Gaming Chess

I don’t play chess – as cerebral as the game is supposed to be, it somehow never really appealed to me, perhaps because the level of abstraction in chess was to high for my tastes.  Sure there are kings and knights and such locked in mortal combat.  But, I’ve always reasoned, at its heart, Chess is really a math problem.  The kings and queens and knights and bishops are just trappings.  You could call those pieces anything you want, and the math works out the same.  In theory, chess can be solved

And I never really found that particularly inspiring.  

Well, now I’ve started a new semester, and one class – called “Strategic Decision Analysis” – has really caught my interest.  Considering that one of the primary topics of study in the class is Game Theory, I suppose that comes as no surprise. 

Game Theory, as the term is intended to be applied, is meant to be a study of the competitive actions taken by two or more “players” whose interactions are, well, interactive, such that the actions of one player affect the decisions and actions of another, each trying to get to some desired outcome or result.  Wow, that’s a lot of words… but what it boils down to is: game theory isn’t about games like you or I know them, it’s about nations, corporations, and individuals struggling to get what they want in a world where other people are trying to get what they want.  In MBA school we study it for its effect on business. 

But even so, the concepts of Game Theory can be applied, no surprise here, to actual games.  You know, the ones you play for fun

And that includes Chess – a game, incidentally, which I typically don’t play for fun – vis-à-vis the aforementioned distaste for the math of it all – but about which I am fascinated nonetheless. 

In class this week, we began looking at an application of Decision Trees in “Sequential Games”.  Sequential Games, boiled down really simply, are games where one player takes a turn then another player takes a turn.  (That’s not really the definition – it’s a lot more complicated than that, and turns don’t necessarily instantly pass to other players, etc. – but it’s close enough for our purposes here.  )  Chess, obviously, is a great example of a Sequential Game.  As the class went, I began imagining the Decision Tree for a game of Chess.  This,  I realized, is how you solve Chess

What does a Decision Tree for a Sequential Game look like?  Well, you have but to ask, and Wikipedia doth provide: 

A Decision Tree for a Simple "Battle of the Sexes" Game

A Decision Tree for a Simple "Battle of the Sexes/Bullfight" Game

In this “game”, a husband and a wife are trying to decide where to go for the evening.  They are both away from each other with no means to communicate, so each will drive to one of the events – either a “Bullfight” or an “Opera”, separately, and simply expect the other to be there.  (In reality, as presented in the description on Wikipedia, this game would be a Simultaneous Game, not a Sequential One, but since we’ve got this handy tree, we’ll treat it as Sequential.)  Each has a decision.  The Wife knows the husband prefers the Bullfight and the Husband knows the Wife prefers the Opera.  How much they enjoy their evening depends on where they end up – indicated by the scores on the right hand side of the tree (higher scores are better).  So, for example, if the Wife decides to go to the Opera, the Husband, to maximize his score, ought also to go to the Opera – even though he would prefer the Bullfight, we prefers time with his Wife even more.  Likewise if the Wife decides to go to the Bullfight, the Husband ought happily to go as well.  If he ends up at the Opera instead, both Husband and Wife will be at their least-favorite destination alone, and both lose

That’s a rather simple game.  There are only two moves, one to each player. 

So, what would the Decision Tree for Chess look like, I wondered?  I began to imagine. 

It turns out, there are about twenty possible opening moves in Chess.  White goes first, and can move any of 8 pawns (each with two possible moves) or 2 Knights (each also with two possible moves).  So, where you see the Wife’s first move in that tree above, the gray box labeled “a”, imagine that with twenty lines coming out of it.  In response, the Black player has another twenty possible moves.  So those twenty lines go to twenty decision boxes for Black’s move.  Each of those twenty boxes has twenty lines coming out as well. 

And so it goes.  Back and forth.  The math gets pretty complex pretty quickly – some moves, once taken, invalidate the possibility for other moves.  Other moves, like crossing the board with your Pawn, open up a whole new universe of possible moves.  In fact, my professor postulated this week, there are more possible combinations of moves in Chess than there are stars in the universe. 

Yes, Chess is a math problem, and it can be solved.  In theory.  But in practice, you would need a super-computer the size of the entire universe to do it. 

So, how is it that Chess Champions do what they do?  How is it that Deep Blue – a super computer not the size of the Universe – beat Chess Champ Garry Kasparov

Well, they’re not solving the whole tree.  Not even Deep Blue.  Instead, man and computer both have typically developed heuristic models of the game – they memorize positions and relate them to other positions in the game, either favorable or unfavorable, and try to maneuver the pieces to their advantage.  Even Deep Blue, which was capable of brute-force calculating the game to a farther degree than any other computer, couldn’t solve for the entire game – it lost to Kasparov in several bouts. 

So, why has this exploration fascinated me that I’ve written such a long blog post about it?  Honestly, it’s hard to pin down.  In some way, a part of me wants to like Chess – but even knowing that as a practical matter Chess can’t really be solves like an equation does little to lessen my distaste for actually playing the game.  And neither does getting beaten at it, over and over, by my laptop (Deep Blue it is not).   In other ways, though, I guess I see Chess as analogous to the history of all games, and in another way, as analogous to the history of the Fantasy genre.  Chess was once the Kingly game.  Is there not certain to be such a game that is common and popular in a fantasy world not only of Kings and Knights but also of Wizards and Dragons?

The Longest Road

It’s been a crazy couple of weeks here at the Undiscovered Author, traffic-wise.  They’ve been my busiest weeks yet!  Some 370 hits last week, and almost as many this week already.

But, the funny thing is, although I’ve had some fairly popular posts these past few weeks (especially “What’s Hot, What’s Cool“, and my essay on Steampunk-inspired Societies, as well as my sci-fi flash, “Kathryn’s Child“) – but it hasn’t been the cool new things I’ve been talking about that have really driven my site stats up.

It’s been this.  In the past week alone, that page has gotten over 130 hits.  What’s driven that traffic has been a single phrase: “Settlers of Catan”.  I’ve gotten 102 hits from that search phrase in the past 7 days, and more from related search phrases (like “Settlers”, “Catan Board Game”, and “Settlers of Catan 3D”)

Frankly… I’m not sure why this is happening.  For one thing, my blog doesn’t appear anywhere in the Google search for that phrase for at least the first fifteen pages (I gave up looking for my blog after that), nor in the Bing search for at least ten (again, I gave up) [Note: I realize I may have actually increased my search ranking for these terms by posting this page, but hey, what’re you gonna do?).  Whoever these people are driving this traffic, they have to be desperate for some news on the game.  (Note, if you’re desperate for news on Settlers, I advise you check the official News page, here, which is easily in the first few hits for those sorts of search terms.)

Anyway, I’m just amused by this.  And a little sad that there’s clearly this hunger out there on the internet for something about Settlers of Catan, and here all I can do is say “yeah, I like the game.  My Dear Wife and I probably play it at least once a month.  It kicks the trash out of Monopoly.”

(Footnote: For those who aren’t familiar with the game, the title of today’s post is an in-joke that refers back to the game: specifically a sneaky way to snatch victory in the game suddenly, even if you’re behind.)

More of the Games We Play

Yesterday, I began talking about board games.  Although I had friends who were avid players of “Settlers of Catan” prior to meeting the future Dear Wife, and although I had the desire to give the game a try, I never actually played until Dear Wife-to-be came along.  Dear Wife was then and is now a very skilled player of Settlers.  I’ve kept stats in the past; she beats me at it roughly 3 times out of 4.  (This roughly corresponds to her win-rate at other, non-Settlers games as well, considered collectively.  There are some we have which I quite literally never win, and some where I actually have the advantage, but as a rule she wins most of our games.  I am slowly coming to peace with this.) 

A fancy version of Settlers

A fancy version of Settlers with a 3-D miniature board set up with the Cities & Knights expansion.

Settlers, for the uninitiated, is a game where you attempt to exploit the natural resources of a small island in order to build towns and cities.  You gain points for each town or city built.  The rules are fairly complex, but once you get the hang of it, the handy reference card that comes with the game is all you’ll need to stay refreshed on what it costs to build this or that.  The game board is a series of hexagonal tiles laid out at random in the shape of an island.  Each tile represents a different kind of terrain, which generates a different resource.  Chips placed on each tile indicate which die roll, on a roll of two six-sided dice, will cause that tile to produce a resource.  Statistically, numbers closer to seven will come up on a “2d6” roll more frequently, so tiles with these numbers are considered more valuable (but the actual value of seven is reserved for a different effect, so that when a player rolls 7, no tiles produce a resource).  Each turn, the active player rolls 2d6, and every player that has a city or town adjacent to a terrain tile that produces a resource on that turn collects some of the resource produced.  Cities and towns are placed at the vertices of the the hexagonal tiles, so each city or town borders on three different terrain tiles.  After collecting resources, the active player can build cities, town, roads, and other things, or trade resources with other players or the bank. 

Because the game board is laid out randomly with each game (the number of tiles doesn’t change, but their placement in relation to each other, and which tiles are associated with which die rolls does), the strategic complexity varies with each play.  The strategy that is most effective in one game may not generate the same results in the next game, because of the dramatic differences brought about by the board layout.  This gives Settlers a lot of replayability.  As the gateway drug for strategic board games, Settlers also introduced many of us to the idea of “expansions” for board games.  In the image above, for instance, the game is set up with the “Cities & Knights” expansion, which adds Viking raiders, knights for defense, and a secondary group of resources called “Commodities”.  There are several other types of expansions, including expansions for number of players (increasing the base game designed for 3 to 4 players to a larger board that can have 5 or 6 players), and multiple other variant rule-changes. 

For Dear Wife, Settlers was only the first of several new games she learned in the years before we met, and she owned copies of several of these games, games like Carcasonne, Ticket to Ride, Fluxx and Guillotine.  (Of those, besides Settlers, Ticket to Ride has been our next favorite.)  Since meeting, however, we’ve added to our game collection, and now I’m pretty proud of the number of games we own!  One of the first additions to our game collection was a simple card game called “Take the Train” and the high-speed Scrabble-like game “Bananagrams“, and “Bohnanza“.  All are fun enough, but the really cool additions have been “Qwirkle“, “Colosseum“, “Shadows Over Camelot“, and our most recent addition, “Smallworld“. 

In “Ticket to Ride” players are attempting to build a railway network connecting the cities on a map.  Each player has a list of routes they are attempting to complete, and must collect different-colored train cards that correspond to the colored routes on the game board.  “Bananagrams” is basically Scrabble without turns or points: the winner is the first person to build a crossword and go out once all the tiles have been drawn.    “Bohnanza” is a fun card game where you are trying to make money by harvesting “beans” (Bohn is apparently German for “Bean”).  Each of the cards is a whimsical type of bean (“Soy Beans” are dressed like yuppies, “Chili Beans” are fiery southwestern types, “Green Beans” look sick to their stomachs).  You try to collect matching beans, because the more of the same type of bean you plant in your field, the more you make when you harvest.  The trick: you have to plant in the same order that you draw the cards, you only have  couple of fields, and you can only plant one type of bean in a field at a time.  “Qwirkle” is a tile game that’s a bit like Scrabble, but with shapes and colors.   You score as you make rows and columns of tiles where the colors and shapes each either all match or are all different. 

A game of Colosseum set up to play

A game of Colosseum set up to play

“Colosseum” is another game that, like Settlers, is pretty complex.  There are a lot of different little bits and pieces to the game, and there’s a lot going on.  But at it’s core, it’s pretty simple.  You’re putting on exhibitional and gladiatorial shows at the Colosseum.  You need certain resources to put on these shows – like actors, gladiators, lions, chariots, and set-pieces – which the players bid on.  Then you try to put on a show using the resources you have: bigger more extravagant shows draw bigger crowds and earn more money, which you can use to buy more resources and other things to help draw bigger crowds, attract the attention of the Emperor, Consuls, or Senators and put on bigger shows.  After a set number of turns, the player who’s put on the single greatest spectacle wins.  

A game of Shadows Over Camelot in progress

A game of Shadows Over Camelot in progress

“Shadows over Camelot” has become another favorite.  Of the list here, it’s the only one that’s a non-competitive game.  In other words, it’s cooperative.  In this game, the players are each one of the mythical Knights of the Round Table, each is endowed with a special power, and all are trying to stave off the dark forces intent on destroying Camelot.  In the game, there are several “Quests” to which the Knights can lend their effort, such as the “Quest for the Grail” or the “Quest for Excalibur” or staving off one of the various barbarian bands laying seige to Camelot.  Each quest has a risk of failure, because at the start of each turn, players have to draw and play a card that causes an evil effect before the player can do anything to try to advance one of the quests by playing good cards.  And even though the players are cooperating, they can’t share information about what they have in their hand.  The game can become really intense (especially if you use the advanced rule that allows for one player to be a “traitor” secretly working for the enemies of Camelot) as the forces of evil progress closer and closer to victory, and the final fate of Camelot comes to hinge on the outcome of a single action. 

Smallworld out of the box!

Smallworld out of the box!

Last, but not least, we recently had a chance to play (and add to our collection) the game “Smallworld”.  Smallworld is an irreverent strategy game of world domination fought between stereotyped fantasy races, like Elves, Dwarves, Wizards, and Zombies.  In this game, players represent one of any number of archetypal fantasy races and attempts to control the map of the small world in which the game takes place.  Eventually, the player’s race will become overextended and will go into decline, and the player will abandon that race to champion a new race.  Players accumulate points by holding more territory and earning gold from their possessions.  After a pre-determined number of turns, the game ends, and the player having earned the most gold wins.  Again, it’s a game with a lot of moving parts (there are around a dozen fantasy races, and even more combinations of special powers, and several more bits and pieces), but the game play is fundamentally simple and yet ingeniously complex in execution.  One neat feature of this game is that a player may have to change strides in mid-game and adjust his strategy when he abandons his old race to start over with a new one.  Each race and power combination will play a little differently. 

When possible, Dear Wife and I don’t like to let too many weeks go by without playing a game or two.  We don’t get cable TV, and we don’t go out to the movies much, so this is one of the most important forms of entertainment in our home.  While the purchase of a single board game may cost us more than a night at the movies, we know it’s an investment in hours of fun that we’ll return to time and again. 

And it doesn’t stop there.  Both of us have a bit of a creative side (I suppose that goes without saying, in my case, since I fancy myself a writer), and some time ago we started batting around ideas for a board game of our own design.  That’s a hobby that’s been on the back burner since my school ramped up in intensity, but it’s one we’re sure to return to in the future.  If and when we do, you can be sure I’ll blog about it, here! 

Happy gaming!

The Games We Play

I’m surprised to realize I haven’t really talked about this before, in any depth, considering how important of a topic this is in my life.You see, Dear Wife and I, we love games.

I don’t mean that in the way that most people like to sit down and play a little Monopoly or Yahtzee or something.  Nothing wrong with those games, per se, but they definitely aren’t on the top of the stack of games we pull out when we want to play a game together.  I mean serious games – strategy games and board games, and other games you’ve never heard of.

I’d say Dear Wife and I sit down to play a game on average about 1.5 times per week – either just us together, with another couple or group of friends, or at a local, organized game night.  Some weeks we go without any games (especially weeks that are busy at school).  Others we might play several games.

A Game of Risk in progress

A Game of Risk in progress

 Myself, I’ve always loved games, I think.  Growing up I’d occasionally play Risk with my dad.  That ended during a particularly contentious match that Dad was losing pretty badly.  I grew weary of his complaining about the bad die rolls, so I threw the game.  (And by “threw” the game, I mean I intentionally lost; I stopped attacking my dad’s territories, which is the only real strategy in Risk.  I didn’t pick up the board and physically throw it, as animated as that might seem.)

A Game of D&D in progress

A Game of D&D in progress

 Around that same time in my life, I discovered “Dungeons & Dragons” and, shortly after, the card game “Magic: the Gathering“.  Those are a couple of games that have earned a really bad rap, undeservedly so.  Dungeons & Dragons (abbreviated as D&D by players and fans), often cited as the first and original fantasy role-playing game, is really a game about the imagination.  It’s a game that takes its cues from fantasy literature – the original edition of D&D listed a hefty group of fantasy novels and mythological source material that served as part of the inspiration for the D&D game, and it included everything from Tolkien’s Lord of the Rings to Vance’s Dying Earth to works by Poul Anderson and Michael Moorcock.  The promise of D&D has always been the opportunity for players to play out the adventures of their favorite fantasy stories, and to give them control over the narrative.  What I’ve always loved about D&D is the cooperative nature of the game.  There aren’t “winners” and “losers” in a game of D&D.  Instead, the players work together to overcome some obstacle or reach some goal (which usually would include defeating some powerful monster in combat).  Some people, it is true, play the game in an adversarial way, but that method of play has never appealed to me.  I think it’s this cooperative nature of the game, and the story-telling potential, that drew me to it.

 Magic: the Gathering (M:tG) is similar, but plays out in cards.  Unlike D&D, it is a competitive game, but it’s also very strategic, as players attempt to outwit their opponent by playing combinations of cards that describe fanciful and powerful magical effects that slowly eat away at the opponent’s pool of game points.  The conceit of M:tG is that the game plays out as a duel between two powerful wizards who are casting spells and summoning fantasy-inspired armies to do battle against each other until either one or the other has exhausted himself and falls in battle.  Again, it’s a game of imagination.

The bad rap these two games have gotten is due largely to the obsessive way in which its adherents play the game.  In my first year of High School out in California, where Magic was big, I remember large groups of people filling one of the quads at school with their M:tG decks pulled out and engaged in one-on-one or multi-party duels for supremacy in the imaginary landscape of the game.  And there are many people who remember the scares in the 1970s that inspired the movie “Mazes and Monsters” the events of which, it turns out, had nothing actually to do with the D&D game.  But it’s true that players of D&D and even Magic will often willingly give up whole afternoons and nights at a time to play the game.  But it’s for more than just the game… for many of its players, opportunities to play these games are also important social events and opportunities to excercise their creative faculties in safe and meaningful ways.

I haven’t played Dungeons & Dragons nor Magic in a good four years: not since I moved to the city.  It’s not for lack of desire to play, but for lack of time and for lack of having a group of friends in the area that I know play these games.  It’s a curious thing: there’s such a stigma on playing games like these that even in the company of other fantasy and science fiction nerds it’s still taboo to mention D&D.  And yet, it’s precisely in this population where I’m most likely to find fellow players.  Still, D&D done properly is a significant investment of time (the stories told in each game typically unfold over multiple gaming sessions), and that’s not time I have to give to it, these days.  Someday, perhaps I will again. 

A Game of Settlers of Catan set up and ready to play

A Game of Settlers of Catan set up and ready to play

For me, I’ve managed to fill the void with some games that scratch a few similar itches.  When I moved to the city, I learned about the first of these that I would eventually play: “The Settlers of Catan“.   Settlers, as players typically call it, is called by some the “gateway board game”.  It’s often one of the first unusual strategy games (you know, a game published not by Milton Bradley, Parker Brothers, or Hasbro, who collectively own the mainstream board game market in the U.S.).  If someone tries Settlers and enjoys the experience, there are decent odds that he or she will eventually move on to try other even more unusual board games.  I had several friends in the city who were avid players of Settlers, and though I wanted to give it a try (thinking it might be a suitable replacement for D&D), I never quite got around to it. 

Not, that is, until Dear Wife came along (in the days before she was Dear Wife).  But that’s a story for another day. 

By which I mean: tomorrow. 

Happy Gaming!