Doug Chaffe

Update [7/14/11]: Catalyst Game Labs is hosting a sale of Doug Chaffe original artwork at Gencon 2001.


Randall Bills writes about the passing of Doug Chaffee. Better go read that first. Here is Randall's opening paragraph.

In 1994 I walked into a game store and beheld BattleTech’s CityTech Second Edition on a shelf. The cover was by an artist I’d not seen before, but it was action-packed, evocative, and wonderfully done…everything a fan could ask from a cover. Of course I left with it under my arm. For the next 15 plus years Doug Chaffee would be an indelible part of crafting the visuals for BattleTech.

I confess I didn't know anything about Doug Chaffee before this, but Battletech players should know his work on sight ...

Image: Chaffee Studios

... because it is nothing short of iconic. Much more to be found at Chaffee Studios.

Here are a few links that my be of interest:
Battletech Wiki: Doug Chaffee
Book Illustrations

The Grinder

\                                                                                                                                                             This edition of The Grinder is brought to you with the assistance of Darwin the cockatiel, who inserted the backslash at the beginning of this post, and bit at my fingers as I type this. I haven't been posting much lately, but I have been writing, and hopefully some of that will find its way back here soon.
Now on with the Grind.

Some fun with Game Theory on the British show QI (short for "Quite Interesting").

[Via Terrence Tao's Buzz]


Airships for the 21st Century
Which has nothing to do with games or math; I just think it's cool.
[Hat Tip David Brin on Twitter]

Some cool new art for Magic-The-Gathering at IO9. 

Mo Rocca visits Gen-Con and plays boardgames: Video at CBS News.


Is it just me, or does everybody have friends that ask them questions about counting problems and combinatorics? (I'm looking at YOU, RR!)
Somehow, I think it's just me.

Ian Schreiber writes about education and games at Teaching Game Design: My Problem With Gamification.

 The Last Cause is a movie in pre-pre-production, but it has mechs and clones, so Battletech players are likely to take notice.
Edit (2016): This early Kickstater success is now considered on of it's biggest early failures. Oh well.



Game Designer, Graphic Designer, Wargamer Extrodinaire, and a bit of gaming history I should probably already know, but somehow didn't: Redmond Simonsen. Go read about him. [Hat Tip 2 Grog News]

Fletcher Pratt's Naval Wargame

John Curry, editor of the History of Wargaming Project, has a new book out:

I first wrote about Fletcher Pratt's Naval Wargame almost two years ago in The Origin of Battletech. At the time a new edition of the book was still in the works, so I waited to get it. This edition includes some previously unpublished material from some of Pratt's original players and umpires.

My copy is on order, and I'm looking forward to seeing it soon. Maybe I will organize a local play session? 

Information link: http://www.wargaming.co/rules/fletcherpratt/homepage.htm

Purchase link: http://www.wargaming.co/purchaserules/homepage.htm

Sicherman's Dice

There is something different about these dice - can you spot it? I'm guessing you'll get it right away ...

Image found at Chuck-A-Con *

You can't see the non-facing sides, but the d6 on the left is labeled with 1-2-2-3-3-4, and on the right labeled with 1-3-4-5-6-8 (like this). That's not our standard 1-2-3-4-5-6, and if someone rolled these on the gaming table the 8-pip is a dead giveaway that something is off.

Now here's the trick: The probability distribution for the sum of these Sicherman Dice is identical to the distribution of the standard 2d6, so if you only see the results (the sum) there is no difference at all.

The mathematics for this gets into Generating Functions and Combinatorics, but essentially it involves doing the algebra to show that:

(x + x² + x³ + x⁴ + x⁵ + x⁶)² = (x + 2x² + 2x³ + x⁴)(x + x³ + x⁴ + x⁵ + x⁶ + x⁸)

Where the left-hand-side is the generating function for the sum of two standard 6-sided dice, and the right-hand-side is the appropriately factored generating function for the sum of Sicherman's dice. (OK, maybe a little harder than that.) There is only one way of doing this with 6-sided dice, but such variations exist for other polyhedral dice. It seems to be possible in general to do this with N-sided dice, and there might be multiple ways of doing this for some. The Mathematics Magazine article "Renumbering of the Faces of Dice" by Duane Broline (1979) goes into some detail, but I cannot access the full article from home. If I can grab it at work maybe there will be an addendum.

The Hard Way

I tried this working out possible numberings for Sicherman-type 2d8 dice by scribbling with pencil and paper until I found a combination that worked. On my third-and-a-half attempt I came up with 1-2-2-3-3-4-4-5, and 1-3-4-6-6-8-9-11. CORRECTION: TPC checked more carefully than I did, and offers 1-3-5-5-7-7-9-11 in place.  It took me a while to work this out "the hard way", but it was probably still faster than I could have factored a 16^th-order polynomial**.

[Hat-Tip to The Endeavor/John Cook. Again!]
[As seen on Eon.]
* Sicherman Dice are available from Amazon, or directly from Gamestation - Gamestation.net is likely the original source for the image I used above.
** "Dammit Jim, I'm a statistician, not a combinatrician!"