## 31 January 2009

### The next best thing to being there

Wouldn't it be great if you could hop into the cockpit of your very own 10 meter tall walking war machine and cruise the battlefield just looking to cause trouble? Well you can ...

... after a fashion. Virtual World Entertainment is a Michigan company that builds the Tesla IITM System cockpit for the BattleTech: Firestorm game, sometimes known as Battletech pods.

From Marmalade Dog: To help celebrate the 25th year of BattleTech as well as the 20th year for its BattleTech VR attractions, Virtual World Entertainment, LLC is taking 4 of its critically acclaimed Tesla II BattleTech: Firestorm cockpits to entertainment events around the United States.

The Tesla II cockpits, featuring the BattleTech: Firestorm software, are fully enclosed military style simulators that feature 7 screens, over 90 control systems, and a 12 speaker surround sound system. When seated in the cockpit or 'pod', the player will pilot his or her own walking tank known as a BattleMech onto the virtual landscape to compete with those seated in the other cockpits for battlefield superiority.

The first stop of the 2009 tour will be at the Western Michigan University Bernhard Center during the annual 'Marmalade Dog' Game Convention hosted by the Western Michigan University Gamers Guild.

I didn't know about this convention, and now it's too late to consider attending. Maybe next year?

[Hat Tip: ConventionFans.Today]

## 29 January 2009

### SKAPH

Some friends and I have been playing a browser based game called SKAPH for about two months now. (Of course the initial attraction was the giant robots angle.) This is created by a German company, and it shows a bit in the translations to English, but the basics of the game are not too hard to figure out.

Battling robots are always nice, but SKAPH is really a game about resources and building. Your base starts with limited resources (you have crash landed on an alien planet) and you must construct mines and factories to create more, plus conduct reseach for new technology and structures. Building construction and resource accumulation is slow, paced so that players can play for a few minutes 2 or 3 times a day. Getting my first base up and running took over a week, but the construction times for basic building have since been radically reduced to help get new players into the game more quickly.

Once you get your base established, you construct a Map Room, at which point you are placed into the harsh world where others can attack you (all the other players crash landed too). Attacks become stronger as players bases grow, and alien attackers soon join the battles too. Damage is easily repaired, but your base will require regular attention. If you are persistent, your base will keep growing even when subjected to regular attacks. The only real way to lose is not to play; your base will be destroyed as multiple attacks strip away defenses and your headquarters is finally destroyed. (Caution: Attacks can be much more serious if you start on "hard", and a player in my group recently restarted to escape an unplayable starting location, surrounded by unhappy aliens.

Manage your resources well, make a few allies among your neighbors, and you will prosper. The majority of players n the game are German, but most know enough English that I can make deals with them (and there is always Google Translate, but the Germans maylaugh at you.). If you start on the "easy" difficulty level, you will be placed among other new players, and any attacks made on you won't be too harsh. Of greater concern is the resources that are stolen from you in attacks, and you will want to build defenses for protection from raiders.

There is a commercial aspect to this game, mostly in the form of ads. Additionally, your base is powered by Reactors with limited supply, and for a fee you can purchase Uranium to feed nuclear reactors, supplying greater power and making your base more efficient. Nuclear powered robots and weapons can eventually be built, but I have not progressed far enough yet to see this. The game is quite playable without spending any money on it.

And playable is the word for it. The pacing is slow, and the development of your base is spread out over weeks. This might seem frustrating, but there is a lot of satisfaction in seeing the game unfold and the difficulties encountered along the way. The game has stayed interesting for me all the while, and I'm looking forward to the next stage of research, so I start building the advanced combat units.

There are some nice animated promos too. I can't embed Flash here, but here are some links to the movies.

I could say more about actual play, and offer some tips, but part of the fun is figuring the game out for yourself. I'm open to answering question though if someone wants help.

Finally, here is a screen capture of my primary base, the green bars indicate some damage I have not repaired yet, and my current resources along the top. The in-game graphics are not so nice as the demo material, but are still effective and nicely done.

--- UPDATE:

## 27 January 2009

### Tic-Tac-Tec-Toc-Toe

Tic-Tac-Tec-Toc-Toe, get five in a row. Metadeb tipped me to this variation of Tic-Tac-Toe. It uses a larger board and the object is to get five in a row. I'm pretty sure I've played this on paper versus other people before, but I don't recall when.

I wanted to give proper credit for this online creation, so I contacted the site owner and he was kind enough to respond:

Brian writes:
You may credit to me, Brian Klug - thanks so much.

It was written for AI class at UMD. Each move, it plays "what-if" by looking at each square as its next move. There are a bunch of heuristics. There are some obvious ones, like, "does moving here make 5-in-a-row", "does this block a winning move by player", the total points earned if you would assign points to total number of pieces in a row (i.e. it will favor a square that makes TWO lines of four squares, i.e. if it formed a cross.). Finally, it also prefers to play the center of the board.

Cheers!

Even these simple rules are enough for the computer to play a decent game, and it beat me on my first try. A bit of thought and a better defense and I am able to beat it regularly. Like the simpler 3-by-3 version of Tic-tac-toe, moving first is an advantage, but it is not clear in the extended version if there is always a play-to-draw strategy for the second moving player. My intuition is that on the expanded board the number of possible moves to be blocked grows more quickly than than the opportunity to block them, and so playing to a draw is much more difficult.

## 25 January 2009

### Make Your Own D6 Rubik's Cube

Instructables has a guide to Build Your Own Rubik's Cube using magnets.

They recommend a drill press, which is not something I count among my tools, but I bet I could make do with a hand held power drill and some patience. Maybe I'll try it for myself.
[Thanks to Metadeb for the tip.]

## 21 January 2009

My wife likes Scrabble™, and she suggested I should write something about it. She pointed out the book Everything Scrabble suggests that Scrabble is a math game more than it is a word game. I hadn’t really thought much about this game before, and it seemed like a difficult topic, but I agreed to think about it and write something here (then promptly went to sleep). To my great surprise, I had the basics figured out within 24 hours. Scrabble is closely related to Nim.

I thought this might make a good example of my thought process when I look at a game, so I’ll give you the gruesome details of a game dissected.

Words: Scrabble is a complicated game, with over 100,000 words in The Official Scrabble Players Dictionary. My first thought was to consider Scrabble with fewer words, maybe even just one, or none at all, just putting down tiles in a row or column. Words are really just a kind of limit to how the tiles can be played.

Tiles: The tiles are worth differing numbers of points, and this is certainly an important part of Scrabble. However, the value of tiles players draw should be roughly equal (random, but fair) especially if we are disregarding words, so making all the tiles worth one point each is a reasonable simplification. Also, a maximum of seven tiles at a time is needed for large vocabulary of words, but without words it is arbitrary.

Board: After the other simplifications, all that is left to play for are the squares that give a player double or triple points for a single tile or entire play. I might even disregards point for tiles entirely and just play for these squares, and the player who can get the most of these squares will win. This was my “AHA!” moment where I started to recognize this as a variation of the game Nim. In scrabble you put tiles down, in Nim you pick pieces up. In Scrabble play to put your tile on the next (or last) double points square, in Nim you try not to take the last peice.

So Scrabble is a complicated sort of Nim with points gained for how and where you play the tiles, and a complicated set of rules for how you can play the tiles (ie: words).

My previous efforts at describing games using this process have all ended up with some sort of a probability distribution (including Markov chains and random walks) after I removed all aspects of player decision. Nim is different, and player decision is the key. There is no probability here, and there is always a winning strategy.

This suggests that this property of Nim, with the first moving player having a winning advantage (sometimes the second player), is a basic property of many games, maybe all games. In some games this might be reversed, with the advantage going to the player that moves second, but the cause in the same. This advantage might be small, or get lost in the added complexity and randomness of the full games (like Scrabble, Monopoly), but it probably never goes away entirely. In fact the first move (white) player advantage in Chess is well known. There are plenty of board games where order of movement is important. Battletech players will immediately recognize the advantage of winning the initiative (a random roll give the last player to move the advantage). How about sports? With the Superbowl fast approaching, Football overtime is a good example; given a choice, taking the ball first with the opportunity to score and win is a clear advantage.

Never played Nim? You can try it here.

## 20 January 2009

### More Metal Fatigue

Following up on my Metal Fatigue post, I have set up a spreadsheet to demonstrate a simple example of the Birnbaum-Saunders fatigue life probability distribution. To quickly summarize, this is the version of the Central Limit Theorem that describes how many shocks or stresses a metal part will survive before the part wears out and breaks. It also happens to describe a probability distribution that applies to many types of games. My goal is to use this as the basis for an approximation for complex games (such as Battletech). The Birnbaum-Saunders distribution (henceforth BS) ranges from 0 to positive infinity, as opposed to the Normal distribution which ranges from negative infinity to positive infinity. The BS CDF formula can be evaluated using the Normal CDF function, which is readily available in Microsoft Excel.

What I did was to set up several spreadsheets that simulate a very simple one-player game. A player starts with 35 points, and every "turn" rolls one 6-sided die and subtracts the number rolled, keeping a keeping track of the remaining points until there are zero (or less) left. The object being to determine how many turns this takes. In terms of metal fatigue, the roll of the die is the shock which makes a crack grow, until it reaches the critical length 35, and the part breaks.
That's it - A very boring sort of game, but it serves the purpose of this demonstration.

The first worksheet (cleverly named "One") demonstrates just a single observation of survival time in this simple game. The first column "t" counts the number of turns or times the die has been rolled (starting with zero), the next column "1d6" shows a random number from 1 to 6, and the column "W (remain)" keeps track of how many points are left. The last column "Game Ends on t=" shows the final turn of the game. This spreadsheet will update every time you press "F9" (in Excel) or click "Recalculate" (Google documents), and show the results for a new instance of the game.
The other columns, "m, v, s" display parameters for the distribution. If you want to tinker with the spreadsheet, you can start by changing the starting number of points in the green shaded cell.

Next I set up another worksheet ("Many") that repeats this game many times, tallies up the results and displays them (blue) along with the theoretical distribution (red). This can be updated in the same way as the previous worksheet to see a different set of results (examples to the right and below). There is some randomness to the results, but they follow nicely along with what the Central Limit Theorem says they should be.

Still awake? Still reading?? I had fun playing with the spreadsheets but an awful time trying to write about it. Boring to read too I'm sure (sorry), but an important component of certain games, and something I needed to establish for some future posts.

## 17 January 2009

### Deal or No Deal

Howie Mandel LIES. I was laying on the couch the other day and my wife has Deal or No Deal on TV. Howie says something like "There is a one-in-four chance (25%) that your case contains $1,000,000!" Exciting, but wrong. Let's start at the beginning. Deal or No Deal is a game show where the contestant first picks one from among many briefcases. Most of the cases contain a small amount of money, a few contain a lot. The contestant knows the "list" of amounts that are inside the cases, but not which case contains what amount. After picking the first case, the contestant gets to open a series of other cases and learn what is inside. With each opened case the contestant gets an offer; they can trade their case for what is offered, or after they open all the other cases first, keep the case they first selected. Now where was I ... Oh yes ... a contestant is down to 4 cases, including their original pick. One of the remaining cases contains a million dollars and then (here we go) Howie says something like "There is a one-in-four chance (25%) that the contestant's case contains$1,000,000", and Howie is wrong.

Let's pretend I am playing and start with 10 briefcases. One contains $1,000,000 and the nine others contain$1 each (we could vary this like the game, but I am simplifying). Not knowing any better, I pick a case randomly, and I have an expectation of a 1-in-10 chance it contains $1,000,000. Next, Howie lets me open 6 other cases (skipping the offers). If I am lucky and none of those 6 contain the$1,000,000 amount, then 4 cases remain and one contains the big money. If I could pick one randomly NOW, there is a 1-in-4 chance it would be the $1,000,000 case, BUT that does not change the odds for my original pick. My first pick is still a 1-in-10 chance, but the other 3 are now 1-in-4 chance(s). The difference is now I know more than I did at the start; I now know 6 cases that do not contain the big money, and this information changes the value of the remaining cases. If this seems confusing, then you are in good company, because this problem has stumped a lot of very smart people. This is a famous problem of conditional probability (famous in Math/Stat circles anyway) known as the Monty Hall Problem. I changed it around a bit to frame it as "chance of$1,000,000" rather than the usual expected value, but it is the same problem.

See The Monty Hall page for a nice online demonstration. One more thing: Howie Mandel is no Monty Hall (sorry Howie).

## 16 January 2009

### Art of The Battery

The art of Greg Broadmore and Warren Mahey at The Battery.

Much more to see at The Battery.

## 15 January 2009

### Houston, we have a problem

[This is something of a failed post - a cool idea that was too complex for a simple demonstration, and a false start on the correct solution. I've been sitting on it for almost two weeks now and haven't had time to rework it. I'll post it anyway, and maybe someone can help me fix it.]

Having discussed a simple graph paper race game, and mentioning that it would be fairly easy to turn it into a "space race" sort of game, I set out to do so. Further, I'm writing this as I'm working out how the game works in an Excel spreadsheet (does this count as live blogging?). Here is my progress so far (This may be a bit cryptic, but this is also a test for me to see if I can convey these sorts of ideas to my readers via a spreadsheet, without going into painstaking detail. Question? Please ask, and I'll try to do better.):
The green shaded cells on row 2 (turn 0) allow you to enter starting conditions for the game. The first six values are ddX/ddY, dX/dY , X/Y are for acceleration, starting vector, and starting position (all initially zero). The next six are "goal" parameters, X-Y coordinates that define the "race course" for this game, here the point (5,10), (10,5), and (15,15). The "ship" must pass within a distance of one from each of these points to successfully complete the course, which is indicate here by the first three gold shaded cells, which are "1" is the goal has been acheived and "0" otherwise. The final gold shaded cell is the number of turns needed to acheive the third and final goal.
In the green shaded columns ddX/ddY I have entered a starting condition, a series of moves that acheive each of the three goals. You can see it tool my ship 14 turns to reach the 3rd goal, and I'd like to do better. Tinkering with this by hand I could probably come up with a good solution, but I want to do this another way. Excel has an "Add-in" tool which used Newton's Method to find the solutions to mathematical formulations that meet certain criteria. This is why I set the goals in the spreadsheet, so I could use the goal to allow the Solver to help me find the best solution. So now I use Tools --> Solver ... and discovered I left something out. I need to be able to limit the thrust (ddX/ddY) to a maximum of one. I'll add this in, but it's now going to turn out a little differently than I expected. Here is the new starting solution: And now I can use the solver ... ok ... more problems ... try to imagine me banging my head on the keyboard ...
... banging my head because the solver fails and goes off to a nonsense solution, ignoring the course after the first goal. This problem trickier than I had realized, and so I have not set it up in a way that Newton's method can find the best answer, or even any answer at all.

Uncle - I give up - for now at least. I do not mind that this problem escapes me for the moment, because I had fun trying. I have a good idea of what I did wrong, so I'll think on it and try again later.

Here is the spreadsheet if you want to try it yourself.

[Epilogue]
Since I wrote that a few evenings weeks ago I came back and made another effort. It turns out my goals were a really bad way to formulate the problem. I made some marginal improvements, but nothing really worth showing off. I've made this work before, and the method deserve a better demonstration that I've given it here.

## 14 January 2009

### Guitar Hero gets a Curtain Call

There is a follow up to last months interview with Alex Rigopulos at Freakonomics, which I had mentioned previously:

There are some interesting comments from musicians on playing Guitar Hero, and comparisons of the two.

## 13 January 2009

### Law of Large Numbers is Alive and Well

I originally wrote this for the newsletter of a local statistics professional group in late August, 2002. Writing "Time to Play" reminded me of this, and after finally discovering the archived-archive where it was hiding, I have dusted it off to present as a bit of recycled writing. The only trouble was I couldn't decide which of my blogs to put it on; Science and Math, or Math and Games? Since I'm facing a bit of a time crunch this week anyway, I'll post it to both. Problem solved! (but I'll try not to make a habit of it.)

Law of Large Numbers is Alive and Well
at 2002 GENCON Games Fair

“All these people came here to play games?” said one astonished worker to another, as they walked through the midst of several thousand people at the 35th GENCON Games Fair, all busily rolling dice or shuffling cards for a dazzling variety of games. I almost trailed them to see if I could overhear more comments, but I needed to get back to my own session. However, I did continue to think about this pair, and about why people like games.

My own exploration of probability began with the boardgame Risk when I was young, and soon I was writing my own simulation programs on an Apple II+. I was fascinated by the thought of enumerating all the possible outcomes and determining the best strategy for winning the game. This self-study soon expanded to include most of my favorite games, got me hooked on computers, and eventually led me to the study of statistics and a career. I still like to study my favorite games; I love to play them, disassemble the rules, study the probabilities, put them back together again, then go play some more.

Looking over the GENCON crowds gathered in the Midwest Center, I have to believe that there are lots of people out there who are quite interested in probability, and whether they know it or not, interested in statistics too. Some of the people I spoke to are very knowledgeable of the probabilities involved in a game. Furthermore, THEY THINK IT’S FUN.

Now, when was the last time your heard someone describe their college stats class as fun? How many times have you seen people get the “your-a-WHAT” look on someone’s face when you tell them of your profession? I have personally met at least half a dozen people still in statistical-shell-shock, twenty or more years after taking an intro level stats course. How many people have you met that would consider statistics to be fun?

I am very happy being a statistician, but I sometimes think that as a profession, we haven’t done a very good job of selling ourselves. Too many people have the impression that statistics has to be dull, boring, or cryptically complex. Too many people think that statistics are something they can’t understand. It doesn’t have to be that way. I think statisticians need to try harder to increase awareness of what we do, what it’s good for, and how it can be of benefit. I think it’s very important to reach out and find ways to attract new people to our profession, and to let them know that it offers excellent opportunities.

There are plenty of people who are interested. There are plenty of people who grasp the basic concepts. I know there are, because I just saw thousands of them at GENCON. All of them were shuffling cards or rolling dice, all of them putting the Law of Large Numbers to the test, and all of them loving it.
Update - Six Years Later: The need for statistics education has not gone away. There is more and more information being presented to us every day, and our ability to process all that information is limited. A working knowledge of math and statistics is a crucial skill nowadays. I don't mean that every person needs to understand high level probability theory (heck - I don't understand all that stuff - at least not very well), but I do mean that every person needs to be educated as a consumer of information. They need to know what the numbers mean, and when they don't mean anything at all. They should have a basic understanding of how numbers are presented (descriptive stats), what they represent (estimation), and how decisions are made on this basis (inference).
I should add for the benefit of students interested in math and statistics at more than a basic level; there are a lot of jobs available to you even as an undergraduate; there are a graduate statistics programs desperate for good students and willing to pay you to go to school; there is a rich field of careers in math and stats to look forward to, and finally - if you work it right - it might be a lot of fun.

## 10 January 2009

### Touchback

I just figured out how to better use my followers list, or maybe there are new features I never noticed. I am skimming thru and picking out anything even slightly gaming related (and a bit more, but not SPAM). This should be considered a partial list. I haven't had time to review all of these in any detail, nor am I certifying the content in any way. This is sort of a way of saying "Thank you" to some of the people that have been paying attention to my ramblings (Thank You!) and building up some blog reciprocity. If I missed anyone who thinks they ought to be included here, email me so I can add your blog here.

VASSAL Notebook, Thoeursday Night Fight Club [sic]
Swizza - Video Game Guru
Creating a t/ccg/card game
Gamer Living in NYC/with Health issues
Puzzles From Monkey
20 Sided Woman
City of Amathar
Toyriffic
Games - Fun - Entertainment
Brandon's Blog, CgCook38's Poker Blog

## 09 January 2009

### A Random Walk Down Monopoly Lane

Since my Candyland post seemed to get a good response, I thought I'd take a stab at a few other games everybody knows. "How about Monopoly?", I thought. [Let's do this right at least once: it's Monopoly®.] A small amount of research revealed a wealth of material on probabilities of landing on each square, expected incomes, expected payback times, probability of landing in jail and much much more. Most of those links take you to the superb Probabilities in the Game of Monopoly page by Truman Collins. Since Truman and others have already done such a good job on this topic, and I already discussed the idea of a Markov chain earlier, I decided I needed a different angle on this game.

Describing the probabilities of landing on each square as a Markov process is useful information, and you might easily use that to improve your play, but it doesn't describe the actual progress of the game. Unlike Candyland, Monopoly isn't about what square you are on and getting to the end, it's about accumulating wealth. ALL the wealth. A full description of how this works in Monopoly would be quite long, but we might learn a bit by constructing a much simpler sort of game which just keeps track of wealth.

Consider a game where two players, call them P1 and P2, start with equal amounts of money, and each turn they trade some random amount of money to the other player. If we think about the difference in wealth between Players 1 and 2 (P1 $minus P2$), and plot this value over a series of turns, it might look something like this (to right). Here I set up a spreadsheet where each player randomly gives the other player between $0 and$19 each turn. This sort of series is known as a Random Walk.

Here is another plot with ten similar random walks. In these instances P1 is behind P2 in wealth at turn 200 (the difference is negative) more often than not. This just random variation, and if we looked at many such plots, we expect should expect that P1 will be winning (wealthier than P2) 50% of the time. In this respect the game is fair; it is completely random and no player has any advantage.

"Now what?", you say. I created a really boring game that no one would ever play. Let's make the game, which I will now refer to as "Monopoly-Walk", a little more complicated by adding or changing some rules that make it a little bit more like the original Monopoly:

1) Let each player start with $2000. 2) Let each player gain$20 per turn.
3) On each turn both players randomly give each other a randomly determined amount of money between 0% and 6% of the other player's wealth.
4) When one player controls all the wealth, the game is over.

Rules #1 and #2 are similar to Monopoly; each player starts with equal wealth, and gain wealth over time. My version has a fixed income every turn for simplicity.
Rule #3 is our random walk, but this time it's different, because if one player gains greater wealth the other will probably end up paying them more money. Neither player starts with any advantage, but sooner or later one player gains a big advantage. This is a big simplification from the original game, but it still captures the essential element of Monopoly: THE RICH GET RICHER.
Rule #4 is identical to our original Monopoly game.

So here are two plots of a game of Monopoly-Walk. These are identical plots, just a different time scales to better show what is going on. This "walk" (red line) looks much smoother than the random walks above, but the scale on the y-axis is much greater and so the difference do not look as jagged. The blue "cone" line represents the total wealth in the game (or maximum difference in wealth) as both positive and negative values. When the red line touches one of the blue, the game is over and one player has won (P1 is the difference is positive, P2 if it is negative).
In this example the players are nearly equal in wealth for the first 60 turns (difference is ~0), but then player 2 gains a small advantage which eventually leads to a win about turn 125.

Here is the spreadsheet I used to create the plots: Monopoly2.xls. You can try adjusting the starting values and see how that changes the game (See my comments for more explanation). If you don't want to try that, here are some more plots you can look at to get a better idea what is going on.

You can see here that the game usually remains somewhat "flat" at first, with no big swings in wealth. Later one, when one player has more than a tiny advantage, that advantage quickly translates into a win. Let's think a bit more about the remaining differences between this simple game and Monopoly. Monopoly has properties which must be purchased, thus reducing a player's wealth. The properties give small rent payments at first, but later on are developed (also reducing wealth) to allow greater rents, earning the owner a greater share of the other player's money on future turns. These things are a delaying effects between first acquiring wealth and turning that wealth into higher rents, and so the game remains essentially random for a longer time before one player gains a decisive advantage. Monopoly also has "taxes" that remove wealth from a player and the total wealth available in the game. This serves as another sort of delay to a player gaining that decisive advantage. These taxes also add additional randomness, making the game even less predictable. Add in three or more players and gentle random walk turns into a wild roller-coaster ride governed by luck and player moxie.

So that's my angle on the game Monopoly. I doubt it will help anyone play better, but it may allow the opportunity to appreciate a different sort of mathematical process, one that also happens to be a lot of fun.

PS: If one reader would try my spreadsheet and report success or failure, that would be appreciated.

## 06 January 2009

### BATTLETROOPS

You never know what you might find at Half-Price Books. On my last trip (just after Thanksgiving) I made a good find, a copy of Battletroops; an out-of-print FASA game set in the Battletech universe. The box was a bit crunched ...

... but upon getting home and opening the box I discovered ...

... a complete set of component in mint condition. I was (and remain) very pleased! I've been meaning to post this for weeks, but first I misplaced the images, then all holiday heck broke loose and I'm still working to get everything tied back down. In any case, I'm looking forward to getting a chance to play this soon.

## 04 January 2009

### Graph Paper Race

I remember playing a graph paper racing game when I was a kid. I'm pretty sure my Dad first taught me how to play, and I know I taught it to several of my friends. I did a little searching and found ...

Graph Racers
Racetrack (also image at right)
Race Car Game
Racetrack_(game) at Wikipedia
Vector Racer (online implementation vs human and AI players)
... no shortage of sites already covering this in great detail. A little more digging and I found several site crediting this game to Martin Gardner, who wrote the Mathematical Recreations column in Scientific American for many years (more). My Dad was always a regular reader of this magazine, so that my educated guess where he found it. There are other site listed the origin of this game as unknown or uncredited, so it's possible Gardner was simply the first to write about it.

[Edit/Update: Another good information source on this game at Chesswanks.com.]

The game Triplanetary features the same movement system on a hexagonal grid, and one of the scenarios is a race where each player must travel to each planet and return to Earth first. (On something of a tangent, one of my favorite books as a kid was Lester Dey Ray's Rocket Jockey, a high-adventure story of a race around the planets). It would not be difficult to create your own "space race" graph paper game either, if one were so inclined (and I might be so inclined).

Oh yes, vector movement, did I mention that before? This game was my first introduction to vectors, and it is still used educationally for that purpose.

Part 2 (finally posted, but it did not turn out too well).

## 03 January 2009

### This and That

Want to know what happens when your blog gets "Noted"? The chart to the right is my web traffic from December 12th through the 31st (via StatCounter). It's actually a bit frightening.
I wrote a full post about it on my other blog.

How simple can a game be, and still be a game? Greg Costikyan writes about MS Paint Adventures at Play This Thing.

A site called SCIFI CHROME; and interesting mix of scifi, martial arts movies, gaming, how to tie a necktie, Battletech novels, anime, and ... wait ... what was that part about neckties again?

Finally, Zero Punctuation reviews Prince of Persia. I don't play the game, I don't plan to, I don't even know what platform it runs on, but I never miss a Zero Punctation because Yahtzee makes me bust a gut laughing every time. If you aren't already familiar with ZP, well ... just make sure the kids aren't in earshot.

## 02 January 2009

### With a name like this ...

With a blog named Giant Battling Robots, how can I resist!

[Found on Stomp Tokyo]
Though I admittedly have little knowledge in the genre of Japanese sci-fi, I do know one thing: when a UFO crashes into the ocean near Tokyo, chances are pretty good that an attack on the city by a giant monster is inherent. Call it intuition.

---
How about a MMORPG, Exteel. I haven't played it, by IO9 gave it a nice review. Apparently it's more combat than RPG.

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[And this, from TVtropes]
Who needs an Abrams tank when you can have a 100-foot man-shaped robot with a glowing sword and a fist that fires off like a missile? There's no argument - fighting robots are just infinitely cooler than ordinary vehicles. Whatever their shape, though, they are all known as "mecha". The "mecha", or "giant robot", concept is ubiquitous in Japanese pop culture, and is more than adequately represented in anime. Despite the name, the robots need not actually be "giant" - some are merely human-sized, and some even smaller. They range from the boomers and hardsuits of Bubblegum Crisis, to the Tengen Toppa Gurren Lagann big enough to use galaxies as shuriken (no, really!).
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Giant Robots Smashing into other Robots.
Needs more smashing!
But maybe they just want to get dome work done.

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Coincidence or Copycat? What is the difference between a Giant Robot and a Big Giant Robot anyway? I suppose there is room enough on the internet for the two of us. ;-)

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[from Mecha Image of the Day - here]
Finally, here is my kind of Giant Battling Robot from the game Battletech.

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So many robots, so little time. Maybe post your favorites here?

## 01 January 2009

### Ars Ludi, and the Battle of Chuck E. Cheese

I don't really get into role playing game anymore, but I can recognize a good thing when I see it. Ben Robbins writes a blog about role playing and RP games. These posts caught my interest ...

Not So Grand Experiments: the Battle of Chuck E. Cheese
and
Not So Grand Experiments: the Battle of Chuck E. Cheese (part 2)

... but there is much more to see. I'm adding this to my blog roll, and recommended it to those who like role playing, or if you want to find out what good role playing games are supposed to be.

### Mind Games

Cognitive Daily has a collection of Brain-Teaser games. Play them! It's good for you!!

[Labyrinth Puzzle from XKCD]

Happy New Year too.