Author Archive

The Optimal Play
December 4, 2009

Ok, so the other day I was playing a 5 player game of Settlers with a few friends. The game got unusually close and heated toward the end, with a 9-6-6-6-6 score. We’ll call the player with 9 points “Alex.” I was sadly one of the sixers tied for second. Alex had just taken Longest Road, which catapulted him from a safe 7 to an unsettling 9 (10 points wins the game). The general consensus was that Alex had the game on his next turn if he was allowed to keep Longest Road. Unfortunately for us, he held the Longest Road by a large margin and we determined that none of us could overcome it alone. After some discussion and plotting, however, we determined that if we all pooled our resources we could grant one of us enough to steal Longest Road (turning the score into 8-7-6-6-6). Alex’s turn had just ended. What would you do?

This is a troubling situation from every player’s perspective. Alex realizes that his best chance at victory lies in us doing nothing. And although we recognize that Alex will likely win if we don’t act, we also recognize that whoever we grant the resources to will be given an enormous advantage and will likely win themselves. This outcome is no better than Alex winning. So what is the optimum play here?

Let’s define what an “optimum play” is (which was what the ensuing argument at our game table was about). Two definitions were considered in the argument: “the play that garners the individual player the greatest chance of victory” (my definition), and “the play that creates the most ‘fun’ and generally minimizes the use of any douchebaggery.” These definitions are each very difficult to assess. How can you measure how an option effects your chance at victory? How can you measure how much fun is generated from your actions? I’ve come to expect that all players in a game should always act in a way that optimizes their odds of victory, but what does “victory” mean?

Let’s switch gears and consider a simple analogous 3 player free for all Starcraft game. Really any multiplayer FFA strategy game will do for this analogy. Player 1 is currently winning, player 2 has about 70% the strength of player 1, and player 3 has about 40% the strength of player 1. Without cooperation players 2 and 3 are essentially doomed, but if they work together they are 10% stronger than player 1. Player 2 should want cooperation the most, as he stands the best chance to come in first once player 1 is eliminated. Now player 3 has little chance at first place, but can choose between second and third (second if he cooperates, third if he doesn’t). The question then is “what is the difference in value that player 3 puts on getting second versus third?” Interestingly, I contend this depends on the particular game and player. In Starcraft, I personally would much rather be second than third. In Settlers, I personally value all non-first places to be about equal (if you’re not first, you’re last).

If the last place players place significantly different values on non-first positions, then we can expect them to behave in a way that maximizes their odds of attaining the highest place they can whereas if they care only for first place they will behave in a way that maximizes their odds of attaining first place. If our Starcraft player 3 cares about non-first positions, then their behavior is easy to predict: they will cooperate with player 2. If they only care about first place, they will behave much more erratically. They might give up hope and just cripple a player based on personal vendettas, they might ally themselves with player 1 and backstab them when they’re weak, they might do the same to player 2 in a desperate attempt at first place. In reality, a player probably experiences some mix of these two victory perspectives, but the mix is probably more or less unique to the specific game and player.

Now that we have defined “victory” I will invoke a concept from basic economics and claim that any “rational” player will act in a way that optimizes their odds of victory. Sure, they could do otherwise. I’ve played with players who get bored of a game and decide to help the winning player just so the game ends faster. I’ve played with players who simply don’t understand the game and make nonsense moves. I’ve played with players who just like “the pretty colors” and make their moves purely on whims. These actions, however, are not rational in the context of the game. In a 6 player game of Monopoly all players could elect to sign over all property and money to a single player and end the game instantly (which in all fairness would probably be the best way to go about playing that horrid game), but do you consider this a “game of Monopoly?” Certainly not. Any reasonable game requires a push and pull of opposing wills struggling for their individual victory. Without that you simply have madness.

So finally, optimal play: “the play that garners the individual player the greatest chance of victory.”

Ok, let’s come full circle to our Settler’s game. If we assume that the players put a reasonable amount of value in non-first positions then we can assume that they would not cooperate to dethrone first place. Why? Because the score would then be 8-7-6-6-6 and dooms the majority to third place or worse. If Alex was allowed to win, then the remaining players (6-6-6-6) would each have a much better shot at second place.

But this was not the case. Apparently, we place high value on first place and very little on even second place in Settler’s. We all conspired to grant one of us (myself as it turned out) nearly every resource available on the table in order to outbuild Alex. This is of course the expected outcome, because if Alex is allowed to take first then it definitively denies it to all other players. Even by widening the 1 point victory gap to 2 points, the majority gives itself just a little more breathing room to get to first.

Sadly we’ll never know how the game would have ended. Everyone felt extremely unhappy about this massive exploitation of the rules and we all gave up after the decision was reached. It’s unfortunate that the nature of the game induced this kind of behavior. An optimal play should never produce such a massive feeling of “brokenness.” This is a failing on the design of the game, and surprisingly I’ve seen this happen many times during my Settler’s career. Tip for game designers: don’t encourage massive acts of collusion. It just makes us upset.


Left 4 Dead: Compelling Co-op
November 12, 2009

On the eve of the release of the sequel to one of my favorite FPS’s of all time, Left 4 Dead, I would like to explore what I believe to be its greatest design strength: its implementation of the classic co-operative mode (one would hope this is its greatest strength, as the whole game is really just one massive co-op romp).

For this analysis, we’ll assume that the players are playing on a difficulty commensurate with their ability (one very good player can more or less solo a campaign on easy mode). Under this assumption, it’s safe to say this game is very hard. This can be a frequently overlooked design choice in a game, but its difficulty is very central to how it appeals to its audience. Make the game too easy, and its boring; make it too hard and you risk frustrating your players. Most games get around the “too easy” problem by adding additional difficulty levels, but the “too hard” problem is a bit more delicate. Hardcore players will strive to beat the game on the hardest difficulty, and accordingly it should be just difficult enough to provide them with an extreme challenge while still being possible to defeat.

Left 4 Dead does an exceptional job of balancing these difficulty levels (often with the help of the AI Director, who makes subtle tweaks to the difficulty based on the players’ performance). The most important effect of this extreme difficulty is it requires the players to work together seamlessly. Even one weak link in the group will bring down the entire party. This is of course a blessing and a curse. For just as it is extraordinarily fulfilling to work together like a well oiled machine, it’s equally irritating to fail time after time due to a less experienced teammate.

One of the annoying problems with many co-op games is that players tend to compete viciously for items and weapons. This rivalry often turns into a meta-game within itself to see who can collect the best stuff, and therefore make the most progress toward the objective (kill the most bad guys, etc.). This does not foster a team mentality and usually detracts from a co-op experience. Fortunately, weapons in L4D are infinite. If everyone wants the shotgun, they can all pick up an instance of the shotgun. Granted, this detracts from the realism, but the benefit in gameplay more than makes up for that. The items that players can get a bit greedy with are the finite health items (med packs or pills) but the player greed here is offset by their will to beat the level. If myself and my terribly wounded partner are the last two remaining in the party, and I’ve been hoarding the last med pack, I’m very willing to give it up because I realize that without him I have no chance of survival. Which brings me to my next point: the dangers of going it alone.

Anyone familiar with the game has come to this unfortunate revelation early in their career: if you’re alone you’re as good as dead. The special zombies have been carefully tailored to wreak the most havoc on lone individuals. The hunter will pin your helpless body down until your dead. The smoker will do the same thing to a loner, but has the added advantage of being able to easily pick off stragglers as well. The boomer, while a bit more complex in that it doesnt explicitly incapacitate the players, makes it extremely difficult for a loner to defend themselves. These foes are designed especially to keep the party tight and working together (if by no other way than natural selection). This ensures that the party doesn’t develop that oh too common hurried leader that runs ahead and kills everything before anyone else gets to have any fun. That guy’s dead outta the starting gate.

One fun twist in the game theory behind surviving the level is that only one person needs to survive for the party to advance to the next level. There comes a point in the game, when the safe room is in sight, when suddenly chaos breaks out and it’s every man for himself. Inevitably, some players will be left for dead (I couldn’t resist). This is often the most tense and usually hilarious segment of the level, when the alliances all suddenly crumble in favor of individual survival. While those left for dead can sometimes feel abandoned and bitter over this, the game leaves them some comfort in knowing that only one of them needs to make it and that they gave their life for the good of the team.

All in all, L4D is truly a model of a well thought out cooperative game. Sure its got its quirks, and player skill can often influence how fun the game is, but its not too hard to get good at (as far as FPS’s go) and has incredible replay value. Way to go Valve! And I anxiously await L4D2 (or, as I was hoping it would be called, L5D).

European Vs. American Style Board Games
October 29, 2009

In a previous post I touched on some differences between so-called “European style” board games and “American style” board games. There are some fascinating differences between the two genres and although I will try to be as objective as possible in this analysis, I will tell you now that I find the European style to encompass much better design choices in almost every respect.

Let’s take a few games to exemplify the genres. We will pick what are probably the two most popular classic American board games to represent “American style”: Risk and Monopoly. For “European style” we will consider Settlers of Catan and Imperial (two games featured previously on this blog).

So let us begin. One of the most prominent mechanics inherent to European games is that players are never thrown out of the game before it ends. Anyone who has played Monopoly enough has experienced the irritation of being the first player to go bankrupt. It could be hours before the game is over and you can reunite with your friends, so your best bet is to go cry alone in the corner while you wait. The same argument can be made for Risk: someone is bound to be eliminated sooner or later and stuck twiddling their thumbs while the rest of the game grinds to an end. THIS IS BAD DESIGN. The point of a game is to have fun, not alienate your friends. If 30-40% of the man hours put into the game is spent doing nothing, then we have some serious design issues. Settlers of Catan and Imperial, on the other hand, have absolutely no mechanic for ejecting a player (in fact if a player leaves for any reason it will seriously upset the game balance). This guarantees that all of your buddies will be hanging in to the bitter end and will all, technically, have a chance at victory. Now doesn’t that sound like more fun?

Now it’s time for a crash course in feedback systems. A feedback system is any system that can influence itself. The classic example is a thermostat system. When a room gets too hot, the thermostat senses it and controls the flow of cold air into the room. When the room gets too cold, the thermostat sends a flow of hot air. The net result is a room that is always nice and comfortable. This particular system is a negative feedback system because when the system strays too far from one state (too hot or too cold) it is pushed back toward the other state. As you can see, negative feedback systems are inherently very stable. The room cannot get too hot or too cold. Imagine now the analogous positive feedback system: the hotter the room gets the more hot air is pumped in, and the colder it gets the more cold air is pumped in. Obviously this makes no sense. It’s an extremely unstable system that will have you spontaneously combusting or freezing to death in a matter of minutes. Positive feedback systems are always unstable. 

Ok let’s apply the concept of feedback to our games. Monopoly is a great example of positive feedback (as is capitalism in general). The rich get richer and the poor get poorer. The problem with this in Monopoly is whoever gets an early lead is more likely to have more money to weather disaster and invest more. This leads to more money from more investments, which leads to more money, etc. If you fall behind early on, you’re pretty much screwed by the opposite reasoning. Again, the same model applies to Risk. If you get an early lead on owning a whole continent or two, you will have more units than your opponents which you can use to capture even more territory and get even more units. THIS IS BAD DESIGN. Basically, this mechanic imposes winners and losers on the game right from the very beginning. The winners are usually going to be someone who has been winning the whole time. Hopelessness is not enjoyable.

European games, on the other hand, tend to impose negative feedback. That is, the further ahead a player gets the harder it is for them to stay ahead. In Settlers, not only does the winning player face discrimination and even trade embargoes from other players, but they will also likely be the one consistenly dealing with the robber, and losing cards when 7’s are rolled. In Imperial, the better your country is the more attractive it will be for other players to steal it from you. In fact, the winning player is going to be the one in constant fear of losing his winning status. Negative feedback is extremely important in any game system because it keeps outcomes upredictable and keeps all players engaged in the game.

There are many other factors at work here, but these two are the big ones. complete participation and negative feedback are the biggest identifiers of a European game over an American game. They are two obvious choices for a better design and ultimately produce better games. It’s a shame that most americans have grown up knowing little more than Risk and Monopoly, and tend to write off board games as a feasible form of entertainment as they get older. I can’t say I blame them, I mean after all, these are goddamned terrible games.

Settlers of Catan And Its Growing Popularity
October 26, 2009

Perhaps it’s just me, but it seems as though the board game Settlers of Catan has reached new heights of popularity with the masses in the last couple years. I certainly agree that Settlers has merit and is worthy of its status as an increasingly popular and well known family game. However, I can’t help but wonder why it has won out over many other similar European-style games to become the american household favorite.

Before I go any further, let me clarify what I mean by a “European-style” boardgame. For some reason, the boardgaming tradition seems to be much more alive in Europe than in America. In fact, Germany (where Settlers was designed and initially produced) produces more boardgames per capita than any other country. Typically these games adhere to some fundamentally different design choices than the common American-style boardgame (such as Risk or Monopoly). European-style boardgames normally do not eliminate players mid-game, they usually incorporate some form of negative feedback, and it usually very difficult to predict exactly who will win, whereas American-style games often lack these traits. (I will cut this discussion short for now as it probably merits its own post)

In college I was exposed to many of these European-style boardgames in addition to Settlers, including Imperial, Power Grid, and Puerto Rico (I guarantee the average American has not heard of these games). Out of these four, Settlers is certainly the worst in my humble opinion. So why has it become the “popular” European game here in the states? I suppose marketing could be at least partially to blame, but if we consider only the game design in our argument what can we come up with?

Randomness. If you’ve played Settlers you are definitely guilty of praying for that 4 to come up just when you need it. And if it does, then awesome! you just garnered yourself 3 more victory points for the win. Settlers is by far the most chance oriented game on our sample list of European boardgames (in fact you might be able to argue that the other 3 have no chance elements at all). Consider our sample hit American Boardgames: Risk and Monopoly. These games are almost all chance. Do Americans gravitate toward games that are more random? I suppose it’s possible. American culture is much less steeped in boardgaming and it’s much more likely that you’re opponents will range greatly in skill from the completely hapless to the uber-leet. This large chance element is the great equalizer in any game. Perhaps our culture puts some special value in allowing anyone to conceivably win.

Simple rules. This is probably the real kicker. I must be a real exception to the population in that I actually enjoy learning new games. Most people seem to think of it as a chore. Consequently, simple games get a much better reception. “It’s easy grandma, you just roll the dice and then you collect your cards. Oh, and you can trade cards too.” Not that I’m an advocate for needlessly complicated mechanics, I’m a firm believer in the KISS principle, but sometimes a little complexity can be a good thing.

These two aspects of Settlers make it ideal for the newbie boardgame enthusiast to break into European-style boardgaming, but it causes the game to seriously lack in content. When I win this game, I don’t feel like it was because I made great decisions, but rather because we rolled 9 threes in a row.

WoW: Why Do We Play?
October 22, 2009

Hi all, Dan here.

I feel it would be fitting for my first discussion to focus on a game that has captured an enormous amount of my time over the last five years or so, and one that continues to occasionally suck me in despite repeated attempts to give it up. I am of course speaking of Blizzard’s World of Warcraft. Is this game fun? Why do I keep playing it? Why does anyone play it? I suppose it must be “fun” in some definition of the word… but when I’m playing that’s not usually my choice descriptor.

Hypothetically, if I max my level and collect every item the game has to offer (which of course entails doing everything that can be done in the game) will I still have the impetus to continue playing? I think most of us can agree that it would be much harder to maintain an interest. Fortunately for Blizzard, they simply need to keep creating content in order to keep us happy.

So it seems that the “fun” part of the game lies in the discovery of the new. New places give us new things to explore, new items to drool over, and new levels/abilities for us to unlock. Surely the climax of each pre-80 level is in the attainment of the next level, yet inevitably we are presented with the task of reaching yet another level. Can anyone else identify with the following statement as it relates to WoW: “I am constantly excited to be doing whatever it is I’m not doing right now?”  Think about it.

Granted, the endgame material and PvP systems help to add some variety. I can honestly say that an arena match is a fun and exciting end to itself. If the game was more PvP-centric then perhaps the fun would revolve more around the journey and less around the destination. Unfortunately, in order to get to the interesting PvP you need to grind your way up to 80 (or 85 in the near future, or 105 in the further future, etc.) But don’t get too comfortable with your PvP-fun-times because sooner or later Blizzard is going to raise the level cap, and you’re back to the ol’ grind.

Ah, there’s the rub: Endgame material is fun. Getting shiny new weapons is fun. But in order to keep giving you new experiences, Blizzard has to keep raising the level cap and thereby keep depriving you of the endgame. It’s a vicious circle of content obsoletion. Whenever I inevitably quit the game after a few months of playing, it’s because I re-realize this paradigm. No matter how hard I work toward that staff-of-ultimate-awesomeness, I know that a year from now there’s going to be the staff-of-even-more-ultimate-awesomeness thats makes mine look like a glittery Q-tip. So why do I even put in the effort? I Don’t.

So what are some remedies to this systemic problem? Well what if there were only a fixed number of some items in the world and they had to be forcibly taken from players? That would make things more interesting… guilds would need to really start working together in PvP and loot would take on much greater values. Or what if the game actually ended at some point in time (ridiculous I know)? This would necessitate some end condition, say either the Horde or Alliance destroying either each other or some mutually hated boss. At this point the game could be declared “over” and one side would win. The game could then begin again fresh. Now clearly these examples are major design overhauls that Blizzard does not plan on implementing, but I hope they make you think about what the game might be like with a redesign of purpose.

As it stands, I simply can’t get into the game for any long stretch of time. The whole process just seems so futile. I’m sure there are those that disagree with me, and I welcome your counterpoints.

October 21, 2009

Hello, world! I’m Dan and this is my new weblog. This blog will, hopefully, be dedicated to all things game-related. Now before you all start hurling bricks through your monitors in protest of “yet another gaming blog,” let me explain. I am by no means restricting the content to electronic entertainment. I would love to see articles exploring board games, card counting, game theory, et cetera. Hopefully this will be a place where the curious mind can explore some of the more esoteric aspects of gaming in addition to the usual ranting review.

I feel like it would be useful to start with a quick introduction of myself, so here goes: I’ve recently graduated from Northwestern University with my BS in Computer Engineering and Animate Arts, and I currently reside in Chicago and work for a proprietary trading firm. I’ve always been a gamer, but my years in school cultivated more of an appreciation for the underlying concepts and theory behind the design of games. I’m an on-again-off-again WoW player, a boardgame junkie, a mathematics enthusiast, a programmer, and of course a fan of just about every video game genre (I could do without sports games).

While I feel I have plenty of material just bursting out of my brain and ready to explode onto the page (that’s kinda gross now that I think about it), I hope to recruit other contributors to provide insights and perspectives that alas I cannot. If anyone out there is ever interested in becoming a contributor, just let me know and we can arrange it!

See ya’ll down the dusty trail,