The Games Journal | A Magazine About Boardgames

Game Theory 101 - Part IV

Jonathan Degann

April, 2004

Nervous Systems. How instability in a game system helps make a game great.

When a game leaves a player feeling that he has little control over the outcome, it is often described as being "chaotic". A well known example of a chaotic system is "The Butterfly Effect", which argues that the flap of a butterfly's wings in Brazil can set off a tornado in Texas. In gaming or in weather, a chaotic system is one which is so unstable and complex that a small change in one condition sets off large unpredictable consequences. Since much of the fun in a game comes from setting up moves with predictable consequences, chaos is usually a bad thing.

There is another type of instability, though, which I think is a good thing. It is the sort in which the effects of your actions are reasonably predictable, but which injects an element of surprise which forces players to adapt and make sometimes radical course corrections. Operations Management professionals call these systems "nervous". A "nervous" system is one where a small external change forces you to alter your plans substantially. A small change won't suddenly turn a winner into a loser, but it may force a winner into inventing a new plan if he expects to maintain his lead.

In the metaphor of storytelling, if the Agonizing Decision provides the characterization, then the Nervous System provides the plot twist.

A game system in which small ripples force players to make substantial changes to their plans helps to inject an element of surprise into the game and to insure replayability. Without sufficient nervousness, a game can become predictable and repetitive. It can enable a player with a leading position to just fall back on his strategy and become unstoppable.

Abstract two-player games tend to provide the best examples of nervous systems, although we'll ultimately focus on multiplayer German style games. Imagine a game of Chess, somewhere in the middle. White is winning, and is up by a couple of pieces, but black has some good threats set up. Black makes an entirely unexpected move that catches white off-guard. White is probably still winning, but oh, man, does he have to rethink his position! The game of Chess has an unstable, nervous, system of threats, counter-threats, and defenses because of the complex and subtle ways in which Chess pieces interact. A small change can have large ramifications for the plans of the players. It is this instability which has helped Chess to endure; small surprises create a new game. Nobody ever complains about Chess's lack of replayability in spite of the fact that there is no luck and every game begins in exactly the same way!

This high degree of instability and precision found in Chess is, to me, what makes abstract games different from German games, which are more forgiving. The element needs to be present, though, in order for the game to be exciting. If players can reliably predict the way that the remainder of the game is going to unfold, the game is over. Players may have complete control over the remainder of the game, but there needs to be the instability that prevents everyone from simply continuing their current strategy undisturbed in order for the endgame to be exciting.

Princes of Florence has sometimes been accused of being too much like multiplayer solitaire. Indeed, there are only several points in the game in which players can affect their opponents. However, Princes has a beautiful instability working for it, so that it only takes a small surprise to force players to reshape their plans considerably.

Sometimes, it can even be a "good" surprise. I came to appreciate how nervousness makes Princes of Florence successful during one play when I bid for a Jester, just to keep the price up, and got it unexpectedly cheap. Fantastic! A Jester is a sort of wild card in Princes of Florence. The Park that I expected to buy would have added value to certain works I expected to build, but the Jester helps every work. Now, if I wanted to, I could just keep playing, sticking to my strategy. I could just get the Park later, knowing that every work I produced would be worth more. Not so easy! There weren't enough turns left now to do it all. And I was running just a bit short on money, and really needed to produce a work soon in order to keep going. Suddenly I found myself frantically rearranging my entire plan in order to insure that my good fortune really was something good.

In spite of the limited direct interaction in Princes of Florence, the game is widely loved and rarely grows stale. It is the nervousness of the system, especially in the consequences of the auctions, which magnifies the effects of this limited interaction, keeps the players on their toes, and prevents the game from just being a logic puzzle.

In a nervous game, an unexpected move forces you to radically reconsider your plans. In a chaotic game, an unexpected move renders your prior moves meaningless, potentially rewarding good play with poor results. The former keeps you on edge; the latter frustrates you.

Fresh Fish is an example of a game which can suffer from being chaotic. Fresh Fish In Fresh Fish, players are attempting to build the shortest possible routes between pairs of tiles on a square grid. The twist is that players don't actually lay track, but instead lay blocking tiles which define the detours that the path must make. A player's best efforts at trying to direct the path may be thrown entirely out of whack by a single unexpected play which can divert the path entirely around the board. To make matters worse, the ability of a player to ruin another player's entire set up can depend on a lucky tile draw.

Chaos arises in a game when relationships are so interdependent that a position can't be judged inherently good or bad, but can flip upside down depending on actions outside the player's control. In Sid Sackson's Bazaar, players are trading groups of colored stones according to limited formulas in an attempt to get particular combinations, with as few extras as possible. A player can advance his position gradually, moving toward a goal, only to be beaten to it—at which point that goal is taken away and replaced with a new one. All the work getting to that goal may not advance your position at all and the extra stones are likely as not to hurt you. So were you advancing your position or not all that time? A player needs to feel that his work earned him something. If a player finds himself getting punished for his efforts, he's going to feel sour and powerless.

But I've come to praise instability, not to bury it, so let's look at the problem that arises when there isn't enough. Such games will have a runaway leader problem if there is nothing a player can do that will force the leader off of his course for victory.

Economic games are often the ones in which there can be a runaway leader problem. The danger comes from the fact that a player's ability to generate more resources is based on how many resources he already has. If a player in the lead can shadow the actions of those behind him, he'll always be able to maintain that lead.

The old 3M game Stocks and Bonds is clearly flawed. Players invest in different securities which fluctuate somewhat randomly. If a player makes a lucky pick early on, he can secure his lead by mimicking the moves of the next best player without restriction. Possibly now the player in third place can take some fresh risks and leap ahead, but there is nothing that player #2 can do to shake off the leader until that happens.

Acquire stocksAcquire also involves investing in shares, but now players are restricted. A player who gets a cash lead can only buy 3 shares a turn. This limit, along with the importance of having majority control, adds an essential degree of nervousness into the game. A leader attempting to secure majority control in Continental may be able to achieve that, but if a third player threatens his control in American, the leader becomes forced to choose between the two. He can't invest in everything at the same time. The counter threat could even change the complexion of his tiles; ones which once promised a majority payoff no longer do. What to do now?

Funkenschlag has all the structural problems of being a "rich get richer" economic game. A player can evaluate his production capacity, plan his routes, and then execute an expansion with only limited interference. Even if a player is beaten to a city, he will have alternative cities or alternative routes to take. Losing your first choice has a cost, but it isn't likely to turn your plans in a distinctly different direction. Friedmann Friese obviously knew he had a problem and injected solutions into the game, some of which are very effective, and some of which are artificial and seem like workarounds. The artificial solution is to give the players at the back of the pack all of the advantages. They get the cheapest commodities, they get to build early, and they have the greatest control in the auction for new power plants. Rather than giving trailing players tactical alternatives which they can exploit to upset the order, Friese gives them handouts. This has always struck me as being a cheat. It turns a game of economic development into a sort of bicycle race where players jockey to draft behind the leader. In contrast, the way that old power plants become retired and new ones enter the game introduces some nervousness which is very organic. You need to replace one of your aging plants, but nothing available is really cutting edge. If you settle for what is available, you'll soon need to replace that too. If you hold off, you'll have difficulty expanding into more cities and your opponents will close out your best routes. Whatever you do, your growth plans need to be reconsidered and adapted on the fly.

A nervous system has a sort of bounce back effect—like when you jiggle one end of a rope and watch the wave travel to the far end and then return to your hand. The unexpected change occurs in the current game turn. The consequences cascade through the rest of the game, but the game is predictable enough to provide feedback, forcing you to make course corrections now.

Compare Acquire with Union Pacific, a game which also has a battle for majority control of shares. Acquire is the more nervous game. In Union Pacific, if someone overtakes you in a stock, the most common response is to redouble your efforts to regain control of the same company. Either way, the consequences have a clear dead end. You get the points or you don't, and you move on. In Acquire, the fact that the merger will pay off in cash means that the majority holder can use his winnings to create an entirely new threat. A player who emerges as the leader in Worldwide might use his earnings to challenge your leadership in Imperial, even though he currently has fewer stocks than you. That challenge forces you to reconsider how to defend your position in Imperial. In Union Pacific, the timing of the payoff is largely beyond your control; mostly all you can do is manage your risk as you decide whether to draw shares or lay them down. In Acquire, the timing of the payoff is critical and it must be actively managed. Now, maybe instead of expanding Imperial, you might buy yourself some time by expanding Worldwide because you can not allow it to be taken over right now. A temporary change in majority control has ripples in the ways players can invest, in the players' strategic positions should the merger take place, and on the consequences of each possible tile play.

Princes of Florence adds nervousness to the system by imposing strict constraints in the number of actions a player may take during the game. The little tile puzzle on each player's mat is a metaphor for the entire game. In each case, a player has severe constraints on what he can do during the course of the game. Each choice creates a series of possibilities, but also closes some off. A small change—whether in the position of a building on the player mat or in the item purchased at auction—ripples through all the subsequent choices the player must make. This would not be as profound if a player's purchases were only limited by his cash on hand, which can be managed flexibly. However, with only seven auctions and fourteen actions to work with, if you change one thing, you must reconfigure your entire game.

The geometry of the game board can go a long way to adding either stability or nervousness into a game. A board that is broken into many small pieces will have the relationships between locations measured in small increments, and will tend to be stable. A board in which moving a piece a single space changes its relevance dramatically will offer its players more variable challenges. You can see the difference characterized in games from the 1980s, which leaned toward more realism, contrasted with modern German style games. Wargames tend to be very stable. They have lots of pieces moving relatively long distances. If one piece can't quite make it to its target this turn, maybe another can. Or maybe you'll just have to choose a slightly closer target or settle for slightly poorer odds in a given combat resolution. Rarely would moving a single piece a single space change much. Similarly, in Empire Builder or any of the crayon rails games, landing an unexpected few dollars on an easy short won't typically open a menu of new opportunities for you.

Taj MahalOn the other hand, board geometry is used to great advantage in Taj Mahal. As the board is laid out, a player will typically try to map out a strategy of specific palace placements that can create large chains and score many points. But if one contest proves to be more draining than expected, suddenly the player no longer has the resources to fight aggressively for a key spot. In Taj Mahal, every palace must be lined up "just right". There is a little wiggle room, but not much. Once you are forced to abandon your quest for a specific placement, you are likely to find yourself forced to reconsider your entire game. The 12 areas and 49 palace locations in Taj Mahal, along with their quirky network of connections, can prove to offer greater strategic challenges than the 1,000+ hexes on many wargame maps.

The power of nervousness goes a long way to explaining the lasting power of Puerto Rico. Some writers have commented on how little luck there is in the game—the only thing that changes is the offerings in the pool of plantations. Shouldn't the game become repetitive? The reason that the answer is "no" is that Puerto Rico offers its players a very nervous system. You can build a coffee plantation and calculate exactly how you're going to earn the money to build the roaster, when to time the sale of your first coffee barrel, and the building you're going to acquire with that money. Then, someone takes the Trader before you thought it would be taken. Or: the player to your right builds a coffee plantation. Or even: you unexpectedly get a windfall by being able to pick a prospector with 3 coins on it. These possibilities don't just delay your plans, they may flip your plans topsy-turvy. Your prior choices still make sense—Puerto Rico is not chaotic—but these surprises do force you to build yourself a very new battle plan. This new plan then has implications for the other players. And so it goes...

Instability in a game shouldn't go too far. If a game is too nervous, you probably won't bother developing a strategy, because there's no point in even trying to plan. If the game is chaotic you become frustrated, the unexpected twists not only force you to rethink your plans, they make you feel as though the choices you already made didn't help you.

Here's what a good degree of nervousness in a game feels like. You get into the game and begin to develop a viable strategy, and then you find yourself in the middle, holding on for dear life, trying to keep your strategy from unraveling, or else you get pulled into a new plan because unexpected opportunities seduced you into trying something unexpected.

Nervousness in a game keeps you on the edge of your seat; it makes you sweat. It's like the fun of riding in a roller coaster—it's been carefully engineered to stay on the tracks, but always feels like it's just a little bit out of control.

- Jonathan Degann

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