Best way to make 4d6 open-ended?

[Sindyr]

I have been working on my game for some time, and the hardest thing for me was to come up with a task resolution system that met many of my design goals.

I believe I have now mostly achieved this.  This is what I have done so far:

Ability score (which may end up being Attribute + Skill) + Roll + Bonuses - Penalities vs a target number of 20.

The target number is always 20.

The average Ability is 10.

The dice mechanic I use is roll 4 special d6, where the "6" side is blacked out.  The "6" side is read as zero, the other faces are read as they are, giving a six-sider with faces worth from 0-5.  4d6 of these generates a total from 0-20, with an average of 10.  (This is functionally equal to 4d6-4)

What I would like to find is a way to achieve numbers above 20 and below 0, to make the dice mechanic open ended,, while at the same time both keeping the bell-curve "smooth" and keeping the way to incorporate the open-endedness "easy"

Any ideas?

[Sindyr]

Possible trigger event for extending the roll...

Color 5's Green, Color 6's (zeroes) Black (or Red)
Having a roll produce an equal number of 5's and 0's triggers another roll of some kind to extend the results.  Equal number = one 5, one 0, one 1-4, one 1-4, OR two 5's and two 0's. 5,0,0,3 would not Trigger and extended roll.

OR having ANY rolls with both 5's and 0's.  In other words, the above AND 5,0,0,3.

OR rolling 3 5's trigger positive extension, rolling 3 0's trigger negative extension?

[Sindyr]

Trigger chances:

trigger = the circumstances that causes another roll to augment the previous ones.


Method = 4d6, rolling a 6 = counts as zero.

Case 1
trigger = rolling at least one 5 and one 6.
probabillity = 23%

Case 2
trigger = rolling only one 5 and one 6, or rolling two 5's and two 6's.
probability = 15%

Case 3
trigger = rolling at least three 5's or three 6's
probability = 3.2%

I think having almost a 1 in 4 chance for an extended roll is not good.  Extended rolls should be rarer than that. So Case 1 is out.

Case 2 isn't bad, 15% is about 2 chances our of 13, or almost 1 in 6.  Plus it has the philosophical component that such a roll is in such balance that perhaps it is a special roll...

Case 3 is ok, but do you guys think that having only 3%, or about 1 in 33 chance for an extended roll is too small?

PS.  Another good things about Case 2 is that it uses "average" rolls as the triggers, meaning that if such rolls do not count for their normal value.  This may be a good thing, as the "hump" of the 4d6 bell curve is a little too fat, and this would thin it out a little.

[Sindyr]

[Replaced by the following]

[Sindyr]

OK, I think I have a workable way - what do you guys think about this?

[*]Take 4 six sided dice.  
[*]Using a black permanent magic marker, color in the "six" face on each die. That face is now read as "zero"
[*]Using a green permanent magic marker, color in the "five" face on each die. That face is still read as "five"
[*]The other faces are read as whatever they are.
[*]When rolled, rolling an equal number of green and black faces is called "Tension".
[*]When "Tension" is present, each pair of green and black faces is called an "Axis"[/list:u]

Thus, if 3,2,0,5 are rolled, since 0 is black and 5 is green, the resulting roll is said to be "Tense".  The single pair of 0 and 5 represent 1 "Axis".

On a roll of 2,5,0,5; the numbers of green 5's and black 0's are NOT equal, and the roll is therefor NOT "Tense", and there are no "Axes".

With a roll of 5,0,0,5; "Tension" IS present (the number of green 5's and black 0's are equal) and there are *two* "Axes" [Axes, pronounced Ack-zeez, is the plural of Axis]

To roll:
[list=1][*] Roll the four dice.
[*] If the dice are NOT Tense, sum the dice for a final total. You're done.
[*] If the dice ARE Tense, remove each Axis and sum the remaining dice, if any.
[*] If the sum is five or greater, this represents a level 1 success. Roll all four dice again.  If this new roll is Tense, increase the level of success by one per Axis rolled, and repeat until a non-Tense roll is achieved.  Sum the dice, and add 5 per level of success.  Some may wish to treat a level 3 success or better as a critical success.  You're done.
Example:

[*]You roll a 4,2,5,0.  The roll is Tense, with 1 Axis. Removing the Axis you have 4,2 remaining, which sum to 6.  Since this is five or greater, you currently have a level 1 success, and must reroll.
 [*]You then roll a 5,2,1,0.  Since this roll is also Tense, you get one increase of success level per Axis.  You rolled 1 Axis in this roll, making you have a level 2 success on this roll currently.  Since you must keep rolling until you get a non-Tense roll, you roll again.
 [*]You roll a 4,5,5,0.  This roll is NOT Tense (and has no Axes), as the number of green 5's and black 0's is NOT equal.  Therefor you do NOT roll again. Summing the dice, you have rolled a 14, with a level two success.  Each level of success is worth 5, which makes your total 24.[/list:u][*] If the sum is 4 or less, this represents a level 1 failure. Roll all four dice again.  If this new roll is Tense, increase the level of success by one per Axis rolled, and repeat until a non-Tense roll is achieved.  Sum the dice, and subtract 5 per level of failure.  Some may wish to treat a level 3 failure or worse as a botch.  You're done.
Example:

[*]You roll a 5,0,0,5. This roll is Tense, with 2 Axes. Removing the Axes, you have no dice remaining, for a Sum of zero.  Since this is four or less, you currently have a level 1 failure, and must reroll.
 [*]You then roll 4,2,0,5.  This is a Tense roll with 1 Axis.  Therefor, 1 Axis means the level of Failure increases by one to a level 2 Failure.  Since this roll is Tense, you must roll again.
 [*]Your next roll is 0,0,5,5!  Not only is this roll Tense, there are *two* Axes, increasing the Failure to a level 4 Failure! You roll again.
 [*]Finally you roll 5,5,5,0.  This roll is NOT Tense.  Summing the dice, you find you have rolled a total of 15, minus 5 points for each level of Failure.  With four such levels, your total roll is a -5.  Also, with that many levels of Failure, something especially catastrophic probably just happened.[/list:u][/list:o]
So, what do you think?

[Brian Leybourne]

Hmm.. the problem is that my eventual result lies entirely on the final roll.

Example:

I roll 4,4,5,0 - axis and one success (+5)
I roll 4,4,5,0 - axis 2 and one success (+10)
I roll 1,0,0,0 - no axis. My total is a measly 1+10 = 11. It doesn't take into acount all the 4's I rolled previously and I ended up with a very mediocre result from a "fantastic"set of rolls.

Do you see what I mean? No, I don't have a solution for you, just pointing out a potential gotya I noticed.

Brian.

[Shreyas Sampat]

Why make the system so complicated?  What I see is this:

"Roll dice.  When you get a Tense roll, reroll those and add 5 to the current result if it's already good, and subtract 5 if it's already bad."

So why not just state it that way?  Maybe you could have the initial roll determine success/failure, and then have the openendedness be a matter of degree or complexity.  What if every time you rolled an Axis, it introduced a new conflict that had to be dealt with?  Let me see if I can come up with an example of this.  

Neo is at work when he finds a weird cell phone.    He runs down the hall, keeping his head down, and ducks into a room.  He rolls 2, 5, 0, 2.  Failure, assuming he has low "getting away from Agents" abilities, and an Axis.  Okay.  Apparently, this room is the next place they're looking, and the only way out is the window.  Crap.  We roll the dice again: 4, 4, 5, 0.  He gets out the window, but what now?  Neo is afraid of heights, and he can't deal with it: 0, 0, 1, 3.  Since he failed his earlier roll, the Agents get him.

So, yeah, that could get a little crazy, with conflicts piling up onto conflicts.  But it could be an interesting way to mechanically fake a crazy constantly changing world.  So, in light of that, what are your mechanics doing?  Why do you need open-ended dice and a bell curve?

[Andrew Martin]

Why do you need open-ended dice and a bell curve?

I agree.
Particularly when there's easier ways to generate curves and have open ended rolls.

[Zoetrope10]

Roll again on any roll of exactly 15, adding the subsequent roll to the original.

Roll again on any roll of exactly 5, deducting the subsequent roll from the original.

I think the likelihood of rolling exactly a 5 or a 15 is 4.32 per cent each so, on average, about one in eleven rolls will be open-ended.

Don't know what this will do to your bell curve (not much I think) but it sure is an easy trigger.

René

[Sindyr]

OK, here's the breakdown of what I am trying to accomplish.

[*]Bell curve. (Because I do not feel that non-bell curved systems represent reality)
[*]Fewer dice is better than more dice. (Cause I thought rolling 20+ dice in White Wolf was silly)
[*]Average roll of 10 (Could be an average roll of 20, and I could readjust my scales, but I want an average roll that is a multiple of ten for elegance's sake)
[*]Open-ended, no limit to how high or how low you can go. (Because there should always be *some* chance that no matter how good or how bad you are, you can still succeed or fail.)
[/list:u]

I have spent years looking at different dice mechanics.  The best I have found so far is 4d6, with 6 = 0.

That does everything except being open-ended. However, the middle part of the bell curve *is* a little fat.

So, I figure by removing pairs of 5's and 0's, we take the chance for the open-ended results from the middle of the curve.  I think this is important because with 4d6, the middle is a little too fat and the ends are a little too narrow.

Redistributing the 5+0 pairs thins out the middle a little (good) and can present an avenue for the extended roll.

NOW, I am all ears if anyone has any suggestions that are better than 4d6, 6=0.

As far as the extension alternates, let me check that out and I will get back to you guys.

[Sindyr]

Brian said:

Hmm.. the problem is that my eventual result lies entirely on the final roll.
Example:
I roll 4,4,5,0 - axis and one success (+5)
I roll 4,4,5,0 - axis 2 and one success (+10)
I roll 1,0,0,0 - no axis. My total is a measly 1+10 = 11. It doesn't take into acount all the 4's I rolled previously and I ended up with a very mediocre result from a "fantastic"set of rolls.
Do you see what I mean? No, I don't have a solution for you, just pointing out a potential gotya I noticed.
Brian.

I see that potential issue.  When you get a "Tense" roll, the actual sum of the I am not *really* worried about it, as the chance of rolling a 1,0,0,0 is pretty darn low.  I would like to see my system in simulation.  I will think further about this.

[Sindyr]

Zoetrope said:

Roll again on any roll of exactly 15, adding the subsequent roll to the original.
Roll again on any roll of exactly 5, deducting the subsequent roll from the original.
I think the likelihood of rolling exactly a 5 or a 15 is 4.32 per cent each so, on average, about one in eleven rolls will be open-ended.
Don't know what this will do to your bell curve (not much I think) but it sure is an easy trigger.

I had 2 reasons to go with the other method:
1) I found it elegant that the sign of extension is have a stress between a highest die and a lowest die. Kinda like that represents an unstable symmetry.
2) Like I have said before, the bell curve of 4d6 is a little chunky in the middle, a little sparse at the ends.  Therefore, it seemed a good idea to use up some of the "middle" dice to add to the "ends"

[Mike Holmes]

Hmmm. Years, huh? And you missed the plus/minus dice method?

This would probably work better with less dice, but assuiming you want to keep the same bell, do this.

First, change the TN to 10.

Then roll two green dice, and two red dice (or whatever colors float your boat, one positive and one negative). Subtract the positive dice from the negative dice. If any come up six, check the opposite color. Opposing sixes cancel. Unopposed sixes are re-rolled.

I think that covers it. And you don't need special dice. Half of rolls or so will have matches making calculation very quick.

Mike

[Sindyr]

Didn't miss it. :)

I didn't use it because the overwhelming response from my playtesters is that they wanted to avoid subtraction whenever possible.

OTOH, I just tried it, and it seems easy enough.

Out of curiosity, given your dicing method, how do you make it open-ended?

PS.  This bell curve is exactly the same as the 4d6 bell curve of course(a little too fat/tall in the middle, a little too short/narrow on the ends), so preferable we would be borrowing "interior" results to create the extended results.  See above posts for references.

[Mike Holmes]

The open-endedness is via the re-rolls I mentioned of unmatched exploding dice; I used the sixes in my example. You could use 1's instead of sixes for the flatter curve you're looking for (counting them as 6's plus the reroll).

Anyhow, as far as ease, well, this is actually used in such "fast-paced" games as Feng Shui although with only two dice. Like I said, with the dice cancelling each other, and the resulting numbers being so small, there's actually about the same amount of math steps. i.e. you rarely have to add or subtract a double digit number (and when you do it's worth it, because the result is very cool).

And anyway, with a 4d6 system that's open-ended low, you're going to have to allow for subtraction anyhow.

Mike