ASSIGNMENT # 41a
AN ACTIVITY ASSIGNMENT
Just to get you thinking about the class...
It will be fully devoted to an activity.
The class will be divided into three teams by a random process.
Each team will construct a casino-type game. In the past two days,we have worked with THREE DICE GAME and ROULETTE. In each of thesegames, you pay something to play... and you get back something ifcertain things happen. And, in each of these games, you canstatistically determine the expected outcome if someone "invests" adollar to play.
I'd like to remind you here that THREE DICE GAME was created bytwo Cate students... and it ended up being published in GreatIdeas for Teaching Math, a publication of J. Weston Walch.
I will have coins, dice, and cards available. Your game doesn'thave to use these items, but, as I say, they will be available. Notethe following...
1. Your game should not be overly complicated, but itshould not be trivial (such as flipping a single coin, winning ifheads, losing if tails).
2. There should be a cost to play the game.
3. There should be payoffs to players if certain events happen.
Your team will, during the period...
1. Describe the game.
2. Establish the cost to play and the payoffs for certain events.
3. Given (2), determine the expected gain (loss) for both theplayer and the casino.
This will be your assignment for Monday.
Now, you won't know your teammates until tomorrow. But, you havean opportunity to think about a possible game. Each team will have toagree on a game... and then follow the directions above. This can beboth fun and educational if you approach it with the right spirit.
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Please be sure you have done the reading assignment and the twoproblems that were assigned on Wednesday. These will be discussednext Monday.
The only difference between what we are doing now (casino-typegames) and real-world applications (business, research, etc.) is thatthe games have theoretical probabilities that can be determined,whereas the real-world deals with probabilities that are obtainedthrough observation and experimentation. I realize that this isdifficult to grasp at this point in time. I'm just encouraging you to"hang in there" and understand (not memorize) what we are doing. Ifyou do this, I think you will eventually be amazed at the POWER OFMATHEMATICS and the POWER OF STATISTICAL THINKING. All I can say atthis time is "you ain't seen nuthin yet."
By the way, did you notice how close those computer outputssimulating THREE DICE GAME were to the theoretical casino gain of 11cents per dollar spent? Please realize that the computers are totallydumb, and they were simply simulating a game. The mathematics(statistics) we did in class pretty much told us what was going tohappen.
MATH POWER TO ALL.