Saturday, November 26, 2016

Tray or Cups?

How to roll dice.

Jay insisted on today's topic. The problem is if players cast dice on the open table, the dice land cockeyed or go off the table entirely. Is there a better way to roll dice?

Tray

In a way we've been there. We would just flip a Holmes set lid over. The dice popped out all the time, though.

Chaosium used to make a 2" deep box which was better at containing the dice. However, the players lean in to see the result and it feels like playing over a craps pit. The dice trays I see for sale online are 1.5" deep, which might be about right.

Trays aren't how the Bookhouse Boys roll, though.

Cups

Smonet Traditional Professional PU Leather Dice Cup

The idea of using cups suggested itself after playing a game of liar's dice. We used plastic cups initially, but they are noisy, so we upgraded to felt lined cups.

Cups are great for storing dice.

Cups aren't great for rolling lots of d6, since the dice tend to stack.

Another downside to cups is players who can't resist playing up the drama with excessive shaking. Jay's catchphrase in this situation is "hurry up and roll, dice bag."

Friday, November 18, 2016

Testing Dice for Fairness

Are Chessex dice fair; are Koplow dice fair; how to test dice.

Testing dice for fairness is tedious but simple: roll the dice a large number of times and tally how often each face comes up.

Here is an example where a set of Chessex dice are rolled 100 times each:

We don't expect the numbers to be exactly the same, even if the die is fair. Any outcome is possible from a fair die, though some outcomes, such as seeing a 6 a hundred times and the other faces not at all, are vanishingly unlikely. How do we recognize implausible results from a fair die?

My time in the statistics department at Ohio State acquainted me with a test statistic which can be used to answer the question.

Let n be the number of sides the die has. Let Oi be the number of times we observe the i-face to come up. Let Ei as the number of times we expect the i-face to come up, assuming the die is fair. The test statistic is:

$$χ^2 = \sum_{i=1}^n \frac{(O_i - E_i)^2}{E_i}$$
The test statistic has a Chi-squared distribution with - 1 degrees of freedom. It is used to assign a p-value to the result, which is the chance that a fair die would produce results as or more extreme than what we observed. If you are interested, here is some code for making the calculation. The closer the p-value is to zero, the stronger the evidence that the die is not fair.

I took a set of Koplow dice and a set of Chessex dice and rolled each die 100 times. The only die which had a p-value less than .05 was the Koplow d6. However, if we compute p-values for 5 fair dice, there is a 22.6% chance that one of the dice will have a p-value less than .05. To account for this, I applied the Bonferroni correction, which raised the p-value of the Koplow d6 to 0.11.

So as far as I can tell, my Koplow dice and my Chessex dice are fair. It doesn't mean yours are too, but you can test them.

Saturday, November 12, 2016

What dice you need; whose dice to buy.

Which Dice You Need

The original edition of the game called for two sets of polyhedral dice and 4 to 20 six-sided dice. Polyhedral dice aren't hard to get these days, so no reason to limit yourself to two sets. Also, modern gamers will want percentile dice.

As a general principle, our group likes to resolve a character's fate with a single cast of the dice. If you find yourself rolling a die repeatedly and summing the numbers in your head, you don't have enough dice! Or so we think.

Another group custom is we expect the host to provide dice for everybody. We stopped carrying dice bags around almost thirty years ago. Possibly related: Jay sometimes calls other players "dice bags" when he doesn't like their style of play.

With that said, here is what I set out for the players:

For the record—and for the search engine—the image shows eighteen d6 with pips, two d100, three d4, three d6 with digits, three d8, three d12, and three d20.

I also keep a set of polyhedral dice behind the screen for sealing the players' fate in secret.

Chessex

My fave manufacturer right now is Chessex, founded in 1987. They sell dice in sets of seven like the one above.

Chessex sells dice with swirls and speckles. The speckled dice were introduced in 1995. They also sell transparent dice. None of these are to my taste. Sometimes I have to poke around to find the solid-colored, opaque dice with high-contrast paint that I like. I want dice that are easy to read.

Chessex dice are made from a hard thermoplastic. They are cast from molds, painted, and then polished in a rock tumbler. The polishing removes paint from everywhere except the indented numerals. The polishing also rounds the edges.

By the way, note the distinct way Chessex numbers the d4. Not many manufacturers use this style.

There are some other traits that can be used to recognize Chessex dice. One is that opposite sides of a Chessex die sum to a consistent number. In the case of a d20, opposite sides always sum to 21.

If you take a Chessex d20 and look at the 1-face, it shares edges with the 7-face, 19-face, and 13-face. I'm not sure if Chessex dice have always had this arrangement, but molds are expensive, so manufacturers don't change them often.

Finally, I'll mention some traits which Chessex dice have and which in my mind all good dice should have.

6s and the 9s should be distinguished. Chessex dice use underlines. However, the underline on the Chessex d20 is so thin it doesn't take paint well.

The d20 should be numbered from 1 to 20, and not 0 to 9 twice.

In a set of percentile dice, the tens die should be distinguished from the ones die with an extra zero digit on each face.

Koplow

I have several sets of Koplow dice. Koplow used to sell sets where each die was a different color. I like these sets because they make it easier to find the die I want.

The dice in the above picture were sold as two sets: a set of 6 polyhedral dice, and a set of 4 "value dice".

Koplow dice are manufactured the same way as Chessex dice. The edges are more rounded than Chessex dice.

Koplow Games was founded in 1974. They make more than dice and I'm not sure when they started making polyhedral dice—I bought a few sets in 2005.

Traits for recognizing Koplow dice: opposite faces on Koplow dice don't always sum to the same value. In my set, the d6 and the d10 do, but the rest of the dice don't. Oddly, among the "value dice", the ones die does, but the the tens, hundreds, and thousands dice don't.

On a Koplow d20, the 1-face shares edges with the 6-face, 13-face, and 10-face.

6s and 9s are underlined, except on the d20, where a lower right dot is used.

I bought the "value dice" because I wanted the percentile dice. The ones, tens, and hundreds dice together make a set of per mille dice. Is such a set useful? The Treasury of Archaic Names contains a table with 1000 entries, but most players will find both the hundreds and thousands die to be superfluous.

Collecting Dice

I'll mention a few more manufacturers. Most of these are no longer in business, but good to know about if you are interested in old dice.

Creative Publications

Creative Publications started selling polyhedral dice in 1972. They were the only supplier of polyhedral dice—at least in the United States—when the original edition of the game came out in 1974. TSR resold them at prices ranging from \$1.49 to \$3.00. The dice were included with the Holmes Basic set. In fact, most dice were probably sourced by TSR directly from manufacturers in Taiwan Hong Kong.

The Creative Publications dice were made from a soft plastic that didn't wear well.  The dice would lose their color and the d20 would become nearly spherical. Players took to calling them "low impact" dice when harder dice became available.

The Creative Publications d20 was numbered 0 to 9 twice. Opposite faces have the same number. The 1-face shares edges with the 5-face, 9-face, and 6-face. Creative Publications dice are easy to identify because the same color was always used for each shape.

Creative Publications was located in Palo Alto, CA. They became a supplier of dice to gamers by accident, as they were primarily a publisher of educational titles. One of these is "Polyhedra Dice Games: For Grades K to 6" from 1978. The book contains 40 games, each of which requires one of the polyhedral dice for play. Each game requires a skill such as counting, adding, or distinguishing odd from even. Otherwise they are simple games of chance and not interesting to adults. The cover shows a sea of dice from the collection of Dale Seymour; a few of the Creative Publications dice are mixed in.
TSR also sold sets of two d20s numbered 0 to 9 twice. They were used for percentile rolls—the pink die was the tens digit. I'm not sure if Creative Publications ever sold sets with a pink die in them.

Gamescience

Gamescience has been run by Lou Zocchi since 1973. They are still in the dice-making business. Most of their dice are sold unpainted; an ultra fine Sharpie works well for inking in the numbers.

Gamescience dice are not polished, so they may have burrs left over from the molding process. The molding industry calls these burrs flash. Some people sand them down with fine sandpaper.

Gamescience made a name for itself by introducing dice made out of harder materials. In fact, if I'm not mistaken, they popularized the terms "high impact dice" and "low impact dice". They also introduced dice in a number of new shapes, the most important being the d10, which they starting manufacturing in 1980. Update: In a 2015 interview, Lou Zocchi credited TSR with introducing the first d10 circa 1980. These were the dice in the Moldvay basic box set. Zocchi also says these were the first sets with a d20 numbered 1 to 20. Gamescience was the first company to introduce a d10 numbered 00, 10, ..., 90 for the tens digit in a percentile role. The die was advertised in the April 1990 issue of Dragon magazine:

Gamescience was an early distributor of TSR products. Zocchi and Gygax were acquainted; both wrote for Guidon Games. As a reseller of TSR games, Zocchi started ordering dice from Creative Publications. Zocchi was dissatisfied with the price and the availability, so he started making his own dice—initially just a d20—in 1974.

The original Gamescience d20 was numbered 0 to 9 twice. Early gamers would ink half of the numbers with a different color so a number from 1 to 20 could be generated. In 1980 Gamescience invested in a mold where half of the faces had + next to the numbers. The dice with + signs aren't common; d20 dice numbered 1 to 20 became the standard soon after.

Some traits useful for identifying Gamescience dice: the d4 are truncated tetrahedra. The d20 has a small capital G on the 1-face in addition to the numeral 1. The d20 1-face shares edges with the 11-face, the 19-face, and the 18-face.

Opposite faces on the Gamescience d20 sum to 21, and opposite faces on the d6 sum to 7. The other dice don't have faces that sum to a consistent number.

The Armory

The Armory was a gaming shop in Baltimore, better known as a dealer in miniatures. I've read that the Armory got started in the dice business by inking or painting Gamescience dice and re-selling them. This was back in the 1970s.
Eventually they had their own molds made. The earliest Armory dice used the letter A instead of the numeral 1 on the 1-face of the d4, d8, and d20. As far as I know this was not done on the d6 and the d12.
The Armory introduced a d30 die around 1982. The older d30 is numbered 0 to 9 thrice, each digit appearing with a plus sign, minus sign, or no modifier. The newer d30 is numbered 1 to 30. The dice were supported with a book called "The Armory's 30 Sided Dice Gaming Tables". It could be used with any of the fantasy RPGs of the time.

In later years, they seem to have outsourced manufacturing to other companies. In 1998 they merged with Chessex. Dice aren't being sold under the Armory brand anymore.

TSR

TSR resold Creative Publications dice for many years. Update: the dice in the above picture come from two different molds. The blue dice came with the first printing of the Moldvay basic set. The green and orange dice came with the first printing of the Mentzer basic set. For a guide on how to distinguish them, see this post and this post.

By 1981 TSR was having their own dice manufactured. Pictured on the left below are dice from the Moldvay basic set; on the right are dice from the Cook expert set.

The dice did not come not painted or inked in. Crayons were provided to color in the numbers.

The dice seem too small to me. The dice in my expert set are a mix of colors, but I think that is atypical. I've seen all-brown and all-orange sets.

The dice in the first printing of the Mentzer basic set were sold separately in a blister pack as "Dragon Dice". They are unrelated to the collectible dice game, also called "Dragon Dice", which TSR introduced in 1995.

Saturday, November 5, 2016

Welcome to Athenopolis

Announcing a new site.

Lew wanted a site, and now we have one. The time has come for those beer-inspired ideas to be written up and posted. Let's hope they hold up to the scrutiny of the discerning public we are sure to attract.

For topics I propose one: how to play the game well. I also move to ban any and all in-world adventure narratives. On the latter point I see nods of approval all around, so I take the motion to be seconded and approved.

Comments will be open to the public. We'll see how that goes. We can just delete anything that isn't polite or on-topic.