The Un-Twenty System

[Hytheter]

There's no remaining 1. 1 and 6 cancel to give 5 leaving 5 and 6 which total to 11. Have to assume you meant 6 1 1 in which case on a re-read you're right.

Oh yes I did mean that, whoopsie.

Updated AnyDice

Yeah that looks pretty much exactly like the graph I made earlier, so we're definitely on the same page. And it's an ugly page. It probably should be removed from the book.

I followed the site back to the guy's twitter. When he posts a link to un-twenty there he says "free of charge!" as though it's something worth paying for...

[Knaight]

So... when you roll three 1s, the entire party dies in your epic failure and it unintentionally ends up being the conditions to summon Orcus, while if you roll three 6s, you kill the BBEG in one shot (doesn't matter where he is, your attack defies the laws of space and interdimensional travel) and impress an angel so much she becomes your girlfriend?

Actually, I don't think those are the absolute best or worst things possible...

Presumably, it's supposed to be in the context of what's being done. That's the sad part about this - the idea of dice imparting an effect beyond the raw total is cool, it's just the single worst implementation I've ever seen. You've got a sufficiently rare extreme failure and success, you've got a mechanic that was used for auto success and failure that would work well for complications and benefits, an then there's just all that other crap on top of it.

[Ravens_cry]

The Ghost die in ye olde Ghostbusters RPG (I bought a copy at a second hand store) did that. If the ghost symbol came up when the baddies rolled, it meant something extra good for the baddies, while if it came up when the players rolled, it meant something bad for the players above and beyond what was rolled on the die. It was a very rules light system, the character sheets fit on an index card with room for a small head shot, so on the fly ruling were a big part of the game anyway.

[Knaight]

The Ghost die in ye olde Ghostbusters RPG (I bought a copy at a second hand store) did that. If the ghost symbol came up when the baddies rolled, it meant something extra good for the baddies, while if it came up when the players rolled, it meant something bad for the players above and beyond what was rolled on the die. It was a very rules light system, the character sheets fit on an index card with room for a small head shot, so on the fly ruling were a big part of the game anyway.

There are a lot of systems that use something similar, which range from pretty rules light to pretty rules heavy (e.g. Shadowrun). In short, there are a lot of working, well designed implementations that the Un-Twenty designer could have used as inspiration, and clearly didn't.

[Solaris]

Wasn't there a mechanic in one of the 3.5 DM books that proposed a similar mechanic?

Yes, although I'm given to understand that it's less of an abomination than this and actually evens out the bell curve.
I like swingy - but this is unnecessarily convoluted, complex, ill-defined, and outright stupid.

[Segev]

I'm with the people asking what problem this is trying to solve.

If it's just that he likes the bell curve, I again recommend 3d6 + 2d(+/-). For clarity, that's 3 normal 3d6, summed, and 2 dice which have an even chance of being a +1 or a -1. Called "fudge dice," these can result, together, in a sum of -2, -1, 0, 1, or 2, and thus can allow any value, when added to the 3d6, between 1 and 20 (just like a d20).

However, the probability curve looks like this.

[Feddlefew]

I'm with the people asking what problem this is trying to solve.

If it's just that he likes the bell curve, I again recommend 3d6 + 2d(+/-). For clarity, that's 3 normal 3d6, summed, and 2 dice which have an even chance of being a +1 or a -1. Called "fudge dice," these can result, together, in a sum of -2, -1, 0, 1, or 2, and thus can allow any value, when added to the 3d6, between 1 and 20 (just like a d20).

However, the probability curve looks like this.

So two coin flips and 3d6?

[goto124]

So two coin flips and 3d6?

The coin lands on its edge!

[Segev]

So two coin flips and 3d6?

That'd one way to do it. I'd recommend two dice of your choice, roll even for +1 and odd for -1, instead, as flipping coins while rolling dice is a bit clunky. Literally; the coins would make clunkish ringing noises that would get tiresome, I expect.

There also exist actual "fudge dice," which are cubes with "+" on three sides and "-" on the other 3.

But as long as you have a typical gamer's set of dice, 3d6 plus 2d(anything else), using evens/odds for +/- 1 on the non-d6s, should be easy enough. Certainly easy enough for any group willing to use the system proposed at the start of this thread.

[Broken Twin]

Huh, I never considered using FUDGE dice to bump the 3d6 range back into 1-20. Now I really do need to pick some up.

As an aside, has anyone considered/actually used d8+d12 for their 1-20 roll? It's a very flat bell curve, which could be either a good thing or not, depending on what you're looking for. Looks like it would work well as a middle ground between the randomness of d20 and the consistent curve of 3d6.

[Segev]

As an aside, has anyone considered/actually used d8+d12 for their 1-20 roll? It's a very flat bell curve, which could be either a good thing or not, depending on what you're looking for. Looks like it would work well as a middle ground between the randomness of d20 and the consistent curve of 3d6.

It retains the problem that it's only 2-20. You could adjust that with a Fudge die, and just treat + as "+0" while - is still "-1," though. (They're really useful for, ahem, fudging one combination of dice's range.)

Even with the ranges restored to 1-20, however, you have to be careful in analyzing the DCs. d20 really is designed with probability-to-succeed being based on the flat "curve" of a single die. Bonuses and penalties mean increasingly more the further apart they push values with a bell curve. (They only mean a non-linear difference with a d20 if they push the difference over 20, at which point they push it from linear to "impossible.")

On the other hand, the more bell-like your curve, the closer to the statistical mode is the choice to "take 10." It's a little under average (10.5 on a d20), but the standard deviation on a flat curve is such that the mode is actually not really a valid thing to examine.

Put the bell curve in place for, say, the 3d6+2d(+/-), though, and your mode becomes either 10 or 11. Which is right there around the average, and which means "taking 10" is going to generate one of the two most likely solutions.

d8+d20 will have 9-13 as the shared mode. Taking 10 is thus still closer to the mode than it is in a d20, but the variance is flat around it, even so. (Technically, the average of the modes is 11 on d8+d12, because of the loss of 1 from the range.)

So, do you like having a flat range in your probability? Do you want it smaller than the whole of the range, with the ends tapering off? If so, d8+d12 will be pretty good for you. But it is an interesting question: why do you want a flat portion of it with tapering edges, rather than a bell curve or just a flat probability?

[Firest Kathon]

I'm with the people asking what problem this is trying to solve.

If it's just that he likes the bell curve, I again recommend 3d6 + 2d(+/-). For clarity, that's 3 normal 3d6, summed, and 2 dice which have an even chance of being a +1 or a -1. Called "fudge dice," these can result, together, in a sum of -2, -1, 0, 1, or 2, and thus can allow any value, when added to the 3d6, between 1 and 20 (just like a d20).

However, the probability curve looks like this.

Fudge dice, at least the ones I own, have two sides blank, two sides with -, and two sides with +. So while the possible results are the same, the distribution looks slightly different. In this system, it makes 1 and 20 even less likely (0.05% each).

Corrected Anydice

[Segev]

Fudge dice, at least the ones I own, have two sides blank, two sides with -, and two sides with +. So while the possible results are the same, the distribution looks slightly different. In this system, it makes 1 and 20 even less likely (0.05% each).

Corrected Anydice

Ah, my mistake. I don't own any, myself.

I would recommend using modified ones that lack the blanks, then, to avoid pushing the 1 and 20 even rarer, though it's not required.

[Feddlefew]

Ah, my mistake. I don't own any, myself.

I would recommend using modified ones that lack the blanks, then, to avoid pushing the 1 and 20 even rarer, though it's not required.

To get a +/- 1 on a pair of fudge dice, there has to be a 0 side. Otherwise the only combinations are +2, 0, and -2.

Edit: You could use a regular d6, with 1 and 2 being -, 3 and 4 being 0, and 5 and 6 being +.

[Segev]

To get a +/- 1 on a pair of fudge dice, there has to be a 0 side. Otherwise the only combinations are +2, 0, and -2.

Edit: You could use a regular d6, with 1 and 2 being -, 3 and 4 being 0, and 5 and 6 being +.

Hm, true. Still works for 1-20 with a bell curve. The question really is just how rare you want the 1 and the 20. With true fudge dice, they're half as likely as with the variant I initially proposed. The variant I initially proposed flattens the whole curve just a little, most notably at the tails.

So again, it's a matter of just how rare you want the outliers to be.

[Altair_the_Vexed]

It is overly convoluted.
It adds complexity without clarity.
Its effects are not clearly understood.
It is intended to solve a problem that is not well defined.

Gygax would have loved it.

I'm putting that in my sig.

[ewoods]

What would be the purpose of a more bell-shaped distribution though? If the designer just wants more rolls closer to 10, why not simply modify the existing take-10 mechanic? Houserule that you can take 10 on any d20 check but if you want something higher than that, you have to actually roll and risk getting something lower as well.

[AstralFire]

What would be the purpose of a more bell-shaped distribution though?

To get more consistent results without perfectly consistent results? Seems kind of self-evident to me. My problem is that of the systems that use d20 inherently, it tends to break them (especially 4E and 5E D&D. 3E's already broken in other ways so you don't notice it so much.)

[ewoods]

To get more consistent results without perfectly consistent results?

Why is that something that's needed though? Is there something wrong with having an equal chance to get any number on any given d20 roll? Maybe it's just something I've never put a lot of thought into.

[AstralFire]

Why is that something that's needed though? Is there something wrong with having an equal chance to get any number on any given d20 roll? Maybe it's just something I've never put a lot of thought into.

Jump results generally have a 1:1 relationship between the total result and feet jumped. This means that a veteran jumper with a +5 on his roll can -- on luck of the draw -- have an equal chance of jumping 6 feet or 25 feet. This is an extremely large variance to have occur on a regular basis.

2E, 5E and 4E don't need bell curve rolls as much for various reasons, but 3E ends up with some really ridiculous results for some things you can use a d20 for.

[ewoods]

I guess that just makes sense to me though. I've never thought of the dice rolls as being part of the character's skill. If you have 5 ranks in jump, your skill in jumping is 5. It's not 5 plus whatever you roll on the die. The die roll represents all of the variables that go into that jump beyond the character's skill. It's the consistency of the ground, the way he planted his feet, wind speed and direction, adrenaline, concentration, etc. If he manages to jump 25 feet it's not because he's really good at jumping, it's because he got exceptionally lucky, and he shouldn't expect to get that lucky every single time. He should expect that he can jump at least 6 feet under the worst of circumstances (which is 5 feet further than a character who has no ranks in jump), and over 100 jumps he'll probably jump an average of 15 feet. As a DM, I believe it's my job to take out-of-game information, such as dice rolls to jumping, and translate it into in-game information. So if he happens to roll a 1 this time and only make it six feet, you don't just say, "Ok, you only jump six feet." You say, "At the moment when you're about to jump, the ground beneath your feet gives way slightly and you awkwardly hurdle sideways through the air, flailing your arms as you manage to land a mere six feet away." A character with no ranks to jump who rolls a 1 just falls flat on his face or merely trips and stumbles forward.

[Broken Twin]

It retains the problem that it's only 2-20. You could adjust that with a Fudge die, and just treat + as "+0" while - is still "-1," though. (They're really useful for, ahem, fudging one combination of dice's range.)

Even with the ranges restored to 1-20, however, you have to be careful in analyzing the DCs. d20 really is designed with probability-to-succeed being based on the flat "curve" of a single die. Bonuses and penalties mean increasingly more the further apart they push values with a bell curve. (They only mean a non-linear difference with a d20 if they push the difference over 20, at which point they push it from linear to "impossible.")

On the other hand, the more bell-like your curve, the closer to the statistical mode is the choice to "take 10." It's a little under average (10.5 on a d20), but the standard deviation on a flat curve is such that the mode is actually not really a valid thing to examine.

Put the bell curve in place for, say, the 3d6+2d(+/-), though, and your mode becomes either 10 or 11. Which is right there around the average, and which means "taking 10" is going to generate one of the two most likely solutions.

d8+d20 will have 9-13 as the shared mode. Taking 10 is thus still closer to the mode than it is in a d20, but the variance is flat around it, even so. (Technically, the average of the modes is 11 on d8+d12, because of the loss of 1 from the range.)

So, do you like having a flat range in your probability? Do you want it smaller than the whole of the range, with the ends tapering off? If so, d8+d12 will be pretty good for you. But it is an interesting question: why do you want a flat portion of it with tapering edges, rather than a bell curve or just a flat probability?

I like it because, while it may not be a bell curve in the strictest sense, it's the flattest 'curve' you can get while staying simple enough for the players. I like the normalization of results that a bell curve offers, but I also like the chances for extraordinary results that a linear system offers. A compromise between the complete randomness of d20 and the relative predictability of 3d6 is nice for me. I like that its average is slightly higher than taking ten, as it means that you're taking a risk by rolling for an on-average slightly better result. And its shallower "curve" screws with the math of d20 systems less. I tried switching to 3d6 in 3.5, but the shear amount of rebalancing that would need to be done to account for the change in probabilities made it completely not worth it. With a more balanced system (5E) that has less number inflation, plus a shallower curve, I think I could get away with little if any rules modification.

Plus, when it comes down to it, my players would much rather roll two dice then three/five.

Edit: Although, now that I think about it, 5E handles things fairly well with the Adv/Dis mechanic, so I'm not sure I'd really even want to introduce it into the game. Mostly because I tend to cap out my players' willingness to roll dice for one thing to three.

[AstralFire]

I guess that just makes sense to me though. I've never thought of the dice rolls as being part of the character's skill. If you have 5 ranks in jump, your skill in jumping is 5. It's not 5 plus whatever you roll on the die. The die roll represents all of the variables that go into that jump beyond the character's skill. It's the consistency of the ground, the way he planted his feet, wind speed and direction, adrenaline, concentration, etc. If he manages to jump 25 feet it's not because he's really good at jumping, it's because he got exceptionally lucky, and he shouldn't expect to get that lucky every single time. He should expect that he can jump at least 6 feet under the worst of circumstances (which is 5 feet further than a character who has no ranks in jump), and over 100 jumps he'll probably jump an average of 15 feet. As a DM, I believe it's my job to take out-of-game information, such as dice rolls to jumping, and translate it into in-game information. So if he happens to roll a 1 this time and only make it six feet, you don't just say, "Ok, you only jump six feet." You say, "At the moment when you're about to jump, the ground beneath your feet gives way slightly and you awkwardly hurdle sideways through the air, flailing your arms as you manage to land a mere six feet away." A character with no ranks to jump who rolls a 1 just falls flat on his face or merely trips and stumbles forward.

And that's a fine approach -- though I'd say you're adjusting the rules yourself, there, because another skill should be invoked to handle slippery terrain. For me, however, I found that sort of thing frequently awkward in 3E D&D when it occurred on a regular basis. The ground can only shift under you so many times before some people get frustrated with their character being confounded by odd luck and consistent wide variance. I generally found it easiest to replace skill rolls with a bell curve; it made the natural 3s and natural 18s much more meaningful.

I don't do it in 5E because of the dis/advantage mechanic, though, which works well enough to represent situations which should have a tighter box of results.

[Jay R]

It's worth noting that if you replace a combat roll in D&D 3E or 3.5E with a more bell-shaped curve, you reduce the chance for critical hits tremendously, and greatly reduce the value of magic items that have powerful critical hits.

[Segev]

I actually do like the RP approach to explaining the results of a die roll being poor as external factors getting in your way. It doesn't always work, but it's a nice way to make it less "ha ha your character is a joke at what he's supposed to be skilled at" than things can otherwise go.

As for flat vs curved probabilities, it is largely a matter of taste, overall. But d20 is designed for a flat curve, so it's something to keep in mind. For instace, a "20" on a d20 happens 5% of the time. That translates to a roll of ~17+ on the 3d6+2dFudge method. A "19-20" would translate to a 16+. It would be difficult to GET the same probability as an 18-20, because 15+ actually jumps to the same odds as 17-20.

So there are oddities to look out for.

...actually, while it wouldn't be exact, I just ran some test numbers. If you roll 3d6, the odds of two of them matching and coming up "6" are 5.55(repeating)%. This is pretty close to the 5% odds of a "nat 20" on a d20. Turns out that the chance of matched 5s or matched 6s is 11.11(repeating)%. That's a little higher than the 10% chance of a "nat 19 or 20." Even "matched 4s, 5s, or 6s" translates to a 16.66666% chance. Again, 1.6(repeating) higher than the 15% that an 18-20 on a d20 would represent.

Also a 22.22(repeating)% chance of matched 3s, 4s, 5s, or 6s (matching nicely to the 20% chance of a 17-20). We're even staying marginally close at 27.77(repeating)% chance that matched dice of at least value 2 will appear (compared to 25% chance that a 16-20 will show up).

If all we require is two matched values on 3d6, that's a 1/3 (33.33(repeating)%) chance. We're definitely higher, now, than the 30% chance of a 15-20 on a d20, but honestly, how many crit ranges get that big?



All of this to say: You can use the 3d6+2dFudge approach and keep the value of weapons which do cool things on critical hits roughly the same (maybe even a little increased) by having, instead of "nat 20," the critical threat check be "did you get matched 6s?"

If your crit threat range increases, then you add more allowed values for the match.

If your threat is on a nat 20, then the new threat is on 2 matched 6s.
If your threat is on a 19-20, then the new threat is on 2 matched 5s OR 6s.
If your threat is on an 18-20, then the new threat is on 2 matched 4s, 5s, or 6s.
If your threat is on a 17-20, then the new threat is on 2 matched 3s (or higher).
If your threat is on a 16-20, then the new threat is on 2 matched 2s (or higher).
If your threat is on a 15-20, then the new threat is on any matched pair.

No extra rolling beyond what you were already doing, slightly (roughly 2%) higher chances of crit threats. Plays with fun qualities people tend to like looking for in dice anyway.

[AstralFire]

It's worth noting that if you replace a combat roll in D&D 3E or 3.5E with a more bell-shaped curve, you reduce the chance for critical hits tremendously, and greatly reduce the value of magic items that have powerful critical hits.

The UA rule that discusses 3d6 die includes equivalents for the new threat ranges, though I personally find them a bit messy. It would probably better to up the power of a critical hit a bit and just allow crit stacking to be geometrically better rather than linearly, in terms of speed of play. Crits are generally weak in 3.x past the lowest levels anyway.

[Segev]

The UA rule that discusses 3d6 die includes equivalents for the new threat ranges, though I personally find them a bit messy. It would probably better to up the power of a critical hit a bit and just allow crit stacking to be geometrically better rather than linearly, in terms of speed of play. Crits are generally weak in 3.x past the lowest levels anyway.

You don't want to stack them faster; that only makes those who take the threat-range increases even more egregious. Matching dice actually turns out to be rather close to the same probabilities, though.

[AstralFire]

You don't want to stack them faster; that only makes those who take the threat-range increases even more egregious. Matching dice actually turns out to be rather close to the same probabilities, though.

Was my point. Crits kind of suck in 3.x, generally speaking. I could easily imagine an overhaul for TWF that was based around bell curve rolls and crit stacking.

...

How much does it say about me that my first inclination when involving any 3.x houserules is that it's acceptable that you'll have to houserule seven other things to get the first one working?

[Segev]

How much does it say about me that my first inclination when involving any 3.x houserules is that it's acceptable that you'll have to houserule seven other things to get the first one working?

I think it says you've experience with the law of unintended consequences and how ANY system will tend to have enough interlocked moving parts that you'll need to watch for at least the biggest side-effects of any given change.

[The Grue]

The coin lands on its edge!

I can't find a suitable screen capture so just imagine I posted Kain's terrifying smile here.