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Temptation and Consequence: Dilemmas in Videogames Monty Hall And The Three Doors An interesting perspective on the mechanics of decision-making can be gained by studying the classic Monty Hall puzzle. The hypothetical scenario involves the famous gameshow host who presents the contestant with three identical doors. Behind one of these doors is the grand prize, while the other two hide worthless gag prizes. With no hint of which door hides which prize, the contestant is asked to select one, which they do with some hesitation . Before the selected door is opened, however, Monty Hall opens one of the unselected doors to reveal that it contains one of the gag prizes. With a sadistic grin, he offers the contestant the choice of either keeping their original door, or switching from their selected door to the unselected unopened door remaining. The puzzle thus poses the question: should the contestant keep the original door they had picked, or should they now switch to the one Monty did not open?
Our first reaction may be that both remaining doors carry the same probability of success. After all, with just two unopened doors the odds must be 50/50 that the contestant will win the grand prize. This intuition, however, is incorrect. By opening one of the unselected doors and revealing the undesirable prize, Monty has unwittingly added potentially valuable information to the original scenario and given the contestant a definite advantage-if they recognize his blunder. The original probability distribution must be held constant, so the door the contestant first selected will always have a 1/3 probability of concealing the grand prize. The other two doors also each have a 1/3 probability, giving them both a combined total probability of 2/3 (1/3 + 1/3) (see Figure 2.). The important thing to realize is that this distribution of probabilities does not change, no matter what new information is supplied, since the contest always began with three doors hiding one grand prize and the prize itself has not moved. Thus, the two unselected doors will always jointly carry the 2/3 probability of concealing the grand prize. By opening one of these doors and revealing it to hide the gag prize, Monty Hall has allowed the 2/3 probability of success to be 'stacked' (1/3 + 1/3) onto the one unselected door remaining. Thus, the original door selected by the contestant carries only a 1/3 probability of hiding the grand prize, while the one remaining unopened door carries the entire 2/3 probability of the unselected doors. The best strategy for the contestant, therefore, is to switch to the unselected door remaining. A mathematical proof for this involves applying Bayes' Theorem (see Appendix 1).
So, what useful principles or techniques can be borrowed from the Monty Hall puzzle in the design of videogames? Let us examine the transformation that takes place in the staging of the puzzle as it unfolds. The contestant's initial selection of a door involves a completely blind choice-that is, they have little more to rely upon for their decision than a "gut feeling," dramatically diminishing any sense of a consequential outcome. These types of dilemmas should be generally avoided in games, as they are largely automatic and provide no meaningful interactivity or sense of controlled fate, degrading the puzzle into little more than a glorified coin toss. However, the layered presentation of additional information makes the dilemma much more interesting. By exposing one of the unselected doors as a loser, Monty has created a situation where the contestant is forced into reevaluation of the available information, and possibly, a reconsideration of their initial selection. At this point, the player's response to the puzzle transforms from one of pure guesswork into one of true cognition, assessment, evaluation, and reasoning. One of the oldest and best definitions of a "game" as it relates to interactive entertainment defines it as a "…closed formal system that subjectively represents a subset of reality" (Crawford, 1982). When facing an in-game dilemma, continuous feedback to the player's response in the form of additional information heightens the experience and creates a very convincing simulation of reality. In our daily lives, we often face situations that require interactivity and an ongoing response, such as the conveying of bad news to a friend. In such a situation, we frequently gauge the verbal and non-verbal responses of our acquaintance and modify our tone, posture, and delivery of the news. Similarly, videogames should endeavor to provide similar ongoing feedback, information, and behavior modification opportunities to the player. Some games do this already, offering information and dilemma possibilities in creative ways. Most role-playing games, such as Baulder's Gate and Ultima Online for the PC, include some element of player customization, which in itself entails a form of dilemma. Does the player upgrade their skills by focusing on their strength attributes? Or do they opt instead to boost their stamina and intelligence scores? One way to enhance this dilemma is to hint at what challenge the player is destined to face in the upcoming level. For example, at the moment before the player's skill upgrade decision, the arrival of a crazed hermit who foretells of a magical beast in the player's future can generate dilemma-based tension. The timing of the introduction of this added information is important, since bringing the hermit to the scene after the player has already made their decision would make it a rather meaningless event. The additional information provided by the hermit's forecast could influence the player to reconsider their current tactics in many ways. Is the hermit telling the truth? If so, should they continue their current proven strategy of boosting their strength and agility scores? Or should they now switch to a wisdom and intelligence focus? Or do they simply dismiss the information as frivolous, a sort of interactive red herring? Either way, the player is likely to reflect upon the situation later in the game and attribute some of their success or failure to their decision. The presentation of interaction-provoking information during gameplay can also be laid out in a less conspicuous manner. In Rayman Advance for the Gameboy Advance, the landscape of the 2D side-scrolling platformer is dotted with several subtle, glowing 'trigger points.' As the player soon realizes, directing Rayman over these tiny points causes certain pre-defined events to be activated, including the release of additional foes and the materialization of hidden bonus items. While the game itself remains linear in its presentation, this simple feature gives players the option of avoiding a particular route and the triggering of a particular event (such as the unleashing of a particularly difficult enemy). The feeling of being "on rails" is thus reduced, providing a greater sense of control and involvement over the events that unfold. Another clever twist on decision-making can be found in The New Tetris for the Nintendo 64 system --a remake of the classic puzzle game. While the original gameplay and falling four-piece block premise remain the same, the designers have included an added feature that allows players to remove the active puzzle piece before it drops into place and put it in storage. This piece remains held in an onscreen frame indefinitely until they player wishes to reintroduce it, at which point it is swapped with the current active piece. The strategic element introduced by this feature is clever and engaging. Players longing to execute a 4-line clear will want to put an "I" shaped piece into storage and return it into play when a suitable path is created for it. Those with a more defensive strategy will rely on the swapping technique to remove undesirable pieces and hopefully get them out of a "jam." In both cases, players are forced into an elevated state of constant evaluation and reevaluation, adding an increased level of depth to the game and encouraging players to abandon the automatic pseudo-hypnotic responses to block patterns they may have developed while playing the original version of the game. ______________________________________________________ |
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