> More than just the d100 he was a pioneer of being very exacting when it came to making polyhedral dice.
Absolutely, but i couldn't fit all of that into the subject line ;) and he's best known for the d100. Many of us remember the articles and ads from the 1980s describing the effort he put into that particular die.
I remember reading his original page - what fun insight into something nobody "really" cared about (casinos care about honest dice but only six-sided).
Met him at GenCon UK in the 1990s. His Doc-From-Back-To-The-Future energy was absolutely mesmeric. He had five towers of D10s in a plastic tubes. Three towers was the standard dice we all had in our bags and two were towers of his Game Science d10s. The standard dice towers all had different heights but the two game science towers were identical heights. He explained that for the regular dice, the smoothing process (which made them nice to hold!) changed the shape enough that they weren't regular sized anymore. The Game Science dice weren't smooth (sharp edged) and so they kept their shape. Of course, if you want a die to roll fairly, it needs to be a regular shape.
I bought a Zocchihedron cos we were playing a game that used percentages (Icar RPG) but rolling it was hilariously haphazard as it was essentially a ball! Loved it tho. I later received the game science dice set as a gift, which I still have. Sadly little time to play these days.
The amount of games that use those kinds of dice make his contribution to tabletop gaming incommensurable. Sad to see him passing. But 91 yo is more than respectable
The "Zocchihedron" is a single die with 100 sides, but most games that use a d100 simulate it with two d10s instead (reading the ones on one d10 and the tens on the other). So the truth is that Zocchi's die is more a novelty and less influential than it might appear at first if you take the title as written.
> Yeah, a real d100 is just too impractical for actual gameplay. Super neat, but two d10s is far more usable.
We had one for our AD&D sessions and we'd definitely be using it. AFAIR it didn't necessarily roll for very long but it was a bit hard to make sure what numbers was really the one at the top. Still: it had a cool factor.
It had never occurred to me that somebody needed to invent polyhedral dice. There must be so many inventions in the world that I’m completely unaware that there was a point in time before which something didn’t exist and after that it did, thanks to somebody.
There are 13 more solids with equal faces and vertex (but not equal edges) https://en.wikipedia.org/wiki/Catalan_solid but none of them has 100 faces (It looks like a nice project for 3D printing.)
You can cut the corners, but now the faces are different and ensuring all the faces have the same probability is a nightmare. Some info in https://en.wikipedia.org/wiki/Truncation_(geometry)#Uniform_... (This include the soccer ball.) (I have no idea if this include the D100.)
The Zocchi d100 isn't face-symmetric and thus isn't a fair die. It's as close as he could get. It's really effectively a golf ball with 100 dimples, but they aren't and can't be arranged perfectly symmetrically.
Any even number dX can be made as a fair die as a bipyramid or trapezohedron. https://en.wikipedia.org/wiki/Trapezohedron These would be the only fair face-symmetric d100s. The standard d10 is this, and you sometimes see a d14 or d18 or something like that constructed this way. It becomes impractical with very thin faces past 20 or so. An odd-numbered fair die is also possible by using one twice as big and duplicating the numbers (like 1-5 twice on a d10.)
Martin Gardner wrote an article on platonic solids in Scientific American, December 1958, and mentioned this in passing: "All five Platonic solids have been used as dice. Next to the cube the octahedron seems to have been the most popular". I have no idea what games using 8-sided dice were somewhat popular (or existed at all) in 1958 or earlier? I wondered about that since I first read that article some decade ago.
I also read a book about games from ca 1880 and it described 12-sided dice (the usual one, numbered 1-12) as if that was a thing some people used for playing games, but none of the games described in that book used them and I also have no idea about other old games using 12-sided dice.
I've seen some octahedrons but they pale in comparison to the six siders - I suspect partially because it's hard to see an octahedron and assume it's fair. It looks like a parallelogram.
Besides gambling games most dice in antiquity were used in rituals or soothsaying.
Slightly related: In a stone shop nearby my home they sell a nice set of Platonic Solids made of semitransparent stones, but the octahedron is an irregular one :((( It's very similar to the ser in this photo https://www.mercadolibre.com.ar/solidos-platonicos-geometria... It's a nice present for a friend that is a mathematician too, but there is high chance that they will notice.
A better term would be "creator", because actually creating a 100-sided die that that rolls nicely and each face being equally likely is a lot more difficult than imagining one.
>> By far, his most significant contributions to the games industry came in the realm of dice design. Zocchi founded Gamescience in 1974. He was the first to create polyhedral dice for the U.S. market, and is credited with designing the D3, D5, D14, D24, and D100. The D100 was named the "Zocchihedron" in his honor (see "Have A Nice Day!").
And I happen to own at least one of each of those specialist dice. And many more still. I think I have a die with faces for most even numbers from 2 to 100 and also some of the odd ones too.
> The internet reports that D100 is impractical to use...
It's a nice novelty but it's not terribly practical. Despite having a d100, 2d10s are invariably more comfortable to use and easier to read. My d100 was purchased back in 1998-ish for its novelty and nostalgia value, not its functional value.
So I think this article is a bit misleading, he did not invent the polyhedral dice, he just made them better. "He was the first to create polyhedral dice for the U.S. market" is a weird sentence, I'm not sure what it's going for, but I think it's referring to the fact that early D&D dice were I believe imported, but I forget the details.
One bit I love from the early history of Gamescience is he didn't have the capital to make a full D&D set off the bat, so he'd get one dice mold made, release that one, then take the profits to make the next mold. Forget which was first but I think the d4 was early.
I've never played any games that require this, but the Wikipedia page makes reference to percentage rolls, but wouldn't you need 101 sides to get 0% and 100% for that?
> but wouldn't you need 101 sides to get 0% and 100% for that?
There is no 0% in d100/d-percentile rolls. Every "how to interpret these dice" paragraph in games which use them will tell you to interpret 0-0 on 2d10 as 100, not 0. Or, hypothetically (but i don't recall having ever seen this), they'll have a stated range of 0 to 99 (inclusive). Either way, the numeric range spans precisely 100 digits.
There are games that use a d100 with 0-99 range, and games that read a d10 as 0-9 for that matter. First that comes to mind is Ambush! from 1983 that did both those things (https://boardgamegeek.com/boardgame/1608/ambush).
Love that game, but it is a bit distracting that probabilities feel one-off. Rolling 5 or lower to hit is 60%, not 50%. And when rolling 2d10 the result is 0-18, not 2-20.
The point of percentile dice isn't to generate a string between "0%" and "100%", it is to test if action with chance of x% success gets done or not. For every o
value of x, there are x out of 100 values which are strictly less than x, or if you count 0 as 100 then there are x out of 100 values which are less than or equal to x. Either way you get x% percent chance for event to happen. If the dice had 101 sides, the probabilities would be x/101 which aren't nice round percents.
It even works correctly for 0% and 100% chance events. Assuming 0 is counted as 0 - For 0% there are 0 numbers less than 0 on dice so chance of throwing number less that is 0/100=0%. For 100% all 100 numbers are less than 100 so no matter what the result of throw is you will succeed.
Not necessarily "done or not" because it's narratively unsatisfying to just "fail". Imagine you watch a heist movie and in the last 20 minutes the gang are like "Stealing the master key to make a copy was vital to our plan but we failed" and they disband and that's the end of the movie. Realistic but not satisfying and the dice are for a game, a fiction, so we can just eliminate that unsatisfying result.
Modern systems tend to come up with some more interesting consequences, so e.g. maybe success is the thing the player wanted to do succeeds as they expected, but failure shades from "Small snag" to "Technically it did work, but..." like from "The target's PA, Betty, noticed you take the key, so now you also need to bribe Betty" through "Our copy won't actually work, we're going to need to keep the original and hope the copy fools them for long enough"
Or maybe we have a timing adjustment, success means that you pilfer the key, duplicate it in five minutes like planned and slip it back, mild failure is it takes a half hour and everybody will need to improvise for those extra minutes, and bad failure is you'll need it all night, change your plans to accommodate that.
No, because in d100 based systems you success is rolling at or below a chance.
So the fact there is no 0% (0 is interpreted as 100) is necessary because if your modifiers are giving it 0% chance, you need dice to start at 1 for that to work
Throwing 2d10 of different colors is equivalent of trowing 1d100. It's nice they have different colors to avoid discussions, but you can throw them in two different bins or one at a time or something. Remember to sum them as (x-1) * 10 + (y-1) + 1, that is a clear indication of why zero-based indexing is better.
(Does someone sell "decade" dice, which faces say: 10, 20, 300, ..., 90 and 100?)
Cool, they also have dice with up to 5 zeros, to build your own 1d-million. I have sizable dice collection but I have never seen a 1d1000000 in person, I need to get one...
I agree, but I'm just now porting a program from fortran to python. They read and write files that use their own convention about indexing and values [1]
And some changes may have to been backported, and it has a lot of tricks with index of arrays of different dimensions, so I'm wrapping the formulas with +1 and -1 and hopping the best.
IIRC the python compiler does not optimize them (perhaps with numba?), but later steps in other programs are slow, so N <= 20 and whatever I do is bounded by 20^4.
[1] If the file says "1 2 7.0 \r 1 2 8.0 \r" should I keep the sum (15.0), the first (I never seen that) or the last? (Raising an error, nah.)
I would say yes, because the physics of rolling two objects is slightly different than one object. I don't have any idea, though, if that would affect the distribution of numbers rolled. It's not an experiment that can be done through simulation.
The study of imperfection in dice that makes them settle on certain favoured numbers by Louis, helps clear superstitious story of Mahabharata whereby the character named Shakuni, had dice made of his dead father's ashes who/which always respects/fall on numbers he desired,threby winning/cheating in game of Chaupad, that ultimately lead to biggest war in human history
More than just the d100 he was a pioneer of being very exacting when it came to making polyhedral dice. See http://www.1000d4.com/2013/02/14/how-true-are-your-d20s/
> More than just the d100 he was a pioneer of being very exacting when it came to making polyhedral dice.
Absolutely, but i couldn't fit all of that into the subject line ;) and he's best known for the d100. Many of us remember the articles and ads from the 1980s describing the effort he put into that particular die.
I remember reading his original page - what fun insight into something nobody "really" cared about (casinos care about honest dice but only six-sided).
Met him at GenCon UK in the 1990s. His Doc-From-Back-To-The-Future energy was absolutely mesmeric. He had five towers of D10s in a plastic tubes. Three towers was the standard dice we all had in our bags and two were towers of his Game Science d10s. The standard dice towers all had different heights but the two game science towers were identical heights. He explained that for the regular dice, the smoothing process (which made them nice to hold!) changed the shape enough that they weren't regular sized anymore. The Game Science dice weren't smooth (sharp edged) and so they kept their shape. Of course, if you want a die to roll fairly, it needs to be a regular shape.
I bought a Zocchihedron cos we were playing a game that used percentages (Icar RPG) but rolling it was hilariously haphazard as it was essentially a ball! Loved it tho. I later received the game science dice set as a gift, which I still have. Sadly little time to play these days.
The amount of games that use those kinds of dice make his contribution to tabletop gaming incommensurable. Sad to see him passing. But 91 yo is more than respectable
The "Zocchihedron" is a single die with 100 sides, but most games that use a d100 simulate it with two d10s instead (reading the ones on one d10 and the tens on the other). So the truth is that Zocchi's die is more a novelty and less influential than it might appear at first if you take the title as written.
Yeah, a real d100 is just too impractical for actual gameplay. Super neat, but two d10s is far more usable.
> Yeah, a real d100 is just too impractical for actual gameplay. Super neat, but two d10s is far more usable.
We had one for our AD&D sessions and we'd definitely be using it. AFAIR it didn't necessarily roll for very long but it was a bit hard to make sure what numbers was really the one at the top. Still: it had a cool factor.
91 is respectable for a reasonable man in the early 21st century. A few unreasonable people want a bit more.
Nothing unreasonable about wanting to live healthy and longer. It's not likely tho.
A guess?
That’s what people always say until science progresses. I remember when we believed HIV would not be treatable.
Science advances one funeral at a time.
And most of them will die before turning 91. Like most people.
> But 91 yo is more than respectable
And it still fits on a d100!
And it's a respectably high roll!
Those of us already over 40 already thats maybe the best we can expect, for 20 y/olds who knows..
https://en.wikipedia.org/wiki/Zocchihedron
I didn't see a picture of Zocchi's d100, Wikipedia has one
Interesting they had to redistribute the numbers to take account of its natural bias.
Sort of crazy they didn't test it for bias before they released it!
It had never occurred to me that somebody needed to invent polyhedral dice. There must be so many inventions in the world that I’m completely unaware that there was a point in time before which something didn’t exist and after that it did, thanks to somebody.
There are only 5 Platonic Solids https://en.wikipedia.org/wiki/Platonic_solid : D4, D6, D8, D12 and D20.
There are 13 more solids with equal faces and vertex (but not equal edges) https://en.wikipedia.org/wiki/Catalan_solid but none of them has 100 faces (It looks like a nice project for 3D printing.)
You can cut the corners, but now the faces are different and ensuring all the faces have the same probability is a nightmare. Some info in https://en.wikipedia.org/wiki/Truncation_(geometry)#Uniform_... (This include the soccer ball.) (I have no idea if this include the D100.)
You also can "cheat" and use https://en.wikipedia.org/wiki/Teetotum that allows any number if you don't care too much about the polyhedral property.
The Zocchi d100 isn't face-symmetric and thus isn't a fair die. It's as close as he could get. It's really effectively a golf ball with 100 dimples, but they aren't and can't be arranged perfectly symmetrically.
Any even number dX can be made as a fair die as a bipyramid or trapezohedron. https://en.wikipedia.org/wiki/Trapezohedron These would be the only fair face-symmetric d100s. The standard d10 is this, and you sometimes see a d14 or d18 or something like that constructed this way. It becomes impractical with very thin faces past 20 or so. An odd-numbered fair die is also possible by using one twice as big and duplicating the numbers (like 1-5 twice on a d10.)
Martin Gardner wrote an article on platonic solids in Scientific American, December 1958, and mentioned this in passing: "All five Platonic solids have been used as dice. Next to the cube the octahedron seems to have been the most popular". I have no idea what games using 8-sided dice were somewhat popular (or existed at all) in 1958 or earlier? I wondered about that since I first read that article some decade ago.
I also read a book about games from ca 1880 and it described 12-sided dice (the usual one, numbered 1-12) as if that was a thing some people used for playing games, but none of the games described in that book used them and I also have no idea about other old games using 12-sided dice.
I've seen some octahedrons but they pale in comparison to the six siders - I suspect partially because it's hard to see an octahedron and assume it's fair. It looks like a parallelogram.
Besides gambling games most dice in antiquity were used in rituals or soothsaying.
Slightly related: In a stone shop nearby my home they sell a nice set of Platonic Solids made of semitransparent stones, but the octahedron is an irregular one :((( It's very similar to the ser in this photo https://www.mercadolibre.com.ar/solidos-platonicos-geometria... It's a nice present for a friend that is a mathematician too, but there is high chance that they will notice.
I too would question the term "inventor" here.
* dice: exist for thousands of years
* me: what if these had 100 sides?
* d100: *invented*
A better term would be "creator", because actually creating a 100-sided die that that rolls nicely and each face being equally likely is a lot more difficult than imagining one.
Everything you've ever seen that isn't sky, water, air, ground, life was invented by someone.
Heck, many specimens of the last two are inventions, that are insignificant as a % of species but are in the worldwide top by biomass.
It's quite difficult to leave the anthroposphere in much of the world.
>> By far, his most significant contributions to the games industry came in the realm of dice design. Zocchi founded Gamescience in 1974. He was the first to create polyhedral dice for the U.S. market, and is credited with designing the D3, D5, D14, D24, and D100. The D100 was named the "Zocchihedron" in his honor (see "Have A Nice Day!").
And I happen to own at least one of each of those specialist dice. And many more still. I think I have a die with faces for most even numbers from 2 to 100 and also some of the odd ones too.
OK now you all know I'm a nerd.
The internet reports that D100 is impractical to use but it's cool if your game design calls for a relatively rare "ritual value".
We had such a ritual in our games back when I was in high school: the start of the campaign luck roll.
The idea was that your starting circumstances would be modified by the d100 zocchihedron roll.
One time, my buddy rolled a 2; our DM grimaced. "Well, you aren't starting off dead... but you might wish you were".
His starting conditions?
Naked. In total darkness. Sealed in a coffin. But at least he wasn't alone: he had a rat nibbling on his toes!
> The internet reports that D100 is impractical to use...
It's a nice novelty but it's not terribly practical. Despite having a d100, 2d10s are invariably more comfortable to use and easier to read. My d100 was purchased back in 1998-ish for its novelty and nostalgia value, not its functional value.
So I think this article is a bit misleading, he did not invent the polyhedral dice, he just made them better. "He was the first to create polyhedral dice for the U.S. market" is a weird sentence, I'm not sure what it's going for, but I think it's referring to the fact that early D&D dice were I believe imported, but I forget the details.
One bit I love from the early history of Gamescience is he didn't have the capital to make a full D&D set off the bat, so he'd get one dice mold made, release that one, then take the profits to make the next mold. Forget which was first but I think the d4 was early.
I've never played any games that require this, but the Wikipedia page makes reference to percentage rolls, but wouldn't you need 101 sides to get 0% and 100% for that?
> but wouldn't you need 101 sides to get 0% and 100% for that?
There is no 0% in d100/d-percentile rolls. Every "how to interpret these dice" paragraph in games which use them will tell you to interpret 0-0 on 2d10 as 100, not 0. Or, hypothetically (but i don't recall having ever seen this), they'll have a stated range of 0 to 99 (inclusive). Either way, the numeric range spans precisely 100 digits.
There are games that use a d100 with 0-99 range, and games that read a d10 as 0-9 for that matter. First that comes to mind is Ambush! from 1983 that did both those things (https://boardgamegeek.com/boardgame/1608/ambush).
Love that game, but it is a bit distracting that probabilities feel one-off. Rolling 5 or lower to hit is 60%, not 50%. And when rolling 2d10 the result is 0-18, not 2-20.
yeah but that means there is no 0% on the scale
The point of percentile dice isn't to generate a string between "0%" and "100%", it is to test if action with chance of x% success gets done or not. For every o value of x, there are x out of 100 values which are strictly less than x, or if you count 0 as 100 then there are x out of 100 values which are less than or equal to x. Either way you get x% percent chance for event to happen. If the dice had 101 sides, the probabilities would be x/101 which aren't nice round percents.
It even works correctly for 0% and 100% chance events. Assuming 0 is counted as 0 - For 0% there are 0 numbers less than 0 on dice so chance of throwing number less that is 0/100=0%. For 100% all 100 numbers are less than 100 so no matter what the result of throw is you will succeed.
Not necessarily "done or not" because it's narratively unsatisfying to just "fail". Imagine you watch a heist movie and in the last 20 minutes the gang are like "Stealing the master key to make a copy was vital to our plan but we failed" and they disband and that's the end of the movie. Realistic but not satisfying and the dice are for a game, a fiction, so we can just eliminate that unsatisfying result.
Modern systems tend to come up with some more interesting consequences, so e.g. maybe success is the thing the player wanted to do succeeds as they expected, but failure shades from "Small snag" to "Technically it did work, but..." like from "The target's PA, Betty, noticed you take the key, so now you also need to bribe Betty" through "Our copy won't actually work, we're going to need to keep the original and hope the copy fools them for long enough"
Or maybe we have a timing adjustment, success means that you pilfer the key, duplicate it in five minutes like planned and slip it back, mild failure is it takes a half hour and everybody will need to improvise for those extra minutes, and bad failure is you'll need it all night, change your plans to accommodate that.
The usual RPG response to the failed critical skill check is that the party just slaughters everyone in the casino instead.
No, because in d100 based systems you success is rolling at or below a chance.
So the fact there is no 0% (0 is interpreted as 100) is necessary because if your modifiers are giving it 0% chance, you need dice to start at 1 for that to work
Here I was thinking he invented throwing two d10 where the other one is marked with tens.
Somebody had to invent that too, right?
I just throw 17d6 and subtract 2.
Problem solved.
(I am joking!)
Joking aside, is throwing 2d10 and using one for tens and one for units different from throwing 1d100?
Throwing 2d10 of different colors is equivalent of trowing 1d100. It's nice they have different colors to avoid discussions, but you can throw them in two different bins or one at a time or something. Remember to sum them as (x-1) * 10 + (y-1) + 1, that is a clear indication of why zero-based indexing is better.
(Does someone sell "decade" dice, which faces say: 10, 20, 300, ..., 90 and 100?)
> (Does someone sell "decade" dice, which faces say: 10, 20, 300, ..., 90 and 100?)
Yes, they do. I used to use them for this exact purpose.
E.g.
* https://boxcarsandoneeyedjacks.com/product/10-sided-decade-d...
* https://extrememathgames.com/product/10-sided-decade-dice-00...
Cool, they also have dice with up to 5 zeros, to build your own 1d-million. I have sizable dice collection but I have never seen a 1d1000000 in person, I need to get one...
Yes, decade dice is fairly standard these days.
Usually you buy 1 D10 and 1 decade dice, and role both of them and add them. Most purchaseable dice sets come this way.
This is just the first result with a picture, but they are really common, all my dice sets have one: https://www.dicegamedepot.com/10-sided-tens-opaque-dice-red/
almost all d10's are zero-based, 0-9. And the "decade" die is 00-90. So it's just a simple matter of adding the rolls, no complicated math. And 0=100.
> (x-1) * 10 + (y-1) + 1
Is that not equivalent to:
> (x-1) * 10 + y
or:
> x * 10 + y - 10
I agree, but I'm just now porting a program from fortran to python. They read and write files that use their own convention about indexing and values [1]
And some changes may have to been backported, and it has a lot of tricks with index of arrays of different dimensions, so I'm wrapping the formulas with +1 and -1 and hopping the best.
IIRC the python compiler does not optimize them (perhaps with numba?), but later steps in other programs are slow, so N <= 20 and whatever I do is bounded by 20^4.
[1] If the file says "1 2 7.0 \r 1 2 8.0 \r" should I keep the sum (15.0), the first (I never seen that) or the last? (Raising an error, nah.)
I would say yes, because the physics of rolling two objects is slightly different than one object. I don't have any idea, though, if that would affect the distribution of numbers rolled. It's not an experiment that can be done through simulation.
You mean 20d6 and subtract 20? :P
The study of imperfection in dice that makes them settle on certain favoured numbers by Louis, helps clear superstitious story of Mahabharata whereby the character named Shakuni, had dice made of his dead father's ashes who/which always respects/fall on numbers he desired,threby winning/cheating in game of Chaupad, that ultimately lead to biggest war in human history