Monty's Hall

The Monty Hall Problem	Commentary
	Monty's Hall project exposes the user to the Monty Hall problem. By providing a game show theme, the player understands the Monty Hall problem. However, this is not as short a game as was hosted by Monty Hall. The player must work their way through a series of doors, decreasing in number. This process starts at ten doors, and works its way down to three in the final challenge. If the player selects the wrong door, they are returned to the previous stage, which they must complete again. This way, with trial and error the player will learn why the Monty Hall’s probabilities are as they are. As well they can see the whole game represented in one stage with the exploratoin mode, where they can play it as much as they like with no repercussions, to explore the probabilities of this complex situation. Through the game, people can learn about the Monty Hall problem. It is a complex idea, but after running through many door sets of different numbers, the player should get an idea of why it works how it does.
This program will apply the Monty Hall problem, which is rarely understood. It is the classic probability problem, started by Monty Hall’s game show. First, the player selects a door out of three. Then, the host removes one of the two remaining doors, leaving two doors, one with a prize and the other without. The player must decide to stay with their original decision or switch to the remaining door. Then that door is opened, and the prize behind it is rewarded. It is known that switching increases your chance of winning, but the probabilities are not intuitive. Taking a larger data set, with perhaps more than seven doors, helps to make the reasoning behind switching understandable. In this version, the host removes all doors except one. The probability of something is desirable results divided by possible results, so the chance of picking right the first time is 1/9. If you chose to switch to any of the other ones, the chance of picking right would be 1/9 as well. However, this is not possible because all but two choices have been removed. It’s as if you have the choice of picking all 8 of the other doors, and if the desired result is anywhere in that set, the whole set is desirable. Therefore, the chances of winning by switching is increased to 8/9, while staying has the chance of 1/9. This is what I hope to illustrate with the experimental side of the app, and with the game demonstrate.
The game host is important part of the game show, as he operates the show. Using an armature created with the bone tool, after the player selects their first door he will walk across the stage and point to the one they selected. This will add a touch of humor or interest into the game, rather than just a simple notification. (Of course, during the experimentation mode of the game no animation takes place, because that part of it should not take up too much of the player’s time.) Also important are the animations of the doors. The doors were created painstakingly using the line tool and fills, based on a picture of a door on the internet. The opening animation is fluid, and the door is reaslistic. A sound also plays. When you get to the end, the final door has "miniature planet" behind it, actually a special type of panoramic photo that makes the picture look like a tiny globe.. The purpose of the art is to make it engaging to play the game, instead of just being an interesting toy you play with for half a minute. Adding the final goal will make it so the player must understand the Monty Hall problem, or it will take a very long time for them to reach it.
The code of any game is the backbone. In my game, almost everything will have to be controlled by actionscript. First of all, the selection of the doors: a door must be randomly selected to be the correct one, and once the player selects a door all but one of the others must be revealed, but not in a way that presents the solution. Then, if the player selects correctly, the door must zoom up so it seems the camera is going towards it, into the next room. While this is happening the code must prepare and display the next level so that when the door animation is complete, the next level is visible. What also needs to be programmed is an experimental tab, wherein the Monty Hall problem is played on a smaller scale. This will be programmed with a programmatic tween when the tab is clicked, and a close button to close it with another. When the host reveals the insides of the incorrect doors, the animation of the door opening needs to be played. Also, when the player makes a wrong choice, the level must be decreased. The mathematical portion of the app remains basically unchanged, because its operation is essentially unchangeable without making the probabilities change, which cannot occur. The Monty Hall problem is simply probability, and while the code used to make the math happen will change undoubtedly, the math shown by the code cannot.