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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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Post Posted: Thu Sep 28, 2006 2:56 am 
 

If DW was gaming with polyhedral dice in 1965, then I am willing to believe that he was the first to do so.  I continue to believe that Tractics (1971) is the first published game to use the 20 sider.  Here is a quote from the 1975 edition, which I suspect is also in the original edition:

Equipment that will be needed to use these rules... a device to generate random numbers from 1-20.  If you do not have access to a die with 20 sides, it is easy to construct a random generator known as a "TOAD" which consists of nothing more than 20 poker chips placed in a small opaque recepticle.  Each chip is consecutively numbered on both sides, from 1 through 20.


The informative Courier Timeline says that the Wargamer's Newsletter anounced the availability of the 20 sider in 1970.  I do not have that copy of the Wargamer's Newsletter, but I have the March 1967 Table Top Talk, which has an article by John Cape called "Hit Probabilities" in which he writes

To have some mechanism which will give the wargamer a random chance of between 1 and 100, all that is needed is a box of poker chips, numbered 1 through 100.


In The First Fantasy Campaign (1977) Arneson writes about the dungeon of Blackmoor

It began with only the basic monsters in CHAINMAIL and was only some six levels deep.  Six levels was chosen since it allowed random placement with six sided dice (no funny dice back then).


A few paragraphs later Arneson writes that

Combat was quite simple at first and then got progressively complicated with the addition of hit location etc.  As the players first rolled for characteristics, the number of hits a body could take ran from 0-100.


which seems to imply that percentile numbers were being generated somehow.  Though the range 0-100 contains 101 numbers....

In a much later interview dated March 15, 2004, Arneson writes that

We were in the very beginning using the six siders, but when we started doing the fantasy games, I dug out some 20-sided dice I'd purchased in England in the mid 60's. I went to a game store — well, a historical miniatures store — in London, right off of... I think it was at Picadilly, I'm not sure. And I went upstairs to their gaming area and they had these little boxes of 20-sided dice, and I thought "oh, how cool!" And so I picked up three pair, and I came back home with them and tried to introduce them into our military games, but the guys would have nothing to do with them. We had several mathematicians, and working out percentages for six-sided die were child's play for them, but it gave me a headache. So really, the dice sat there for three or four years. Then we did fantasy, and I said "hey, let's use this stuff for it." So when we started on Blackmoor, we started using 20-sided dice at the same time. Go figure. They're gamers, you know?


Thus Arneson appears to be taking credit for introducing the 20 sider into gaming.  There is an article on the web which claims that

The first RPG use of such dice was in the first RPG—the famous Dungeons & Dragons (D&D) game.  However, D&D did not invent the dice. D&D co-creator E. Gary Gygax, who was the first gamer to use polyhedral dice, told me he originally found them in a school supply catalog from California, where they were sold as tools to teach math and probability.


However, Gygax has never claimed to have introduced polyhedral dice into gaming in any of the many interviews that I've come across.  The article goes on to say that

Gygax found his dice in 1972 and used the new statistical spreads they made possible to create the rules of D&D from the wargame Chainmail. However, the supply of dice was too low to sell them at first. So from 1974 to 1980, D&D came only with marked cardboard chips that were pulled randomly out of a bag.

  


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Post Posted: Thu Sep 28, 2006 9:39 pm 
 

"With non-isohedral dice, additional factors come into play which previously could be discounted due to shape alone. "

True.   Mathematicians want to restrict the discussion to Isohedral dice for just that reason.  However, all of the isohedra were examined and considered for use as dice at least 30 years ago, and most were rejected.
Some were rejected for landing edge-up or point-up, or for being too tricky to machine molds for (in the pre computer assisted design era), but most were rejected for giving the same number of sides (6, 8, 12 or 20) as the existing regular polyhedra dice.   THe interest has been in coming up with shapes that give fair dice with something other than 4,6,8,12 or 20 sides.  

If one leaves the easy world of isohedra and tries to precompute the necessary dimensions of a D5 or D7 or D10, it quickly becomes clear that there are a lot of "obvious" rules that do not hold up in practice.  All faces do not have to be identical, or of equal areas, or subtend equal soild angles about the center of mass.  Unfair dice can be made with each of these features (my alternative D100 design has been tested and shown to not only land with a point up, but to favor some faces over others by a significant amount: I designed it to give equal solid angles and I was wrong).   The problem is GIGO.   AS I learned in my computer simulation  classes many years ago, Garbage In, Garbage Out.  If you make the wrong assumprions it your models, no amount of cool mathemetics will guarantee that the results are correct.  

It is easier to find oil by exploration, than by theory, and it is easier to determine fair non-isohedral dice by experimentation than by computation.

Again, I did not do the tests to determine if the D7 is fair, so I will not vouch for that, but the argument that it CANNOT be fair are like the 18th Century philosopher watching the Montgolfier balloon floating overhead:
"It is impossible.  This cannot be happening!"
"But how can you deny it, M'sieur?"
"Quite simply: All things which fly, have wings.  It does not have wings, and therefore, it cannot fly!"

From a practical point of view, the "craps hustler" rolling techniques used to control the roll of an ordinary D6 can be used just as easily to control the roll of a drum-shaped D7 or D5.   After all, a cube is a drum shaped die with four-sided ends, while a D7 is a drum with five-sided ends and a D5 is a drum with three sided ends.  Dice which are more spherical are harder to control.    This argues in favor of using a D10 numbered 1-5 twice instead of the drum-shaped D5, or using a D14 numbered 1-7 twice instead of the drum-shaped D7.   But these are not arguments about fairness of the design, but of its employment.

  


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Post Posted: Thu Nov 30, 2006 1:01 pm 
 

Summit (try to find a copy of that one!)


I assume This version of Summit is the game you mean.

:-) I love seeing obscure references. I've had this game sitting in my game stack for many many years. I never really played it other than trying it out solo (by running all the players), but it is a cool looking game.

This argues in favor of using a D10 numbered 1-5 twice instead of the drum-shaped D5, or using a D14 numbered 1-7 twice instead of the drum-shaped D7.


I love Zocchi's octohedrons numbered 1-4 twice for d4s, and I still prefer icosohedrons numbered 0-9 twice for d10s.

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Post Posted: Thu Nov 30, 2006 3:41 pm 
 

THis is the game, though the box art I remeber is the one  captioned

2001-07-04 10:53:52
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at the site you linked to, rather than the one the link goes to directly.
I suspect that at least one of the boxes is a pre-MB "Indy" version, just like "Boxcars" was the Pre-AH Indy version of Rail Baron.  One cute point in the SUmmit game is that the round tokens for "consumer goods" that one used in exerting economic control (as I recall one could build three kinds of tokens and compete fro economic, military or diplomatic control in a given country) if you look very carefully, are decorated with 1960 Ford Edsels!   Not just Edsels, but the almost impossible to find last model year  that looks different from the classic "Oldsmobile sucking a lemon" that people usually thinks of when they hear "Edsel".  Of course this fits, since the 1960 Eisenhowere-Krushchev Summit that was cancelled by the U-2 incident was the inspiration for a game called Summit, and it was probably created just before Ford cancelled the Edsel.   How appropriate to use a cancelled car in a game about a cancelled summit...

I think some historian could make interesting observations on the assumptions the game makes about international relations, peaceful cooexistance, and the future balance of power, given the period in which it came out and the way thing really turned out since.

I have often thought that it is too bad that Wargaming was not widespread a long time earlier, as the ideas of most wargames are better playtested than the speculations of pundits (even military ones).  Thus, if there had been a rash of commercial wargames published during, say the American Civil War, we would have a much better illustration of how people saw the war than we do from the "How I knew it all along and it wasn't my fault" writings in, say, Battles and Leaders.

In fact I even designed a mock "antique" contemporary Civil War wargame, ("On To Richmond!  - an entertaining and educational game for 2-4 players about Restoring the Union, from F.L.Games, a division of Frank Leslie's Illustrated Magazine, (c) 1862, FLG, Inc.)  but realized that I have the same unfair advantage of knowing more about what was really true than the game designers than could have, so it could only be a hoax, and not as valuable as a real contemporary wargame would have been.
Of course, the Prussian General Staff probably had someone in 1861-65 who was running wargames on the US war as training exercises or staff studies, using their latest Kriegspiel, and if the reports of these games survived, they might be fun to read, but they would represent only one very sophistacated viewpoint.

My break is over, time to get back to work.

  


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Post Posted: Fri Dec 01, 2006 12:15 pm 
 

Any ideas on who, when, or where the 4-, 8-, 10-, and 12-sided dice came into D&D or did they come from other places/games?

  


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Post Posted: Fri Dec 01, 2006 4:22 pm 
 

I think I amswered this in detail about six postings back, but here's the quick answer.  I am the person who first started uisng 4-, 8-, 10-, and 12-sided dice in games.  

Back in 1965, I read the rules to a game published in 1880 that said one could use a "12-sided teetotum" instead of a 6-sided die,  for resolving odds of 6:1, 7:1 etc up to 11:1, but did not explain what a teetotum was or how to make one.  I had seen a set of models of the regular polyhedra in my High School trig class, and decided that a "12-sided teetotum" must be the 12-sdied thingy (a regular dodecahedron) I had seen in the set.   Wanting to try out the game, I went to school, got out the "Edmund Scientific Supplies" catalog, and ordered one set of the polyhedra from them for $6.00 (gasolene was $ 0.20 /gallon then, so that would be about $66.00 in today's money).  This set of five polyhedra came with the faces already numbered, to make it easy to see that there were 12 sides on a dodacahedron, or 20 on an icosahedron, which made them easy to use as dice.  So they became the ancestors of all the D4, D6, D8, D12 and D20 sets ever sold.  There have been other shapes, and other ways of numbering them invented since, and there alwys were six-sided dice (though using the numbers 1-2-3-4-5-6 instead of pips or painted dots is a feature of the classic "D6" used by D&D, that I do not remember ever seeing before then).  

Someone tried to patent using these solids as dice at about the same time that I started using them, and since I have never met this guy, I am willing to assume that - like the airplane and the lightbulb - a lot of other people could have thought of it, and he did not necessarily get the idea from me.  I only learned of the 1965 patent application very recently, and was amused to find that he was granted a patent on not the idea but on his "design" for the five regular polyhedra (invented back in 150 a.d.) he sent in with the application, which were the same colors and numbering patterns that were already being sold by Edmund Scientific...
Rather like submitting a '59 Chevrolet when applying for a patent on inventing the Automobile, and being granted a patent on the shape of the tailfins.

I thought using them for dice was (1) already implied by the 1880 game rules and (2) so obvious that no one could get a patent on it.  I guess I was wrong.

SO why are my dice the ancestors of all the D&D dice?

Well, while I only saw value in the D12 and D20, the other guys in our wargaming group thought they were all "cool", and we used them in our wargames (and kept buying these expensive sets from Edmund Scientific as they wore out).  When Dave Arneson (one of the guys in our group) invented his fantasy role-playing game, and took it to Gary Gygax to be cleaned-up and published, they decided to use the cool polyhedral dice, even though I told them that they should just use regular dice, because "No one is going to buy your game for $10 if they then have to spend another $6 to get the special dice before they can play it".  But they ignored me and of course, "Dungeons and Dragons" did not sell, and no one has ever heard of it.

By the way, a 12-sided teetotum is not a D-12!  I finally found one in a game published in 1828, which I paid a lot of money for, just to get the teetotum (the game is REALLY stupid, but the teetotum is kind of clever).

If you want more details in this, go back and read my earlier postings.

  


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Post Posted: Sun Dec 03, 2006 6:11 pm 
 

Here is an interesting die from the 1920's if the seller is to be believed.




** expired eBay auction **




I've seen 8-sided dice used for a poker game as well; 7,8,9,10, jack, queen, king,ace. I have no idea how modern they were though.

  

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Post Posted: Sun Dec 03, 2006 8:48 pm 
 

ifearyeti wrote:
I've seen 8-sided dice used for a poker game as well; 7,8,9,10, jack, queen, king,ace. I have no idea how modern they were though.




Eight-sided poker dice go back to the 19th Century -- there's an 1896 patent. (Note, though, the corners were truncated, like the 8-sided d4 that was introduced in the 1980s.)   Kevin Cook has a page of photos on his site.



Koplow Games currently sells 5-packs of 8-sided poker dice.  Available on Amazon.

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Post Posted: Tue Dec 12, 2006 1:45 pm 
 

ifearyeti wrote: interesting die from the 1920's if the seller is to be believed

The images are a little hard to make out on my PC, but this looks like a numbered "soccer-ball shape" with mixed hexagonal and pentagonal faces.  This would not be a "fair die", as somne faces would come up more often than others, but for a lot of game purposes, it would not matter if the die was fair or not.  Typical six-sided pip dice, used in ordinary games are not all that perfectly made, which is why they are not used in casinos, but when playing Monopoly, who cares?  

It could be that this die was part of a "soccer" board game: It would seem to be a natural way to make a special die with more than 6 faces.

  

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Post Posted: Tue Dec 12, 2006 2:20 pm 
 

It could be that this die was part of a "soccer" board game
-roulette die

  


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Post Posted: Tue Dec 12, 2006 2:53 pm 
 

Rakeesh sah Tarna wrote "-roulette die"

OK- that makes the 00 face more reasonable.  I take it that a roulette wheel does not have 100 numbers?  Or this was for a 'parlor" game that did not really try to simulate roulette in perfect detail, soit would not care if the die was not "fair".

  

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Post Posted: Tue Dec 12, 2006 3:50 pm 
 

OK- that makes the 00 face more reasonable.  I take it that a roulette wheel does not have 100 numbers?  Or this was for a 'parlor" game that did not really try to simulate roulette in perfect detail, soit would not care if the die was not "fair".

- import to US probably safe to guess with 00 and 0 instead of just one 0
should be 36+0+00 for real roulette but d38 difficult to make?
not sure but possibly imported as fortune telling type device but actually used for gambling when legal issues were more a problem. discussed here

later? US patent equally vague

  


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Post Posted: Tue Dec 12, 2006 4:42 pm 
 

These are genuine dice, it would seem. Neat, anyway.
http://www.dicecollector.com/diceinfo_h ... hapes.html

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Post Posted: Tue Dec 12, 2006 4:48 pm 
 

These are genuine dice, it would seem. Neat, anyway.

http://www.dicecollector.com/diceinfo_h ... hapes.html



- fortune telling cover is a wrong lead on the 1920s-30s crystal ones then

same people with that link discussion on post above :/



usually sell for $10-30 on ebay. not totally rare

  
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