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Post Posted: Mon Sep 18, 2006 1:30 am 
 

Oh, and I never met anyone who actually played the Mentzer Basic D&D Boxes sets.


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Post Posted: Mon Sep 18, 2006 5:40 am 
 

Contrarian wrote:
OK, I just want to make sure I'm clear on this: Are you saying you had to actually put numbers on unnumbered polyhedron models?


This is the question!


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Post Posted: Mon Sep 25, 2006 5:55 pm 
 

The models came with numbers already inked on them, presumably in case the student could not manage to count all the way up to 20, 12, 8, 6 and  4!  The Hexahedron ('D6') was rather useless - but they came as set, so we had to buy one every time we wanted another D8, D12 or D20.

I did modify the icosahedron (numbred from 1-20, so what came to be called a "true D20") into a "D10" by reinking the leading digits in 10-20 to make it numbered from 0-9 twice.  And I also reinked three of these D10s with red, white and blue so they could be used to generate 3-digit uniform random numbers on the range 000-999 (I thought the sequence Red-White-Blue was obvious, but some players never seemed able to remember it!)  It was many years later that Lou Zocchi came  out with a "true" D10 with only 10 faces.  

As Lou would point out, painting the 10-20 faces would change the odds of a given face coming up (it is surprising how sensitive dice are to minor modifications).  However, the "polyhedral solids" were not made to really high standards to begin with, so the paint probably did not make a real difference.  If you want the low-down on how irregular early polyhedral dice were, get Zocchi's toungue-in-cheek pamphlet "How to Roll Winning Dice".  It shows which numbers are most and least likely to come up on the dice from each of the early US suppliers.  And you thought "lucky D20's" were only a superstition!

These early "polyhedral solids" sets can be told from the earliest intentional polyhedral dice sets that appeared a little later by the following:
--D20 numbered from 1-20, not 0-19 or 0-9 and 0+ to 9+
--D4 numbered simply 1-4 in the center of each face, (making the "rolled" number the one not visible).  Later D4 are numbered 1-2-3,  2-3-4,  1-2-4 and 1-3-4 around the three edges of each face so the numbers "rolled"  are the ones visible on the three bottom edges.  
--Each of the five solids was of a unique opaque color.  I do not have one of our original sets here to look at, but I think the colors were:
D20 - white
D12 - light blue
D8 - light green
D6 - pink
D4 - yellow
Some early US dice suppliers copied these colors but in different shades.
Many were just buying them from the same Chinese manufacturer that Edmund Scinetific bought their "polyhedral solids" sets from, so the colors
should have been the same, buy may have changed randomly whenever the Chinese ran off another batch.

The polyhedral solids sets also suffered from being made of rather soft plastic, and the corners on the D20s in particular would round off in a rather short time (producing still more "lucky" or "cursed" dice that never woudl stop on some numbers).   Lou Zocchi revolutionized the business by producing the first really sturdy "High Impact (R)" dice that were pretty close to indestructable and never seemed to wear out.   He followed those with transparent dice that (like the dice in Las Vegas casinos) let you see if there were any off-center bubbles inside them.  Bubbles are another cause of  "lucky" or "cursed" dice.   Starting with the true D10 (which I told him was impossible) Lou has since invented a number of new polyhedral dice shapes.  Some of these were Platonic solids - or "semi-regular polyhedra" known for centuries, but never used as dice before he solved the problem of how to number them (not as obvious as you might think) and manufacture them.  Others are shapes never described before, but which are suitable for dice.  

Invention is not just having an idea, but actually making it work.  Note that electric light bulbs were being made 20 years before Edison made his first bulb, but he is remembered because he made a bulb that gave enough light, lasted long enough,  and was cheap enough to replace a gas lamp, while his predecessors made bulbs that basically worked the same way as his, but were too dim or too expensive.  

Inventing polyhedral dice is like inventing the lever.  
"Its just a big stick. Og.  We've been digging up dirt with sticks forever, so what's the big deal if we use one to dig up a big rock?"

  


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Post Posted: Mon Sep 25, 2006 8:13 pm 
 

================================================
I think Christmas 1967 is right.  I went off to Grad school in '67 and had months to plan the game, and no one to game with, so I came home with the burning desire to do something "memorable".   Some of the guys who were in the game have suggested that this was a year later, after I enlisted in the USAR (June '68), but before I reported for active duty (July '70), or even earlier (Thanksgiving '67 or '68).   I know Dave Arneson was publishing a club newsletter at the time and he may have an old issue that would settle this.  In fact, he probably had to settle this date as part of the "Who Invented D&D" lawsuit between him and Gary, so I guess it would be well documented somewhere.   I know I was home from college and went back feeling that Braunstein had flopped.  
My next vacation (Christmas '67 or Easter 68?) I came back to discover that everyone wanted another Braunstein.  I created BS 2 (set in Latin America)  before the next vacation (Easter or summer '68?) and ran it twice (two flops) with heavy rule changes, so I think of the second run of BS 2 as 'BS 3'.  Then I figured out what the key to making it work was, and developed BS 4 - A much nicer scenario, complete with about 100 Airfix civilians and soldiers, tanks, helicopters and armored cars marked with the national insignia ('en vert, bannana rampant or') a lot of other props and a map of PIEDRAS MORENAS the capital of BANNANIA [SHofD&D has mis-spelled this], which I set up on the folding plywood ping-pong table [this historical object is still preserved, waiting for the national D&D hall of fame to be founded] in Dave Arneson's basement.  Fortunately, BS2 and BS3 had been played by only four people each time, so there were still a lot of people waiting for my next Braunstein.  I ran the one game, it was a big hit.  I went back to school.  Dave ran several more on the same table, shuffling the players and changing some of the objectives between my visits home.   I went off to the Army, telling Dave he could keep running the games without me (he asked if it was OK, which seemed awfully polite, since it was all set up in his basement).  And I also expected to go off to Vietnam and get killed, so I did not really care a lot about who "owned" Braunstein.

Looking at this time line, it seems very possible that, since I left for active Duty in Oct'70, the first BS 4 or "Bannania" game could have been as late as early summer '70 and the  original Braunstein in Christams '68.   As I said, Arneson has it documented somewhere.

Unless one defines "fantasy" as "imagining you are a spy in Central America" I did not run a "first fantasy role-playing game" in 1969, but I did run a "first role-playing game" at least as early as late 1968, and maybe 1967.

While I was in the Army (for three years in the US and Alaska, but not in Vietnam, as it turned out) Arneson ran a series of Braunsteins in Bannania, and the one of the other guys (Duane Jenkins, I think) did some Western Braunsteins (in Brownstone, Texas, I think) with the Mexican Bandid "El Pauncho" (David Arneson) crossing the border to rob the bank,
so sort of inspired by the 1916 Poncho Villa raid, but mostly by hollywood westerns.  I only heard about these games dimly, getting a few letters from Dave.   The 1919 Russia Braunstein and the 1941 Polish Braunstein were planned a lot while I was off in the army, but before I got back, Dave had started Blackmoor, the fantasy precursor to D&D, and further Braunsteins never got going.   I still have the Authenticast WWI tanks and WW2 planes I was going to use for props... "So Comrade, are your mechanics going to finish assembling and testing the new MiG3 fighters for our squadron, or are they going to attend my lecture on The Inevitable Triumph of the Proletariate under the Leadership of Marshal Stalin?"
(Correct answer is "Yes Comrade Commisar!")

By the way, it was shortly after I came back on leave the first time that
David Megarry discovered "the Dungeon"  Arneson drew up the first Dungeon map for a Blackmoor adventure that was expected to run one day and then (probably) the map would be brough back out if anyone ever went there again.   We played, everyone agreed that the game had gone really smoothly, and the next day we were back out in the kingdom, escorting some merchants through the woods or whatever.  Then Dave Megarry arrived with teh prototype "Dungeon" game under his arm.  He had distilled the complex, open-ended Blackmoor dungeno crawl into a simple but practical board game.  He had also identified that, by restricting the players to a limited set of options (go left, or right, or back, and not  "NbyNW for three minutes. Now can the dragons see them there or not..." the Dungeon made everything manageable.  He and Dave Arneson discussed this, and from then on, the Dungeon was where most of the action was going to take place.

Of course we played Diplomacy.  It was one of the very few intelligent "war" games on the market (besides those published by Avalon Hill) back in the early 60's  It was a multiplayer game - which the early AH games really were not - and we also played Risk, Summit (try to find a copy of that one!) and Conflict as well as Monopoly, Clue, Carreers, etc.
I think I was more inspired by Careers (each player sets their own secret victory conditions) than by Diplomacy (every players only objective is to conquer the world).

The Midwest_Military_Simulation_Association was founded on 18APR64 by Ray Allard, noted amateur historian and reinactor (now deceased).
The first meeting was attended by Dr. William Musing, Loren Johnson, Ron Lauraunt and Winston Sandeen, Ray Allard Junior and David A. Wesely.
Ray was about 54 at the time, the next four were all about 30 and the last two were teenagers.   Besides age, the gropu was split by interest, with the five older guys being historians, collectors, modelers and paiters of military miniatures, and the two youngest being wargamers.
The older guys put up with us, (and Winston Sandeen even played in a few miniatures battles) partly because we hung on their every word when they told war stories about WWII and the Korean War.
The group expnaded with the recruitment of a more friends of these starters.  Dan Nicholson joined up, bringing in another group of gamers who had each checked Strategos, the American Game of War out of the UofM library (he got their names off the library card in the back of the book): amoung them were Jim Clark and Gregg Scott.  
Eventually, there were enough wargamers that the collectors and gamers drifted apart, meeting toghther only occaisionally.  I and the gamers started gathering every weekend at the home of Greg Scott (who soon started CinC Soft Metal Casting).   Pete Gaylord, Dave Arneson, and a group of Avalon Hill gamers who knew Arneson in High School joined. Eventually, the group became too large again, and the younger, more wargame-oriented members moved over to Dave Arneson's house (which made me and Dan Nicholson the old men of the group)
The group had reached about 60 people (including some who had moved away and were still playing in Arneson's Napoleonic Campaign by mail) by the time I ran the first Braunstein, but only 8-12 would usually show up for a game at one time.    Looking back, this implies that we were one of the largest gaming groups in the US, not counting the non-gaming mimiatures collectors centered around Ray Allard.

I think MMSA is still officially alive with a new set of gamers and collectors running it.  I dropped into a meeting back in the 1990's and found them discussing whether to split up into a collector/modeler/painter goup and a gamer group... They were pretty amazed when I told them who I was, and that we had had the same meeting about 30 years earlier...

Arneson produced COTT ("Corner of the Table Talk" a title inspired by "Table Top Talk" the newsletter Jack Scruby was running for his lead soldier company and wargaming group in California).     This documented the on-going Diplomacy-by-mail game, the current ACW or Napoleonic Campaign in progress, and various club news, rules modifications, etc.

We were students, so we could meet for 72 straight hours very weekend, and a few nights a week (at various peoples houses to keep the parents from going nuts).  I see us in every issue of Knights of the Dinner Table,
even before we were doing RPG's.   We recruited other gamers taht we ran across in "opponants wanted" ads in The General or S&T, we were recognized as an official student organization at the UofM and at the University of St. Thomas, and ran "welcome" tables at fall registration,
we invited relatives and people we met in school to come and take a look.
And we got older and settled down and left the recruiting to "the kids", so now I do not know anyone in the MMSA, but there is a pretty busy group that meets at The Source, our local game store, and other groups that run our local Cons.

The first Braunstein used my self-published "Strategos-N" rules, or it would have, if there had actually been a battle (which I did not intend to happen, but I had some copies of those rules around to keep the players thnking one might).   I also had a set of really cumbersome rules no one got to see, that spelled out how each player could score points and how to decide who won (highest score, "obviously").  I wound up with far more players than I had planned for, made up new characters off the top of my head, and could not begin to keep up with the action, so aside from ruling that the dead players could not win, I just gave up and threw out the scoring system.   No those rules did not survive, but I did try to reconstruct them all of my talk at GenCon05.  

The rules for BS2 and BS3 were also tossed when they flopped.

Some of the rules and props for BS4 - "Bannania" - survived, and I reconstructed the rest of the rules  for my talk at GenCon05.  If I get a bunch of fan mail asking me to put on the game at GenCon07 - instead of one of my typical talks like "Gas, Bugs and Nukes", "Women as Warriors",
"Bombs and Bombing in World War II", "Field Artillery in the American Civil War", "Tank and AntiTank", etc.  I will probably run BS 4, since a bunch of modern RPG'ers would find BS 1 pretty unimaginative and it would be just as uncontrollable as it was the first time.  

Hope this does some more good-

  


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Post Posted: Mon Sep 25, 2006 11:41 pm 
 

killjoy32 wrote:
NEVER MIND THAT!!! SPY HUNTER!!!! OH WOWZA!

one of my all-time fave arcade games. that game was so amazingly cool.

Al



I do remember the arcade Zaxxon--too many times I would play with someone and it would be 20+ minutes before I finally blew up (and obout 400,000-500,000 points)! :oops:   :)   and they would have to go to class  :( !

  


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Post Posted: Mon Sep 25, 2006 11:48 pm 
 

[quote="weseld1"]
-----------------------------------------------------------------------------------

While I am beating my own drum, I would like to lay claim to having
"invented" polyhedral dice.  I was the first person to USE what were then
being sold as "Models of the five regular polyhedra" (for mathematics
teachers to show to their students), AS DICE.  I have since seen a book
that claims that the Japanese were already using three D-20s, numbered
0-9 twice, to generate 3-digit decimal random numbers at some time
before 1976.  So it may be that they also invented this use for polyhedra,
but I was unaware of them so I am at least an independant re-inventor.
And it was my introducing the D4, D8, D12 and D20 to our gaming group
in 1965 that led to them being used in RPGs and D&D.

===============================================

Do you happen to know who invented the 30-side, 50-side, and 100-side dice (I call the latter the "golf ball" because the first 100-side die I had was white with what looked like little dimples (the numbers 1-100).
Anyway, how DOES one read a 50-sided die? :?:  The one I have reminds me of a top without the handle to push-start it spinning, or (memory test) half of the original large Cylon warships in the 1970's version of Battlestar Galactica .

  


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Post Posted: Tue Sep 26, 2006 12:36 am 
 

sleepyCO wrote:Do you happen to know who invented the 30-side, 50-side, and 100-side dice (I call the latter the "golf ball" because the first 100-side die I had was white with what looked like little dimples (the numbers 1-100).

The 100-sider is sometimes referred to as a "Zocchihedron", after it's inventor, Lou Zocchi.  

The 30-sider is clearly a "rhombic triacontahedron", and the 50-sider is better known as a "icosakaipentagonal dipyramid".  Everyone knows that.  :lol:

http://en.wikipedia.org/wiki/Zoccihedron

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Post Posted: Tue Sep 26, 2006 12:42 am 
 

Howdy All,


Does anyone have a list or link to the names for all of the polyhedral shapes?

You know tetrahedron, isocohedron, etc.


Futures Bright,

Paul


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Post Posted: Tue Sep 26, 2006 1:10 am 
 

sleepyCO wrote:Do you happen to know who invented the 30-side, 50-side, and 100-side dice (I call the latter the "golf ball" because the first 100-side die I had was white with what looked like little dimples (the numbers 1-100)


The 30-sided die was originally released by The Armory.  I don't know the specific inventor -- I was actually searching the U.S. Patent database for that yesterday, but couldn't find the patent!

The 100-sided die, as someone said, it the creation of Lou Zocchi.  He's also designed 3-, 5-, 14-, 16-, and 24-sided dice.  He really keeps busy for someone who's supposed to be semi-retired.

The Collector's Trove wrote:Does anyone have a list or link to the names for all of the polyhedral shapes?

You know tetrahedron, isocohedron, etc.


http://www.mathpuzzle.com/Fairdice.htm shows all the shapes that would work as dice.

http://hjem.get2net.dk/Klaudius/Dice.htm uses a lot of math I don't understand to explain why those are the only shapes that would work for dice.

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Post Posted: Tue Sep 26, 2006 1:37 am 
 

weseld1 wrote:And I also reinked three of these D10s with red, white and blue so they could be used to generate 3-digit uniform random numbers on the range 000-999 (I thought the sequence Red-White-Blue was obvious, but some players never seemed able to remember it!)  It was many years later that Lou Zocchi came  out with a "true" D10 with only 10 faces.


Weird coincidence: There's a 1980 patent for a ten-sided die the recommends the same red-white-blue sequence!   I guess it really was obvious.

If you want the low-down on how irregular early polyhedral dice were, get Zocchi's toungue-in-cheek pamphlet "How to Roll Winning Dice".  It shows which numbers are most and least likely to come up on the dice from each of the early US suppliers.  And you thought "lucky D20's" were only a superstition!


I think Lou still uses that pitch, actually -- he had an enlarged photocopy of  his "stacks of dice" advertisment at his Gen Con booth this year.

These early "polyhedral solids" sets can be told from the earliest intentional polyhedral dice sets that appeared a little later by the following:
--D20 numbered from 1-20, not 0-19 or 0-9 and 0+ to 9+
--D4 numbered simply 1-4 in the center of each face, (making the "rolled" number the one not visible).  Later D4 are numbered 1-2-3,  2-3-4,  1-2-4 and 1-3-4 around the three edges of each face so the numbers "rolled"  are the ones visible on the three bottom edges.


Those sound exactly like the dice shown in the this 1965 patent.  Apparently, somebody was trying to invent new dice games with them at almost the same time you were introducing them to fantasy games.  One of those weird instances of coincidental invention, I guess.

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Post Posted: Tue Sep 26, 2006 10:56 am 
 

The Collector's Trove wrote:Does anyone have a list or link to the names for all of the polyhedral shapes?


More than you'd ever wanna know about uniform polyhedra:

http://en.wikipedia.org/wiki/List_of_uniform_polyhedra

If you look at the "truncated isocahedron", that's what mere mortals call a soccer ball. ;)

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Post Posted: Tue Sep 26, 2006 4:50 pm 
 

Contrarian wrote:
http://www.mathpuzzle.com/Fairdice.htm shows all the shapes that would work as dice.

http://hjem.get2net.dk/Klaudius/Dice.htm uses a lot of math I don't understand to explain why those are the only shapes that would work for dice.

===============================================
I hope this comes through better than the last time I tried to post a reply.
There is something about this tool that I still do not have figured out: Other tools I have worked with have a fairly obvious "reply" button, while this one does not.  I keep trying to use "quote" to "reply with quote" but about half the time, after I am done entering my response, and I click "Submit" I am sent off to a screen that asks me to enter my password again, and then sent to a BLANK screen that lets me type in the reply all over again.   I have learned to save the text of my replies to my clipboard so I can just keep pasting them into the blank screens until one responds to "Submit" with a "successsful submit" message, but it is really annoying to have to keep swatting at this thing until it accepts the message.  Kind of like shouting to make up for a bad cell phone.  Does nayone know what I might be doing wrong?  We have a T10 line here, so I ought to be getting a good connection.

Back to the subject.  
The author of http://www.mathpuzzle.com/Fairdice.htm has fallen into one of the errors common to discussions of polyhedral dice.  His claim that
"This page contains a complete list of all possible Fair Dice."   is incorrect. He shows a lot of shapes that can be used as fair dice, but blows off all the non-ISOHEDRAL shapes as  being dependant on how they are rolled.  Well, so is the classic cubical die.  Read "Scarne on Dice"

There is a reason that casinos will not accept craps rolls that do not bounce off the far end of the craps table: with practive one can control the dice on short rolls, by holding them with the desired (or the undesired) sides against the palm, and throwing them to not bounce and roll too many times, the odds of the selected side being on top when they stop can be improved.  With a lot of practice and a few other tricks, they can be improved right up to virtual certainty.  If anyone suggest you play craps, and he first has to get a blanket to throw the dice on, watch out!  I have seen that kind of "craps hustler" manipulation used in our kind of games for years, and it works just as well with most ISOHEDRAL dice, as with cubes.   The answer for this kind of manipulation (if you really are worried about it) is to require dice to be thrown (1) with a cup, so no special holding is possible and (2) to rebound off a backboard and bounce multiple times.

Of course, if you are worried about "craps hustler" die rolling techniques,  you have to worry a lot more about rigged or selected lucky/cursed dice.  
Scarne also explains how EASILY (cubical) dice can be shaved or loaded to make them roll different numbers more often than they should, and how hustlers will use this to give them at least a statistical advantage in their games, even if the dice are not so stunningly loaded as to always roll the same number.   "How to Roll Winning Dice"  explains this for badly-made ISOHEDRAL dice.  

But clever manipulation, poor manufacture and intentional shaving or loading can apply to ALL dice shapres equally well, so ISOHEDRAL dice have no real advantage over non-ISOHEDRAL shapes.  

For anyone who has not seen http://www.mathpuzzle.com/Fairdice.htm
I will explain that  ISOHEDRAL shapes have all faces identical, and include all the classic, early, polyhedral dice, and would exclude the following dice that you have probably seen: D7 (a "drum" with two pentagonal faces and five rectangular facets around the sides); D5 (another "drum" with two triangular faces and three rectangular faces) and the D2 - otherwise known as the PENNY - which has two large circular faces connected by a very short rim that is essentially impossible to land standing on...  All of these non-ISOHEDRAL shapes work just fine for generating uniform random results with a chance of 1/7, 1/5 or 1/2 of a given face coming up.   One can also develop a nice D3 by gluing pennies together until the resulting cylinder will land on edge 1/3 of the time, (so heads or tails will share the other 2/3 of the time).  The correct number of pennies can be determined by throwing cylinders of different numbers a lot of times - say 10,000 - and accepting the one that averages closest to landing on edge 1/3 of the time.  A number of other non-ISOHEDRAL shapes have been evaluated by this method and shown to make perfectly useable fair dice.  If Lou lives long enough, they will all eventually appear, but it takes a lot of money to tool up to produce each of them (and he doubts that a fair D20 that just looks different from the current D20 would sell all that well).

Now the D7 has the problem of landing with an edge up 5 out of 7 times
so one has to either read the face that is down, or number the edge - this problem is shared with the D5 and also with the D4 and some of the other ISOHEDRAL shapes that are not currently used as dice.  I think this makes them poor shapes from a practical point of view, though the makers of the D7 did a nice job of dealing with this problem.  

When Lou told me he was going to make a D10, I explained why it was impossible: "The Ancient Greeks invented the five regular polyhedra and proved there ain't ever gonna be any more of them, Lou."  When he handed me the D10 the next year, I realised I wasn't as smart as I thouht I was.  When he told me he was going to have a D100 at the next Origins, I believed him, and set out to figure out how he did it.  When I got there, and saw his, it was NOT the design I had developed!  I showed him mine, and he said "well, yes, but that one alays lands with a point up, instead of a face, so I did not use it."   Another epiphany!   Since then we have discussed a LOT of shapes for dice, and - believe me - they are not limited to ISOHEDRA.  

One important question is how to arrange the numbers on a polyhedron to reduce the ability of a "craps huslter" to manipulate them to roll high or low.   There is a reason that all classic six-sided dice have 1 and 6, 2 and 5 and 3 and 4 on opposite sides, though only superstition dictates that all are numbered clockwise.  (One wargame company did have six-sided dice made that were numbered counter-clockwise.  I do not know the reason, but they may have thought they could patent them that way).  Lou put in a lot of work to get the numbers on the D24 in the best possible order.

I am rather interested in the 1965 patent application for the five "original"  polyhedral dice.   Can anyone tell me who made the application?  I doubt that anyone was granted the patent, considering how hard it was for Lou to get the D100 patent on a shape the ancient Greeks had not invented.
He also had to do more than just invent the shape to turn it into a useable dice; he invented the braking system that keeps it from rolling "forever" like a worn D20.

As for the D50, I think its cute, but I have trouble reading it too.

  


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Post Posted: Tue Sep 26, 2006 5:43 pm 
 

The pattern is "simple" - if you know how to count in Greek!
The suffix "-hedron" (plural -hedra) means "solid with faces"
just like "-gon" means "shape with sides".
A one surfaced solid would be Unihedron (or maybe a Unahedron)
A two                                    Bihedron
  three                                 Trihedron     
  four                                   Tetrahedron  
  five                                    Pentahedron
  six                                     Hexahedron
  seven                                 Septahedron
...and so on.  Unfortunately, I cannot count very high in Ancient Greek, so I cannot tell you how to say 71-surfaced solid except to say that it would be a "(71 in Greek)-hedron"
A D100 would be be a Hectahedron,
a D1000 a Millihedron and
a D10000 a Myriahedron
"Poly", by the way means "many" so I guess a "Unihedron" could not,
technically, be a kind of polyhedron.

The wording gets more complex when trying to describe the shape with more detail.  The common D12 is a Pentagonal Dodecahedron, because it has 12 pentagonal faces.  Pentagons are "regular" polygons (all angles and sides are the same) so this shape is also a "Regular Dodecahedron" , one of the "five and only five, there ain't never gonna be ny more of them" "regular polyhedra" (which we think of as D4, D6, D8, D12 and D20)
There is also another D12 in existance, though not easy to find, which is a
"Rhombic Dodecahedron".  It has 12 identical faces, that are all 4-sided rhombuses with two sharp points and two blunt points (they look like the diamonds printed on cards).  The four sides of each rhombus are the same length, but the four angles are not all the same, so they are not "regular" polygons and the Rhombic Dodecagon" is not one of the "Regular Polyhedra".  
All-in-all, it is a lot easier to describe these as "D4, D6, D8" and so on.
"A D8 numbered 1-4 twice" is clearer and tells one more about its use as a die than the Greek geometric name.

  


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Post Posted: Tue Sep 26, 2006 7:44 pm 
 

weseld1 wrote:The pattern is "simple" - if you know how to count in Greek!
A one surfaced solid would be Unihedron (or maybe a Unahedron)

It would called a monohedron.  I have no idea what that would look like, but probably a single point on a sphere would describe it best.
(Uni-/bi-/multi- are Latin.  Mono-/di-/poly- are Greek.)  ;)

The polyhedral requirements for "fair" dice seem to be (in theory, manufacturing and shady craps tables aside):
1) convex -- line between any two vertices remains within the bounds of the polyhedron
2) face-uniform -- all faces the same size/shape

This would include all Platonic solids (5 total: d4,d6,d8,d12,d20), Catalan solids (13 total, including the d30), dipyramids (d8*, d16), and trapezohedra (d6*,d10,d34,d50).  

The last two categories have infinite numbers of possibilities, but they get very hard to read as you add large numbers of sides.  The first two more or less resemble a sphere and are better suited for dice, for that reason.  As well, some of the polyhedrons (d4!) have a vertex or edge facing upward when at rest, making them relatively poor choices for dice due to the difficulty in numbering them appropriately.

The d100, while innovative, is not a polyhedron at all, it's a dimpled sphere -- but it's cool.

This guy wrote it up much nicer:

http://members.aol.com/dicetalk/polyh1.htm

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Post Posted: Tue Sep 26, 2006 10:56 pm 
 

weseld1 wrote:There is a reason that casinos will not accept craps rolls that do not bounce off the far end of the craps table: with practive one can control the dice on short rolls, by holding them with the desired (or the undesired) sides against the palm, and throwing them to not bounce and roll too many times, the odds of the selected side being on top when they stop can be improved.  With a lot of practice and a few other tricks, they can be improved right up to virtual certainty.  If anyone suggest you play craps, and he first has to get a blanket to throw the dice on, watch out!  I have seen that kind of "craps hustler" manipulation used in our kind of games for years, and it works just as well with most ISOHEDRAL dice, as with cubes.   The answer for this kind of manipulation (if you really are worried about it) is to require dice to be thrown (1) with a cup, so no special holding is possible and (2) to rebound off a backboard and bounce multiple times.

Of course, if you are worried about "craps hustler" die rolling techniques,  you have to worry a lot more about rigged or selected lucky/cursed dice.  
Scarne also explains how EASILY (cubical) dice can be shaved or loaded to make them roll different numbers more often than they should, and how hustlers will use this to give them at least a statistical advantage in their games, even if the dice are not so stunningly loaded as to always roll the same number.   "How to Roll Winning Dice"  explains this for badly-made ISOHEDRAL dice.  

But clever manipulation, poor manufacture and intentional shaving or loading can apply to ALL dice shapres equally well, so ISOHEDRAL dice have no real advantage over non-ISOHEDRAL shapes.

For anyone who has not seen http://www.mathpuzzle.com/Fairdice.htm
I will explain that  ISOHEDRAL shapes have all faces identical, and include all the classic, early, polyhedral dice, and would exclude the following dice that you have probably seen: D7 (a "drum" with two pentagonal faces and five rectangular facets around the sides); D5 (another "drum" with two triangular faces and three rectangular faces) and the D2 - otherwise known as the PENNY - which has two large circular faces connected by a very short rim that is essentially impossible to land standing on...  All of these non-ISOHEDRAL shapes work just fine for generating uniform random results with a chance of 1/7, 1/5 or 1/2 of a given face coming up.   One can also develop a nice D3 by gluing pennies together until the resulting cylinder will land on edge 1/3 of the time, (so heads or tails will share the other 2/3 of the time).  The correct number of pennies can be determined by throwing cylinders of different numbers a lot of times - say 10,000 - and accepting the one that averages closest to landing on edge 1/3 of the time.  A number of other non-ISOHEDRAL shapes have been evaluated by this method and shown to make perfectly useable fair dice.  If Lou lives long enough, they will all eventually appear, but it takes a lot of money to tool up to produce each of them (and he doubts that a fair D20 that just looks different from the current D20 would sell all that well).

Now the D7 has the problem of landing with an edge up 5 out of 7 times
so one has to either read the face that is down, or number the edge - this problem is shared with the D5 and also with the D4 and some of the other ISOHEDRAL shapes that are not currently used as dice.  I think this makes them poor shapes from a practical point of view, though the makers of the D7 did a nice job of dealing with this problem.  



I'm with you on the problem of blanket rolls. (I actually have lectured other D&D players about inadequate dice-rolling techniques.  I'm a dork like that.)  I use dice cups a lot.  (In case anyone cares, the World's Most Annoying Dice Cup is a glass peanut butter jar -- makes a hell of a racket when you roll 3d6 with it.)

I'm still suspicious of the d5 and d7 though.  I know Lou says they've tested fair in lab conditions, but I don't play D&D in a lab.  It's just too hard for me to trust those two shapes, and I'm a Gamescience fan.

weseld1 wrote:One important question is how to arrange the numbers on a polyhedron to reduce the ability of a "craps huslter" to manipulate them to roll high or low.   There is a reason that all classic six-sided dice have 1 and 6, 2 and 5 and 3 and 4 on opposite sides, though only superstition dictates that all are numbered clockwise.  (One wargame company did have six-sided dice made that were numbered counter-clockwise.  I do not know the reason, but they may have thought they could patent them that way).  Lou put in a lot of work to get the numbers on the D24 in the best possible order.


I've been told by some dice-collectors that "left-handed dice" (the counterclockwise ones) are traditional in some Asian countries.

weseld1 wrote:I am rather interested in the 1965 patent application for the five "original"  polyhedral dice.   Can anyone tell me who made the application?  I doubt that anyone was granted the patent, considering how hard it was for Lou to get the D100 patent on a shape the ancient Greeks had not invented.


Actually, that's a granted patent (the database doesn't include applications). Filed Feb 1963 by  "Fredda F.S. Sieve" of New York city, granted September 1965.

As I understand it, that isn't really a patent on the dice, that's a patent on a method of using the dice -- in other words, it's a patent on a game mechanic.

Game mechanics (as you probably know) can be patented.  There are all sorts of odd game mechanic patents in the USPO database, many of them completely useless (like weird patents on variations of craps, or new betting systems).  I suspect a lot of game patents are never really used commercially, because the patent-holders never figure out how to market their ideas.

I have no idea if the 1965 patent was ever licensed, used, or contested.  Of course, it's probably academic now, since the patent is long expired.

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Post Posted: Wed Sep 27, 2006 2:43 pm 
 

various replies to celmive, deimos3428 and contrarian:

You're right.  I was wondering about Uni and Bi when I wrote them, but just assumed that they sounded strange because the Unigon or Bihedron could not really exist.  Evidently, I am more at home in Latin than in Greek (which is not saying much for my Latin).  "Fas est ab hostii docerii - itae ad quonset hut."  

http://www.mathpuzzle.com/Fairdice.htm is certainly interesting, but you said it more clearly.

===============================================

"The polyhedral requirements for "fair" dice seem to be (in theory, manufacturing and shady craps tables aside):
1) convex -- line between any two vertices remains within the bounds of the polyhedron
2) face-uniform -- all faces the same size/shape"

These conditions for a polyhedron to be used for a fair die are sufficient -
BUT NOT NECESSARY - just like all squarea are rectangles, but not all rectangles are squares.  

I have designed dice in which not all of the angles  between faces are convex.  This means that some of the "faces" will never touch the table on which they are rolled, but these are simply not numbered.  The key here is that the concave faces must be symmetrically distributed, so all of the numbered, convex faces will be equally likely to come up.   A fairly stupid example, but one that is easy to visualise, would be a cube with each of the six facesa hollowed out into a shallow, truncated pyramid, and a number put on each of the little squares at the center of each face.  This has NO convex sides, but works just fine as a fair D6.  My designs were a lot more decorative than this concave cube, and provided various numbers of sides.  While they worked just fine in testing, Lou never produced them, because, he pointed out, the molds to make them would be very complicated compared to those for convex polyhedra and the percentage of dice that would come out missing corners would be very high.  That is, while I could spend $200 worth of my time making a prototype, these dice could not be mass-produced and sold at a price the market would accept.

The easiest example of a fair dice with non-identical sides is the cylindrical D3 I described previously, but that is not a polyhedron.  The D7 and D5 are polyhedra and are fair dice.  The insistance on regularity comes from the desire of most researchers to treat this as a problem in mathematics, not engineering.   I give you this example:
Thomas Edison was interviewing an engineer, who had applied for a job.
He handed the young man a light bulb and said "Determine the volume of this bulb. You may have any tools you need."
The young man measured the diameter of the bulb at the widest part, and the diameter at the base, the radius of curvature in the tapering sides and
the height.  He carefully prepared a drawing of the bulb and used a polar planimeter to measure the area of the cross-section.  He used this to refine his estimate of the formula for the compund curve of the bulb profile.  He then solved the integal equation for the volume produced by rotation that curve about the long axis of the bulb, evaluated the solution over the interval from 0 to 2pi and took his results back to Edison.
"Well let's check your work", said Edison, and dunked the bulb into a graduated cylinder full of water.

There are mathematical solutions and engineering solutions, and the engineering ones work.

The polyhedra illustrated in http://www.mathpuzzle.com/Fairdice.htm include several that could be used for dice, but which would share the disadvantage of the D4, D5 and D7 of coming to rest with either a point or an edge on top.  Some of the other shapes are really two different names for the same shape, or are "degenerate" versions of one of the other shapes, arising when the angles of some of the vertices are selected to cause the adjacent triangular faces to beome coplanar with the triangular faces of the alternately adjacent vertices, forming rhombuses.  A good example of this is the D24 formed by erecting shallow pyramids on each of the faces of a cube, and the "rhombic dodecahedron" that results when these pyramids are made a bit taller.   By the way. garnet can crytalize into rhombic dodecahedra.   The first time I saw one of these crystals I though, "Gee, another way to make a D12.  But who would need one?"

I agree that the "glass peanut butter jar" solution is noisy, but it is one way of solving all the "craps hustler" problems, without getting a full sized craps table to roll the dice on.  For those who do not know about this - one puts a pair of dice into a peanut butter jar and screws on the lid.   Everyone uses this jar to make their die rolls by shaking the jar six or more times and then slapping it down on the table.   There is no way to use a special grip on the dice, grease them, or switch them for a shaved or loaded pair.   This does not quite solve all problems, as the owner of the dice can put in a pair he knows will roll low numbers much less often that normal, and then take large bets that the shooter will not make his point whenever it is 3.  One problem is that in the excitement, some players will bang that jar down too hard and need several stitiches when it shatters.  

For our games, one can use an unbreakable plastic jar instead of a glass one, and it would probably be necessary to have more than one jar, to provide all the possible polyhedral shapes (or combinations) needed for a
game.   My own gaming is nearly all done with either 2D6, 3D10 or 1D20, so I could get along with three jars, but I do not bother.  Then again, the only other guy in our group who knows about this stuff is not likely to be trying a KC-swap in a friendly game.

================================================
While the D&D/RPG/Strtegos/Totten/Occult connection is really tenuous, I agree that ANYTHING would be a smoking gun for Mothers Against Dungeons & Dragons, even if I said the Arch-Angel Gabriel gave us the rules.  Totten after all, was convinced that everything he was writing ("Ancient Hebrew as the Undoubted Ancestor of the American Indian Languages") and the British Israelite Movement he supported, were based in Scripture, but that would not make him any more acceptable to MADD.

However, when I look at some RPGs and the things some GMs have done with them, I am "bothered about D&D", or at least about how it and its decendants can be misused.   I think I know how the Wright brothers must have felt when people started using airplanes to bomb civilians.

  


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Post Posted: Wed Sep 27, 2006 7:15 pm 
 

weseld1 wrote:I have designed dice in which not all of the angles  between faces are convex.  This means that some of the "faces" will never touch the table on which they are rolled, but these are simply not numbered.

Ok, good point.  You could use a convex die, if you only numbered the concave faces.  That gets some serious "coolness" factor, which doesn't matter to polyhedra, but matters a great deal with dice.
"Gee, another way to make a D12.  But who would need one?"

I forgot that requirement!  Any polyhedron considered for dice must be cooler than an existing one of the same number of faces, and not too difficult to make.  That's really more of a marketing thing, along the lines of sparkly dice.

Regarding the d7/d3, I'm not yet convinced that a 100% fair die is possible.  Stop me if you've heard this one before, but here's my reasoning:

1.  There is a length at which the prism/cylinder's weight is distributed fairly (evenly?) between all faces.  
2.  With non-isohedral dice, additional factors come into play which previously could be discounted due to shape alone.
3.  There is a length at which each factor becomes fair.
4.  All of these lengths must be the same for a fair die.

If there are multiple lengths, but they are close, you could average them and call it a day.  That won't satisfy a mathematician, but it's more than fair enough for D&D.  I suspect that's what is done in reality...

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Post Posted: Wed Sep 27, 2006 11:17 pm 
 

I'm not following most of this, but I have to say it's a fascinating thread!  :)

Bad time for faro/harami to stop contributing! (re: the historical perspective)

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Post Posted: Thu Sep 28, 2006 12:36 am 
 

zhowar wrote:I'm not following most of this, but I have to say it's a fascinating thread!  :)

Bad time for faro/harami to stop contributing! (re: the historical perspective)

I don't really know much about dice or polyhedrons; to be honest, I'm just being facetious.  :lol:

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Post Posted: Thu Sep 28, 2006 1:06 am 
 

deimos3428 wrote:I don't really know much about dice or polyhedrons; to be honest, I'm just being facetious.  :lol:


Ouch, flip any more of those side-splitting comments and I will just die.

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