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Formal Analysis: Scotland Yard

(For a CTIN541 assignment.)

Overview

Scotland Yard is a strategic cat-and-mouse game in which one player takes on the role of a criminal and is pursued across the game board by the other players. The game board depicts a complicated network of numbered nodes that are connected by differently-colored lines: red, yellow, blue, combinations of those three colors, and black. The nodes represent locations in the city of London, and the lines represent routes between them. The colors indicated the modes of transportation that can access the route: taxi, bus, tube, and boat.

Players

Scotland Yard is a game for 4-6 players and features a unilateral interaction pattern. As such, the game is asymmetric, not just in its starting conditions, but in the rules and procedures that apply to each player. One player dons the (literal) Mr. X hat and faces off against the others, who are unlikely to win unless they cooperate. This cooperation is the biggest interaction element. The players embodying detectives must collectively study the game board, sound out theories, propose strategies, and decide on a course of action. Disagreement and uncooperative behavior amongst the detectives makes their success much less likely.

In my (admittedly limited) experience with this game, it seems to me that there is an balance problem that centers on the number of players. Given the size and complexity of the game board, three detectives (the number in a four-player game) are at a significant disadvantage. Five detectives (the number in a six-player game) would be considerably more effective in achieving their objective. (In games that involve a larger number of players, an advantage is given to Mr. X as well, but based on what I have seen of the game (which, I stress again, is very little) it is not enough to completely counterbalance the effect of additional detectives.) If this is indeed the case, then the game experience, for both the detectives and Mr. X, could change significantly based on the number of players. (It seems that a variant of the game exists that attempts to make it more consistent. It will be discussed further in the section on procedures.)

Objective

Mr. X and the detectives have two different and opposing objectives. For the detectives, the goal is to find Mr. X - that is, for a detective to occupy the same space on the game board at the same time as Mr. X. This objective is impersonal, in the sense that all detectives succeed equally regardless of which of them actually satisfies the winning condition. Because of this, the interaction between detectives is exclusively cooperative.

For Mr. X, the objective is to evade capture until play ends (after a maximum of 22 rounds). This is the exact complement of the detectives' objective, which means that the game will always have a winner, and that only one side can win.

Procedures

Setup Procedure: The first step for a group of players is to choose Mr. X. There is no procedure specified in the rulebook for this; it is left up to the players to determine how Mr. X will be decided. It could be decided randomly or given to a volunteer. Random selection has the advantage of varying the play experience. Different players will have different approaches and strategies when embodying Mr. X, which will give the game variety. Just as importantly, it gives each player an equal chance to play the game from the perspective of Mr. X, which is a completely different experience. Conversely, picking a volunteer makes it more likely that all the players get what they want, and may make the game more fun for all the players involved.

After the board is set up (which consists simply of placing the board on an appropriate surface and organizing the other game pieces so that they are accessible), each player draws a starting tile. This is the extent of the setup procedures that are common to Mr. X and the detectives.

Each of the detectives chooses a pawn which will represent her. They each place their pawns on the board at the position indicated by their starting tile. Each detective should also take a number of transportation tickets: 10 taxi, 8 bus, 4 tube. Once the pawns have been placed, the detectives can begin analyzing the board layout and negotiating a play strategy.

(This is where the previously mentioned variant of the game comes into play. Instead of determining the number of detectives based on the number of players, this variant proposes that the number of detectives be fixed at either four or five, depending on the source for the rules. If there are fewer players (excluding, of course, Mr. X) than the fixed number of detectives, then some or all of the detective players will control multiple pawns. For example, if the game were played with four players and the number of detectives was fixed at five, then two of the detective players would control two pawns, and the third detective player would control only one pawn. Again, how these pawns are divided amongst the detectives is left up to the players. It is important to note that, in any permutation of this variant, each pawn is set up and controlled as an independent unit. If one of the detective players controls two pawns, for example, then during setup she would take the appropriate number of tickets for each pawn, and then take one turn each round for each pawn without sharing tickets between them, and so forth.)

For Mr. X, the setup procedures are slightly different. Before doing anything else, Mr. X must don the special "Mr. X" baseball cap included with the game. The cap serves three purposes: it clearly identifies which player is Mr. X, it separates that player from the rest of the group, and it allows the player embodying Mr. X to shield his eyes while looking at the game board, so that he doesn't reveal where his character is positioned.

Mr. X does takes a smaller supply of tickets than the detectives did: 4 taxi, 3 bus, 3 tube. He also takes two double-movement cards and a variable number of black "Mr. X" tickets, one for each detective (or, in the variant, for each detective pawn). He does not put his pawn on the game board at the start of the game, as the detectives do. Instead, he prepares the logbook by inserting a fresh sheet of paper and readying a writing implement. Now he, too, can study the initial layout of the board and consider his own strategy.

Once the game is set up, the first round begins. Mr. X always has the first turn, and then play proceeds clockwise around the table.

Turn Procedure: The basic structure of a turn is the same for Mr. X and the detectives. The player examines the game board and chooses an appropriate destination space, based on that player's current location and their overall strategy. This destination is a node on the graph that is connected by a colored line to the node that the player currently occupies. It must be exactly one degree of separation from the player's current location, and it cannot already be occupied by a detective. The player then pays the fare to use the route indicated by the line by giving up a ticket: taxi for yellow, bus for blue, tube for red, and a black "Mr. X" ticket for black. If the line between the nodes is multiply-colored, then the player can choose any of the appropriate modes of transportation and pay a ticket of that type. The player's location has now changed to the new space on the board.

This procedure represents more or less exactly what each detective will do on every turn. When she chooses a destination, she may be limited by her remaining tickets. The destination must be reachable using the modes of transportation she has at her disposal. (Since the detectives start with no black "Mr. X" tickets, boat travel, represented by black lines, is never a valid mode of transportation for a detective.) When she pays the fare, she gives the ticket directly to Mr. X. To finish her turn, she moves her pawn to the destination. If Mr. X is currently occupying this space, then the detectives win and the game ends. Otherwise, she will start her next turn from this new location. Every detective turn follows this pattern.

There is a little more variety in Mr. X's turns. Like the detectives, he chooses a destination that is reachable from his current location according to the tickets he currently holds. In practical terms, the restrictions of tickets apply only to boat travel, since he will receive more tickets for other transport types from the detectives. Instead of moving his pawn to reflect his new location, however, he writes down his new location in the logbook and covers it with the ticket that he used to pay the fare. The logbook is publicly visible, so all players know what tickets Mr. X is using to pay for his travel, but only Mr. X knows his current location.

Mr. X also has some additional options. The black "Mr. X" tickets are the only type of ticket that can be used to pay for boat travel, but they can also be used for any other mode of transportation. Mr. X can choose to play a black "Mr. X" ticket in order to disguise the mode of transportation he is using on a particular turn. (This is especially effective when Mr. X is near the river, and the detectives might assume that the black "Mr. X" ticket was used for boat travel.)

Mr. X also has two special double-movement cards, which he can play on any of his turns. The effect of the double-movement card, in a practical sense, is that the detectives all lose one turn. Mr. X therefore takes two turns in a row and moves twice, paying two tickets to do so. He must give up a card each time he does this, so he is limited to doing it only twice per game.

Rules

Much about the rules of the game is captured in the discussion of the procedures for play. The activity of the game consists almost entirely of player movement, which is restricted by the graph depicted on the game board as well as the player's supply of tickets, as described above. Each player can only move once per turn, and therefore can only move to an adjacent node. Each player starts with a set of tickets which is dictated by the rules and mentioned above, and the detectives lose tickets every turn while Mr. X gains them. For the most part, we have already covered these elements.

There are a few additional rules, however, that should be noted. The most important is that, while Mr. X's location is generally kept secret and known only to the player embodying Mr. X, there are several game events in which Mr. X "surfaces" and that information is made public. These events are predictable and based on the number of rounds that have been played: they occur at the end of Mr. X's turn on the third, eighth, thirteenth, and eighteenth rounds.

There are also rules that govern the end of the game. If, at any point, a detective moves to the space that Mr. X currently occupies, then the game ends. In this case, it is Mr. X's responsibility to announce that he has been caught. It's interesting to note that this is not in Mr. X's best interest, from a game perspective, since in results in him immediately losing the game. There is, technically, a record kept of Mr. X's movements, but in a practical sense it is not feasible to use this to verify that Mr. X was never caught after the game is over. It is taken as a matter of faith, then, that Mr. X will obey the rules and announce the end of the game if the conditions are met. The detectives are expected to trust the player embodying Mr. X, and Mr. X is expected not to betray this trust.

The introduction of this interesting social dynamic to the game is not mentioned in any version of the rules I have seen, and I imagine it rarely has a real effect on the game. It may not be completely unintended, however, and certainly it is not insignificant that the game first asks one player to take on the role of a criminal, and then forces that player to face a moral dilemma. The fact that this decision can have consequences that carry on beyond the boundaries of the game - who is perceived as the winner and, if the cheater is caught, deterioration of the social relationships of the players - makes it even more powerful. Even if most players in this role choose not to cheat, or do not even consider it, it can still have an emotional impact.

Resources

Just as Scotland Yard is asymmetric in its procedures and rules, it is asymmetric in its allocation of resources. In this case, the resources which are valuable and scarce for the detectives - tickets - are plentiful for Mr. X. A detective starts with a certain number of tickets and must spend one each turn. When she runs out of tickets such that no space is reachable from her current location, then the detective can no longer move and is unable to reach the winning condition. When all the detectives have run out of usable tickets, the game is over.

Tickets are individually valuable because each allows the detective to make a different kind of movement (taxi, bus, or tube trip). It is possible for a detective to use all of her tube tickets, for example, and then she will be unable to use tube transportation. But tickets are also used as an abstraction for time, and as such, they are collectively valuable. The number of tickets remaining to a detective represents the number of rounds during which she can still potentially win. As these tickets are used, they provide a clear visual and tactile indicator that time is running out.

Mr. X, of course, does not deal with resource management in the same way. His supply of taxi, bus and tube tickets is effectively unlimited, because every round he receives more than he can spend. He does, however, have a limited supply of double-movement cards and black "Mr. X" tickets, and these resources must be managed.

More interesting is the concept of escape routes as resources. These are not a tangible resource, but they are a core factor to Mr. X's strategy. Each node of the graph depicted on the game board offers subsequent potential moves, but some nodes have more connections and therefore more subsequent moves. This movement potential becomes more complicated as Mr. X considers the second- or third-order moves offered by any given node. And it is further complicated by different modes of transportation. Mr. X must always keep the movement potential of nodes in mind as he moves around the board, but it is particularly important when a "surfacing" event reveals his location to the detectives. At this point, the detectives will quickly converge on that spot on the map, so it is important for Mr. X to have many routes of escape that don't give away his subsequent locations.

Boundaries

The magic circle created in a game of Scotland Yard is not substantially different from that of most board games. The game board and the associated props - the tickets and the logbook - are at the core of it. The pawns are restricted to the physical space delineated by the edges of the board, so all activity is centered around that space.

The cooperative elements of the game mean that Scotland Yard is necessarily a social game, and moreover, a game that makes great use of verbal and physical communication. Other games with other interaction patterns, like chess, for example, might be played in relative silence, since the game does not require a great deal of communication between players. In this situation, the chess players might be oblivious to the world outside their game, and likewise, the game does not intrude much upon the outside world. Scotland Yard, in contrast, does necessarily intrude upon the outside world. Although it certainly doesn't preclude the mixing of players and non-players in the same physical space, it has to be taken into consideration that the entire area within earshot of the board will be aware of the discussions and strategies of the players, and of the progress of the game, so will be involved in the game as spectators, at least to some extent.

Perhaps more interesting are the internal boundaries set up by the asymmetrical and unilateral nature of the game. There is a semi-permeable partition between the detectives and Mr. X. Strictly within the alternate reality derived from the rules of the game - the magic circle - there is no interaction between the two groups. The special "Mr. X" cap reinforces this concept. Pulled low over his eyes in order to allow him to look at the board without giving away his location, the bill of the cap sketches a plane that separates the social world of the detectives from the solitary world of Mr. X. The game board lies in the middle, where these two worlds intersect.

Of course, it is unreasonable to think that there will really be no interaction between all the players during the course of a game. In reality, players are continuously pulling down the veil that divides them in order to converse, or even to communicate nonverbally. This action is related to the interactions that a game player might have with a non-game-player in the same room, which breaches the boundaries of the magic circle, with one important difference: all participants in this activity are also players of the game, and therefore under the effect of the magic circle.

What real consequence does this have? Perhaps none. Is it substantially different from two players having a conversation about a subject unrelated to the game? Perhaps it is not. Maybe it is merely the fact that an internal boundary has been so explicitly created that calls attention to the act of crossing it. But it is certainly a testament to the design and implementation of the game that players can cross that boundary and then are willing to return and restore the veil so that the game can continue.

Outcome

There are two possible outcomes of the game: either the detectives catch Mr. X, or Mr. X escapes. In the first case, all the players who embodied detectives take equal part in the victory. In the second case, only the player who embodied Mr. X is the winner. Because of the complimentary nature of the two sides' objectives, there cannot be a case where no one wins, or where all players win.

This outcome is certainly not known at the beginning of the game, and remains highly uncertain throughout, although it is possible in the last turns for players to suspect that Mr. X will make a clean getaway. Unlike many multilateral board games focused on resource collection, where one player may take the lead and be the apparent winner (correctly or incorrectly) long before the game is over, Scotland Yard is designed so that the detectives will always be close to catching Mr. X, and doing so will cause them to win the game instantaneously. Therefore, the uncertainty of the outcome is preserved for longer.

That said, in my (let me reiterate) extremely limited experience, the odds do not seem to be consistently balanced between these two potential outcomes. In a standard game with four players, where three players embody detectives, it seems that a victory for Mr. X is more likely than a victory for the detectives. As the number of players (and hence the number of detectives) increases, Mr. X's advantage decreases, and the odds of each outcome changes. This is what makes the previously-described variant of the game appealing. Of course, I may be entirely wrong about this effect. I would like to see the results of a study that would examine the outcomes of games based on the number of players involved. In the meantime, I will have to build up my own dataset of personal experiences with the game.

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This page contains a single entry from the blog posted on September 15, 2008 6:20 PM.

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