The Games Journal | A Magazine About Boardgames

Game Theory 101 - Part III

Jonathan Degann

January, 2004

The Agonizing Decision. How presenting the player with impossible choices helps make a game great.

The problems of the human heart in conflict with itself... alone... is worth writing about, worth the agony and the sweat.

William Faulkner

Last time we looked at how events with magnified consequences add urgency to the playing of the game. That urgency takes on the greatest meaning when the player feels that he can control the effects, but is caught in a seemingly impossible conflict over just what choices need to be made. That's what we call the Agonizing Decision.

I like to see every element of gaming that we're examining as having a parallel in storytelling. The "Story Arc" described in Part I is the overall sweep of the story. The "Bomb" of Part II represents those soul-threatening events that drive the character to take extraordinary actions. The Agonizing Decision is at the heart of characterization. These are the dilemmas that confound the character—and that ultimately define him. It is Hamlet's decision over whether to kill his uncle. It's Rick's decision over whether to stay in Casablanca or leave with Ilsa.

In gaming, it is those difficult decisions which determine whether you, the player, will come out victorious or blow your best opportunity and hand the game to your opponent. In the story of the game, you are the protagonist, and in the best games, the human heart... and mind... is in constant conflict with itself.

What makes a decision agonizing? Clearly the results must be substantial. A Bomb, which makes the consequences of a choice more extreme, helps achieve that effect. A player is more likely to work up a sweat when he is confronted with moments that bear heavily on his victory. Additionally, the player must face uncertainty. Any move made with a great deal of confidence can't be all that agonizing. Finally, the decision will have been framed as a limited set of conflicting alternatives with clear possible consequences. To this effect, an agonizing decision is different from the broader challenge of creating an optimal strategy. It's in-your-face, it's immediate, and you know exactly when it's happening to you.

It's not about solving a problem that is so complex it hurts your brain. It's about confronting a problem that has no solution. The agonizing decision doesn't hurt your brain. It wrenches your gut.

The game which I find provides the player with the most relentless and delicious series of Agonizing Decisions is El Grande, by Kramer and Ulrich. The conflicts are evident from the very beginning, when a player must decide which power card to play. El Grande power cards A high numbered power card might enable him to bring more caballeros onto the board and to score some points—but at the cost of depleting his court and using up a good power card which will be helpful later. He decides to play a high card—but just how high should it be? A "13" will guarantee him first choice, but maybe that's not necessary? Maybe he should cut corners a bit? Playing an "11" might enable other players to get in ahead, but at a high cost. How motivated are they? If one or two players choose higher cards it could really mess things up. The board seems arranged so that no one else is quite that motivated to go first… but you never know.

Uncertainty is the heart of what makes the agonizing decision so agonizing. The truly agonizing decision defies analysis. Its consequences may be sufficiently subtle and far reaching that no formula or decision tree can provide reliable guidance. It depends not only on things within the player's control, but on the foggy motivations of other players.

There are different ways that a game can have uncertainty. There can be the uncertainty of chance. In Can't Stop, you don't know whether your next roll will advance you or send you back to the beginning—but you can calculate it or at least estimate it. There is the uncertainty of other player's actions. In Through the Desert, you don't know whether the player to your left is going to take a water hole that is contested by him and a third player, or whether he's going to close you out of the oasis you counted on reaching. Finally, there is the uncertainty of those things whose consequences are sufficiently complex so as to defy analysis. In Puerto Rico, do you take the Small Market or the Coffee Roaster? The decision tree that follows is too complex to fully evaluate.

Of these three types of uncertainty, I think that the uncertainty of other players' actions provides the most satisfying, and agonizing, type of decision that a player can confront. The uncertainty of chance leans toward being analyzable if you're good at estimating probabilities. The uncertainty that occurs because your decision has subtle long-term consequences can lose its emotional impact because no alternative feels like an "absolute must". There is an especially delicious agony, though, in trying to resolve conflicting alternatives when the outcome depends on the decisions of your opponents. Now, the agony comes not just from playing the game, but from playing the players.

Can't Stop is a lot of fun—and it is the uncertainty of the luck—and the weighty consequences of guessing wrong—that can knot you up over the decision to roll the dice "just once more". The probabilities of getting a successful roll are difficult to calculate, which helps enormously in moving the agony out of the brain and into the gut. Still, it is about you, the dice, and some probabilities. Union Pacific takes the element of chance but jazzes it up with player interaction. You either have to pick up a share in a company you're fighting over, or else lay down shares to insure you get points in case a scoring card comes up soon. Which is best? The chance-uncertainty of whether a scoring card is about to show up certainly creates tension. The player-uncertainty—how motivated is your opponent to challenge you for control—keeps it from being just a probability estimate.

The anxiety of trying to anticipate your opponents' actions is especially sweet in El Grande. Every possible power card you can play has vexing implications in terms of who can get ahead of you or behind you in player order. It presents a painful trade-off in terms of the resources you'll have available (the earlier in the player order, the fewer caballeros you get to bring to your court). In turn, your position in the player order might present exceptional scoring opportunities (if you get the action card you want), but might compromise your position greatly (if, say, you are forced to empty your court, or if the king is moved so that a flood of enemy caballeros will take away your majority position). It so often occurs in El Grande that you are confronted with some very simple alternatives with very clear consequences. What makes the decision so difficult is the unpredictability of opponents' actions. "If I only knew that Glenn will do the 'rational' thing, take the points, and not shaft me this turn, then my choice would be so easy!" But that's the problem. You don't know.

It is uncertainty that makes an agonizing decision different from a brain burning decision. Games like Tikal or Princes of Florence often present you with situations in which you know exactly what you're trying to achieve, but you can have a hell of a time figuring out just how to achieve it. Tikal action points summary Tikal can challenge the player to figure out the best way to use his 10 action points. He wants to take control of a certain temple, and not abandon control of one he already has and grab that artifact. He works through all the possibilities, juggling explorers and action points. "Ow! My brain hurts!" If he can solve the puzzle ingeniously, he's faced a brain-burner—which is not the same thing as an agonizing decision. If he can optimize his move, however complex, by adding up the victory points he'd earn under each alternative, he has faced a brain-burner. If the puzzle can't be solved, and the player must choose between two alternatives, and each seems imperative but there is no reliable way to determine which the right choice is, then he is confronting the delicious agonizing decision.

All of this uncertainty is only agonizing if the consequences are substantial. This gets back to the value of "The Bomb" in a game. The game needs to have rewards and punishments which are steep. In El Grande, leaving the king where he is can create a power vacuum which sucks caballeros into an area and dramatically erodes your position. Holding off on playing your high valued power card now can enable another player to pluck the action card which enables him to force your caballeros out of your most valued province, and leave them scattered ineffectively all around the board.

There is a balance that needs to be struck for a decision to be truly agonizing. On the one hand, it has to be subtle enough so that a player can't just calculate his way out of it. On the other hand, if it is too subtle, it doesn't make an emotional impact. The third element of the successfully constructed agonizing decision is that it presents clear conflicting alternatives to the player, each of which seems like an absolute "must".

"I really really need to play my #13 power card because anything less will enable another player to force me to evacuate my court, and that will devastate me. But. I really really need to hold onto my #13 power card because I know that playing it in round 9 can enable me to control the king and the entire endgame."

In a game of New England:

"I've got to bid whatever it takes to insure that I get that 10 point development card that just came up. The problem is, I don't know what it takes. If I bid 10, all my opponents can bid low and drain my resources. If I shade my bid, someone can outbid me, take the development card, and I'll be kicking myself for the rest of the game."

The clear alternatives of the agonizing decision are much more focused than is "strategic depth" in a game. The clarity and immediacy of the agonizing decision are what give it the emotional wallop. It is the feeling of being caught inside a contradiction. Will you take the red pill or the blue pill?

Well, it's not always that clear. Sometimes the decision is an explicit either/or alternative. In Union Pacific, you either take the share or play your shares to the table. The game design where an agonizing decision only emerges from playing the game is especially ingenious. Let's rejoin our game of El Grande. The player has the opportunity to move the king. What he really wants to do is to move the king next to some critical region, toss some caballeros where he needs them most, and then move the king away, protecting his investment. Too bad the rules prohibit him from doing that. He is forced to move the king only once. He must either put his caballeros into some region that isn't so important and protect them or else move the king first and place his cabs exactly where they're needed—but in so doing, leave them vulnerable.

Even in an auction, games can add a level of agony by imposing arbitrary restrictions on the bidding. If a game is trying to have some element of realism, especially in an economic game, then an auction with open outcry, in which the bidding increment is very small, is the way to go. The open auctions in Modern Art and Monopoly are good examples. You can pretty much set your maximum bid and keep going until you reach it, or until everyone else drops out. If a designer wants to add a more "gamely" element, he can make the bidding increments very large, or impose a "once around" (you only get one bid) rule. In Industria, bids typically range from 1-4. Deciding to bid 1 vs. 2 can make a big difference in whether a property is worthwhile or not—and whether you'll be able to freeze the next guy out of the bidding. Big increments introduce a mini-bomb into the bidding. Similarly, in that game and Medici, both of which use the "once around" method of bidding, you don't get a chance to raise your bid. Now there is an element of uncertainty as you need to anticipate your opponents' reactions when you set your bid. There are many "make or break" auctions in these games, and much agony involved in setting the bid just right.

My five year old daughter expressed the essence of the agonizing decision when her mom proposed an alternative one early Sunday at 3 AM: either she would be accompanied to bed until she fell asleep, or she'd get an extra glass of chocolate milk, which she wasn't supposed to have. My daughter's reaction went: "First I want you to come with me. But when I pick that, I change my mind and want the milk instead. So I pick the milk. But as soon as I pick the milk, I decide I'd rather have you come to bed with me. And it goes back and forth like that, faster and faster, forever!"

There it is, the feeling laid out in its most primitive form.

Gaming is about many things, from a social experience to an intellectual challenge. One thing unique to gaming is that it challenges its participants to make hard choices, and then lets them see how those choices play out. The agonizing decision is the essence of gaming crystallized into its most critical moments. In gaming, the Agony is the Ecstasy.

- Jonathan Degann

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