMO, is that the bell curve becomes much higher in the middle.

 

If you want a 0 in a 3d6 curve, you could just roll 3d6 and subtract 11 (or 10 if you prefer). Granted, it isn't *exactly* in the middle of the curve, but that allows for a 50% chance, as has been pointed out already.

 

I still like the idea I suggested on an earlier thread of using 3d12. (Though I still haven't implimented it in my games.) This creates a bell curve with the exact same shape. Then you just change the 11- to 20-. Allows for finer granularity.