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May 11, 2016 9:25 PM   Subscribe

Perhaps you've heard of the recent release of the 120-sided die, which is certainly impressive in its way but not really that… weird. If you're really looking to stand out, why not order yourself some 34-sided dice?
posted by DoctorFedora (57 comments total) 14 users marked this as a favorite
 
On the opposite end, a 1-sided dice. Every roll is 1.
posted by T.D. Strange at 9:44 PM on May 11, 2016 [15 favorites]


FELT INCLUDED!
posted by clavdivs at 10:01 PM on May 11, 2016


Three 34-sided dice minus 2 (3d34-2), added together, produce numbers from 1 – 100 on a bell curve distribution, which is extremely helpful when producing percentile stats or determining percentile successes.

So something with a 2% chance of happening would happen one time out of every ten thousand?
posted by justkevin at 10:06 PM on May 11, 2016 [4 favorites]


He's using the 3d34-2 to set the numbers to roll regular d% against.
posted by LogicalDash at 10:09 PM on May 11, 2016 [1 favorite]


Nothing to do with rule 34, then.
posted by sebastienbailard at 10:09 PM on May 11, 2016


Not without a proper flange, no.
posted by notyou at 10:16 PM on May 11, 2016 [16 favorites]


I like the comment from Noah Easterly: for a normal distribution of 0-100, you don't need 3d34-2, you just need d4+d6+d8+4d10+d12+2d20-10.

Something tells me that a DM should never allow Noah Easterly as a player.
posted by zompist at 10:33 PM on May 11, 2016 [9 favorites]


That trick with the 3d34-2 to get a bell curve is kind of like how you can approximate a Gaussian blur with 3 box filters.
posted by L.P. Hatecraft at 10:49 PM on May 11, 2016 [4 favorites]


zompist: "d4+d6+d8+4d10+d12+2d20-10"

If you roll all ones you get a zero, not a normal result for dice based games.
posted by Mitheral at 10:50 PM on May 11, 2016 [3 favorites]


If you're interested in dice, particularly stories about loaded dice, I highly recommend reading magician Ricky Jay's Dice: Deception, Fate, and Rotten Luck, which is filled with Rosamond Purcell's wonderful photographs of old celluloid dice in the process of inexorable decay. There's beauty in watching a source of entropy succumb to the very thing it makes.
posted by a lungful of dragon at 10:52 PM on May 11, 2016 [5 favorites]


Agreeing with justkevin's (implied) criticism: if you want to deal with a normal distribution, why misleadingly label it as "percentiles"? Someone has a 2% chance of being in the bottom 2% of a population. You don't need to correct it to make it smaller; 2% is small but not so small the odds of hitting it less than 2%.

In these head scratching moments I worry that someone had a subtle insight I've missed, but the conversation in the comments about just averaging 3d100 not accomplishing the same thing makes me think this is not the case here.
posted by mark k at 11:00 PM on May 11, 2016 [2 favorites]


if you want to deal with a normal distribution, why misleadingly label it as "percentiles"?

Because that's what the D&D manuals call numbers in the range 1-100. Asking "GamerJargon dot net" to have more precision than that is like demanding Linnaean nomenclature for owlbears.
posted by RogerB at 11:22 PM on May 11, 2016 [5 favorites]


If you roll all ones you get a zero, not a normal result for dice based games.

Yeah, but since that should only happen once out of 9,216,000,000 throws on average, maybe just worry about it when it comes up?

Then again, I've seen the luck my fellow gamers have had with their dice. It'd probably happen with disturbing regularity.
posted by radwolf76 at 11:26 PM on May 11, 2016 [1 favorite]


Yeah, but how does it roll with Dorito dust hands, pinballing through six empty Jolt cans? I demand a real world test.
posted by jimmythefish at 11:27 PM on May 11, 2016 [1 favorite]


Because that's what the D&D manuals call numbers in the range 1-100. Asking "GamerJargon dot net" to have more precision than that is like demanding Linnaean nomenclature for owlbears.

Missing the core of my confusion. I don't see any reason to use the range 1 to 100 unless you are thinking in terms of percentiles. If you just want a normal distribution 3d6 or 4d8 or whatever works just fine. Using 3d34 - 2 for "success rolls" to see if you exceed a "percentile" difficulty ranking seems designed to confuse everyone's intuition and for zero benefit.
posted by mark k at 11:46 PM on May 11, 2016 [3 favorites]


I used to keep a marble in my dice bag and call it a one-sided die. Sure was inconvenient to roll though. I had to aim it at a pile of dice to make sure it stopped.
posted by CrunchyFrog at 11:49 PM on May 11, 2016 [2 favorites]


To waste yet more time on my unnecessary and useless point, the author is clearly thinking in terms of percentages and not just using gaming jargon. From his own statement in the reddit thread he links to:

You get to simulate real-world statistics (offering 1-100 percentage chances of events occurring), but with a more realistic bell curve.

This is misunderstanding percentages, or probabilities, or realism, or bell curves, or some other concept that led him to say what he just said there.
posted by mark k at 11:59 PM on May 11, 2016 [10 favorites]


Serious question: has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere.
posted by the quidnunc kid at 12:29 AM on May 12, 2016 [4 favorites]


How would an object have less than one surface? You're steering this conversation into territory where topologists daren't tread.
posted by DoctorFedora at 12:31 AM on May 12, 2016 [5 favorites]


his is misunderstanding percentages, or probabilities, or realism, or bell curves, or some other concept that led him to say what he just said there.

Yes, it does seem so.

You have a 75% chance of rolling 75 or under on a d100, because every possible number in the range has an equal probability of occurring. But if the 1-100 numbers are evenly distributed along the x-axis of a bell-curve, you might end up with something like a 90% chance of rolling 75 or under.

There's really no need for special dice to simulate bell-curve effects in RPGs, though. If you want 90% of your players to end up with outcome A, equivalent to 1-75 on the curve in the above scenario, just set the bar at 90+ on a d100.
posted by rory at 1:23 AM on May 12, 2016 [2 favorites]


How would an object have less than one surface?

Fractal dimension
posted by biogeo at 2:12 AM on May 12, 2016 [1 favorite]


By extension of your argument, a Menger sponge-shaped die would function as a d2.726833.
posted by sebastienbailard at 2:27 AM on May 12, 2016 [6 favorites]


Depends on whether it has a suitable Menger sponge-shaped surface to roll against, I guess?
posted by biogeo at 2:33 AM on May 12, 2016 [3 favorites]


if you want to deal with a normal distribution, why misleadingly label it as "percentiles"?

If an owlbear is an owl combined with a bear, why is a bugbear not a bug combined with a bear*? In conclusion, D&D is a land of contrasts.

(*it's like a giant goblin)

Serious question: has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere.

You're looking for Woolingworth's Impossible Dice (level 18 Conjuration spell).
posted by EndsOfInvention at 3:09 AM on May 12, 2016 [3 favorites]


Serious question: has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere.
posted by the quidnunc kid


Taking into account the tendency for rules-lawyering in tabletop fantasy games that allow such things as plane shifting and grappling rules, there's NO DOUBT WHATSOEVER that someone spent a lot of time considering fractional movement (physical/temporal), as suspension of disbelief can only account for _% of certain motions per turn being considered free actions.

How would an object have less than one surface? You're steering this conversation into territory where topologists daren't tread.
posted by DoctorFedora


It wouldn't, unless phasing was taken into account. See above.
posted by Smart Dalek at 3:11 AM on May 12, 2016 [1 favorite]


Serious question: has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere.

We tend to save the non Euclidean dice for more advanced games of Call of Cthulhu.
posted by robocop is bleeding at 3:34 AM on May 12, 2016 [10 favorites]


I guess fractional dice would just be a pair of them, one for the denominator? We're already counting d% as "a die" so...

But if you really need some specific probability it's probably better to use cards. There are roleplaying games that do.
posted by LogicalDash at 3:35 AM on May 12, 2016 [2 favorites]


Nice Rush reference in the title, btw.
posted by svenx at 4:07 AM on May 12, 2016 [4 favorites]


By the way, if you like weird sided dice, the company that makes the d120 also sells d3, d5, d9, d11, d14, d16, d18, d22, d30, and d60.
posted by MythMaker at 5:05 AM on May 12, 2016


I have a set of decimal dice with thousands, hundreds, tens, ones, and tenths. The tenths die doesn't get a lot of use (but it's handy for worrying people by making them wonder what the heck my Magic deck is going to do such that I'd need one.)
posted by NMcCoy at 5:07 AM on May 12, 2016 [1 favorite]


I always keep a few unusual dice around in case I have to cast Death Muffins.
posted by delfin at 5:09 AM on May 12, 2016 [2 favorites]


Nine d12s gives the same result while still using Platonic solids. Personally, I think 0% and 100% are both necessary possibilities. Is anyone making d26s? If not, you could always roll 20 * d6s and subtract 20.
posted by Joe in Australia at 5:38 AM on May 12, 2016 [2 favorites]


Asking "GamerJargon dot net" to have more precision than that is like demanding Linnaean nomenclature for owlbears.

Linnaean nomenclature handles this well actually. They would call them xOwlbears.
posted by srboisvert at 5:59 AM on May 12, 2016


If an owlbear is an owl combined with a bear, why is a bugbear not a bug combined with a bear*? In conclusion, D&D is a land of contrasts.

(*it's like a giant goblin)


Because an owlbear is something Gygax made up based on a toy (and how he got "owlbear" out of looking at that toy is a mystery to me), while a bugbear is a mythological creature that is a hobgoblin in the shape of a bear.
posted by Caduceus at 6:03 AM on May 12, 2016 [2 favorites]


Because an owlbear is something Gygax made up based on a toy (and how he got "owlbear" out of looking at that toy is a mystery to me)

A really, really, REALLY bad roll on the Random Harlot Table.
posted by delfin at 6:13 AM on May 12, 2016 [1 favorite]


Does anyone make casino-grade polyhedral dice (machined from plastic rather than molded)? The only machined ones I've found are metal and therefore hella expensive.
posted by middleclasstool at 6:21 AM on May 12, 2016


Three 34-sided dice minus 2 (3d34-2), added together, produce numbers from 1 – 100 on a bell curve distribution

They most certainly do not.
posted by escabeche at 6:51 AM on May 12, 2016


How would an object have less than one surface? You're steering this conversation into territory where topologists daren't tread.

Introducing the new d0!

I am see this being useful in some circumstances -- that time in a Call of Cthulhu game when one guy decided to take on a shoggoth by charging at it with a .38 revolver.
posted by ricochet biscuit at 7:09 AM on May 12, 2016 [2 favorites]


Great Gravity Falls link, dolfin!

I had no idea that the "34-sided die" from Gravity Falls' Dungeons, Dungeons, and More Dungeons was a real gaming reference. I need to turn in my Nerd Card. :(

looks it up

Oh, Gravity Falls had a "38 sided die" (represented in the cartoon as a d20), it wasn't a reference to this 34 sided die. Whew.

And the fact that I have a already ordered my 120 sided die from the Dice Lab probably protects my nerd card a while longer.
posted by edheil at 7:09 AM on May 12, 2016


a Menger sponge-shaped die would function as a d2.726833.
Nope. The Menger sponge has a dimension of 2.726833, sure, but an icosahedron has a dimension of 3 and it's still a d20.

Functionally a Menger sponge is a d6, since on a flat surface it has 6 stable orientations modulo rotational symmetry around z. Geometrically it's either got an infinite number of sides or zero sides, depending on your definitions.

Either way, not what we're looking for. So how do we actually get a fractional die roll?

A dN die can be thought of as a provider of discrete communications of log_2(N) bits of information each. So if you wanted the output of a d1.5, for example, you could start with a d2 (i.e. a coin flip), but reduce the information quantity further by using an unfair coin. A coin that always landed heads would convey 0 bits of information from each flip, in the extreme case.

If we want 1.5 bits of information, then we could use a coin (okay, realistically a computer random number generator) whose probability p of landing heads satisfies

p*log_2(1/p) + (1-p)*log_2(1/(1-p)) = log_2(1.5)

i.e. p needs to be either about 86% or about 14%.

But what about a d0.5? For that case, we need to provide log_2(0.5) bits of information, i.e. -1 bits, with each roll.

So what we're looking for is a die that erases a tiny bit of information from your brain every time you roll it. That actually sounds more Lovecraftian than a die with half a side, not less...
posted by roystgnr at 7:32 AM on May 12, 2016 [12 favorites]


Lady Luck is golden;
She favors the bold. That's cold.
Stop throwing stones --
The night has a thousand saxophones.
So get out there and rock,
And roll the bones.
Get busy!
posted by prepmonkey at 7:57 AM on May 12, 2016


demanding Linnaean nomenclature for owlbears.

Stirgursium Gygaxii. I thought everyone knew that?
posted by cirrostratus at 8:29 AM on May 12, 2016 [3 favorites]


rory: "There's really no need for special dice to simulate bell-curve effects in RPGs, though. If you want 90% of your players to end up with outcome A, equivalent to 1-75 on the curve in the above scenario, just set the bar at 90+ on a d100."

A conventional d100 roll gives you a result from 1-100 with equal probabilities of each result. While we refer to this as a percentile roll we often use it as a selector for comparison to a table with 100 entries.

A "problem" though is each of those results is equally likely. But maybe you don't want them to be equally likely. By combining two or more dice you can make the entries near 50 more likely than the entries near 1 or 100. Personally I'd love to rework the 13th Age Chaos Mage High Weirdness table to be more bell curvy. This could make play a little more consistent and make the really weird things a bit more special.

However the problem with a scheme like d4+d6+d8+4d10+d12+2d20-10 to get the curve is the curve has a really tall and narrow bell compared with 3d34-2. IE: results near 50 are much, much more likely to happen than the result near 1/100. Or as radwolf76 calculated there is only a 1 in 9,216,000,000 of getting a minimum result compared to the 1 in 8000 chance when rolling three dice.

13th Age players are well aware of the effects of rolling large numbers of dice then summing them together. So much so that at high levels where you might be rolling 8, 9, or 19 dice for damage the rules suggest don't bother rolling instead just take the average for the roll.

Now sure a person could just make tables with 60 entries instead of 100; players probably wouldn't notice. But for long time players the idea of a selector chart having 100/1000/10000 entries is really ingrained. A 60 entry table feels wrong.
posted by Mitheral at 9:03 AM on May 12, 2016 [1 favorite]


Serious question: has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere.

In Jay's book is a story called "The Broken Dice", which is kind of along those lines:
Olaf Haraldsson, an eleventh-century king of Norway, metamorphosed from a Viking warrior into a Christian saint. Dubbed Olaf the Thick (a characterization based on corpulence rather than lack of cunning), he wagered a kingdom in a game of dice. Not even the healing waters that were said to spout from his grave can match the miraculous tale of the broken dice. King Olaf and the king of Sweden were gambling over competing claims to the island of Hising. The Swede rolled the highest possible score, two sixes, and arrogantly suggested that there was no need for Olaf to take his turn. "Although these be two sixes on the dice, it would be easy, sire, for God to let them turn up again in my favor!" Olaf insisted, basking in the self-confidence of his recent conversion. He then cast two sixes. The Swede again threw two sixes, and so, again, did Olaf—but at the end of this roll, one of the dice split in two, and both a six and an ace landed face up, yielding an unprecedented roll of thirteen.
posted by a lungful of dragon at 10:06 AM on May 12, 2016 [3 favorites]


middleclasstool: Does anyone make casino-grade polyhedral dice (machined from plastic rather than molded)? The only machined ones I've found are metal and therefore hella expensive.
Artisan Dice's Alchemist line is machined acrylic. They also have dice cut from metal, wood, stone, and bone.
posted by ob1quixote at 10:09 AM on May 12, 2016 [2 favorites]


Wow, those are spendy. Beautiful, though.
posted by middleclasstool at 12:56 PM on May 12, 2016 [1 favorite]


Box-Muller transform takes an evenly distributed set of numbers and produces a normal distribution.

The first number in the output graph legend of anydice is the mean, and the second number is the distribution for those who are trying to figure out a normal distribution with a mean of 50.50.
posted by BrotherCaine at 2:56 PM on May 12, 2016


middleclasstool: Wow, those are spendy. Beautiful, though.
Yeah, I read the first half of your sentence and charged off to find the link because my gaming group was on about them a couple of months back. I only noticed your "hella expensive" caveat like an hour later. They're expensive but they're very nicely made.

You can get 12-die sets of Gamescience dice for as little as $30. An 8-die set of "ugly" dice in undesirable colors is only $5. They aren't machined, but they have nice, sharp edges and are specially processed to roll true. Rumor from a couple of years ago was that production had ceased, but they're active on Facebook and were talking about new stock in the last week.

All of that being said, when I needed new dice when the new D&D came out, I bought the half-pound, 4 matched sets of 15, tumbled dice for $17 and they've been just fine.
posted by ob1quixote at 4:53 PM on May 12, 2016 [1 favorite]


Now sure a person could just make tables with 60 entries instead of 100; players probably wouldn't notice. But for long time players the idea of a selector chart having 100/1000/10000 entries is really ingrained. A 60 entry table feels wrong.

May be, but FWIW the table you linked to isn't 100 entries all equally likely. It's maybe 50, with some things (additional quick action, on a roll of 51 to 55) far more likely than others (one arm becomes a tentacle, on 17).

Not really qualified to say what RPG communities want to see these days, but once you get to percentiles that's what I'm most familiar with--lots of entries, commonness determined by percentile ranges. If you need more options like "91-100: Special event! See table B17 on page 32 and roll twice." More control on the exact frequency and easier to interpret than trying to figure out how much less likely a 17 is than 53.

Also, while irrelevant to the larger point, I'm compelled by a geas to calculate simple probabilities when I see them and thus say that the chance of a "1" on 3d34 - 2 is one in 39,000.

Three 34-sided dice minus 2 (3d34-2), added together, produce numbers from 1 – 100 on a bell curve distribution

@escabeche: They most certainly do not.


How so?
posted by mark k at 8:03 PM on May 12, 2016


They most certainly do not.

Perhaps I'm missing something, but if a 1d34 is fair, each of the three rolls gives a uniform and independent random variable between 1 and 34. The sum of three rolls of a 34-sided die gives you random variables 3 through 102 — you can subtract 2 to get random variables 1 through 100. The sum of uniform independent variables gives a result that follows a binomial distribution, which should converge to a normal distribution as more rolls are added — for the purposes of tabletop gaming, you have effectively constructed a good-enough bell curve for a distribution of random variables between 1 and 100.
posted by a lungful of dragon at 12:43 AM on May 13, 2016


Much more prosaic d4,d6,d10,d12,d20 stuff, but I liked this photoset about making dice using jewelry foundry techniques.
posted by sebastienbailard at 1:54 AM on May 13, 2016 [2 favorites]


has anyone made any "fractional" dice, e.g. a d0.5? I cannot even conceive of how, or why, anyone would do that - therefore, it must be on the internet somewhere

Thank you to T.D.Strange, DoctorFedora, biogeo, sebastienballard, EndsOfInvention, Smart Dalek, robocop is bleeding, LogicalDash, NMcMoy, ricochet biscuit, roystgnr, a lungful of dragon (et al) for your excellent advice and suggestions on this point!

Based on your comments, I propose the following for the "meaning" of 1d½, which meaning - for reasons that will become apparent - only applies within a Dungeons & Dragons game (or similar game):

1. Firstly, I note that the “d” terminology for dice in Dungeons & Dragons is used to refer to a type of die by reference to the number of its sides, e.g. d4, d6, d8, etc.

2. However, the language of D&D suggests a subtle difference between "d6" and "1d6": the former refers to a kind of die, the latter to an action performed on such die (let us call the number which appears on the top of any dN the "result" of throwing such die). Thus 2d6 means not the noun "two six-sided die," but rather implies the command "roll two six-sided die, or one six-sided die twice (and add the individual results together)".

3. Furthermore, it should be accepted that rolling (say) 1d6 does not require any physical dice to be manipulated. A computer program which generates an integer from 1 to 6 at random (each outcome being equiprobable) would be an entirely acceptable "d6" in the context of playing D&D, as far as mathematics is concerned (but perhaps not as regards aesthetics, a player's psychological enjoyment of the process, tradition, etc). Similarly, as there is only one possible result of rolling a d1, no physical die is required at all in order to “roll 1d1” (although, we are gladdened by T.D.Strange's report that the d1 does exist in physical form).

3-bis. Thus, "AdB" is in the nature of an action, not a physical object (this is to address Doctor Fedora's sensible comment about the physical impossibility of a die with fractional sides).

4. Let us further note that, when playing D&D (or similar game), dice are not rolled merely for their own sake, but in order to generate some consequence within the game. Hence every roll of dice must (to be an action within the game of D&D) have some interpretation, which leads to a consequence. Thus when a player rolls 3d6, an interpretation could be (for example) that the result of throwing 3d6 is to be her character's Strength value, and the consequence is the specific number which becomes that Strength value.

5. Thus rolling 1dN (where N is a positive integer) means, within a game of D&D: perform a process which gives one of N different equiprobable results, and then apply the relevant interpretation to such result to produce the consequence within D&D.

6. We note that when rolling (say) 1d6, each result (i.e. an integer from 1 to 6) is equiprobable. Once the result is obtained, the consequence (in D&D) will be fully determined, i.e. with 100% probability. If a we roll 1d4 for our hit points, the result of the throw may be 4 (with 25% probability before the throw), but if the result of the throw is 4, the number of hit points we have is then 4 with 100% probability ("post-throw", so to speak).

7. Let us turn to 1d0. I propose that, unlike 1d1 (which always gives the same result), 1d0 should give no result. Obviously there is a "result” in a general sense - the result is “no result”. But for us this means the throw of the dice is not given a consequence in D&D, e.g. the character’s Strength value (say) is not established within the game - this is different from it being zero. To refer to ricochet biscuit's comment above: I propose that someone attacking Cthulhu with a revolver should fail whenever 1 is rolled on 1d1 (i.e., always). If 1d0 were rolled, there would instead be no failure and no success, i.e. no defined consequence within the game.

8. By analogy from 1d0 and 1d1, I propose that 1d½ should give a result and thus a consequence only half the time, i.e. 50% of the time rolling 1d½ produces the same consequence as rolling 1d0, and 50% of the time it gives the same consequence as rolling 1d1. This can be achieved by tossing a coin with the numeral “1” on one side, and on the other the words “no result”.

9. Similarly, other fractions can now be accommodated. 1d1½ is a process whose potential results are 1 (of which there is a 50% chance), 2 (25% chance) and "no result” (25% chance). The fractional part is the "sub-probability" of obtaining the next-highest integer, as opposed to obtaining no result.

10. And in general, where X is a number between different positive integers A and B, 1dX can produce any number between 1 and B-1 with equiprobability C%, and also the number B with probability (C% times the non-integer part of X (“D%")), and “No Result” with probability (C%-D% (“E%”)), such that all of the C%s, and D% and E% sum to 100%. Thus rolling 1d5½ gives results: 1 (⅙ of the time), 2 (⅙ of the time), 3 (⅙ of the time), 4 (⅙ of the time), 5 (⅙ of the time), 6 ((⅙ x 0.5 of the time, i.e. 1/12 of the time), and "no result" (1/12 of the time).

It now remains only to extend this system to negative and complex values so that we can roll 1d(-1) and 1di.

On the other hand, allowing a "no consequence" result would, it seems to me, be the same as "dividing by zero", i.e. a thing to be avoided on pain of inconsistency of the system, and hence fractional dice must never be used. To allow someone to roll 1d½ would be to introduce the possibility that Mom will come down into the basement and order us to stop playing this devil-worshipping game. But until that happens: HAIL SATAN!
posted by the quidnunc kid at 2:44 AM on May 13, 2016 [7 favorites]


mark k: "May be, but FWIW the table you linked to isn't 100 entries all equally likely. It's maybe 50, with some things (additional quick action, on a roll of 51 to 55) far more likely than others (one arm becomes a tentacle, on 17). "

True; one of the reasons I'd like to rework the table.
posted by Mitheral at 5:18 AM on May 13, 2016


quid, I did not think it was possible to make set theory or probabilities nerdier, but goddamn, you done did it.
posted by middleclasstool at 5:53 AM on May 13, 2016 [1 favorite]


I propose a different interpretation of fractional "d" notation.

An instruction given in the notation "xdy" where x and y are non-zero positive integers, indicates we should select x equally probable integers between 1 and y, inclusive.

If we were to be given an instruction in the notation "xdz" where x is an non-zero positive integer and z is a real number, we could select x equally probable real numbers between 1 and z, inclusive.

As an example, 1d½ would indicate that we should select a real number between 1 and ½. Possible results would include 1, ½, 0.9, 0.768923401353458792, or four-fifths.

1d1½ would simply indicate that we should select a real number between 1 and 1½.
1d0 would simply indicate that we should select a real number between 1 and 0.
1d-34 would simply indicate that we should select a real number between 1 and -34.
Indeed, there's no reason why z could not be equal to π, e, the square root of 2, or any other real constant.

It is possible to imagine a case in which the returned result is an irrational number or contains an unwieldy number of digits to the right of the decimal point. I propose an extension to fractional "d" notation whereby an additional variable is added in order to state the requested number of digits to the right of the decimal point. For example "1d6d0" would have the same possible results as a regular six-sided die. "1d½d3" could return 1.000, 0.500, or 0.732 as possible results.
posted by arcolz at 3:47 PM on May 14, 2016 [1 favorite]


I like quidnunc's reasoning, but "no result" bugs me; it sounds like "die rolled behind the radiator", where you'd normally just roll again.

How about "don't know"? That would fit a lot of the contexts where you're rolling to see what happens. (quidnunc's Strength example suggests that this is what he meant, but "don't know" would be clearer.)

I suspect there are different kinds of "don't know" (or "no result") though. E.g.

* quantum DN -- you don't know if you can pick up the object till you try (but then you get a determinate value)
* existential DN -- you never know what you can pick up (it varies each time)
* conspiracy DN -- events always conspire so you never have to know (someone else always arrives to pick up the thing)
* contaminating DN -- indeterminacy spreads whenever you use the statistic; e.g. if you pick something up, you don't know how heavy it is
* illusory DN -- you think you know but the DM secretly rolled a different value
* many-worlds DN -- whenever the stat is checked, the timeline branches, for success and failure, and both timelines have to be played out
* unreliable narrator DN -- the DM may misinform you about what happened
posted by zompist at 8:46 PM on May 14, 2016 [2 favorites]


many-worlds DN -- whenever the stat is checked, the timeline branches

*puts on evil beard, sharpens arm-cutting-off saw*
posted by the quidnunc kid at 1:08 AM on May 15, 2016 [1 favorite]


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