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timer Asked: Apr 21st, 2020

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We will now use what he have learned in the probability unit(s) to develop your own game of chance to try out on your peers at our very own Casino Day. You must utilize strategies, supported by probability theory, to create your own game. You will also use your carefully honed instincts about chance to play, and win, the games developed by your peers.

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Statistics Probability Design Your Own Game of Chance We will now use what he have learned in the probability unit(s) to develop your own game of chance to try out on your peers at our very own Casino Day. You must utilize strategies, supported by probability theory, to create your own game. You will also use your carefully honed instincts about chance to play, and win, the games developed by your peers. Features of the Game: The game can be modeled after a game you already know (snakes and ladders, black jack, etc.) but it has to be original in its content. The game must be entirely based on chance, not on skills of any kind, and you may choose a specific theme to make it more interesting. Make the game interesting and fun. Make sure the players have some sort of wins, and don’t get eliminated after the first roll of dice. It must involve winning and losing some (virtual) money. We are not using real money, but keep it at a reasonable level (you will not win one billion dollars!), and also have some wins more appealing: have a variety of money amounts and you must have at least one item worth more than five dollars. If the player plays against the house, the house must have an advantage. You may work alone or in a group of maximum THREE students. This is a four-part project. In order for the following requirements to be met, you must keep a project journal. In your journal, you must write daily entries for every class day (so three times a week), describing how your work progressed on that day. You will write the rules of the game, test them in your group or with your family members, and finalize them in a clear and concise way for your classmates to follow. You will create a probability distribution table and decide the prices and their economic returns for each aspect of the game. When we play, you will keep track of the outcomes and compare the experimental probability with the theoretical one. You will finally make a statistical analysis of the game. Your project will be graded based on: - Originality Clarity of the instructions Professional look Correct calculations of each probability Good balance of winning and losing chances Most of all fun!!! You will play your classmates games and then assess them based on the same criteria. The project will receive a total number of points that will be distributed to each member of the team according to what you consider fair. Part I: Research (5 points) Proposal Due Date: Thursday, April 16. 1. Decide on a game that you would like to develop. Your game must rely on chance, and students should have the opportunity to bet and win or lose money on your game. 2. Test your ideas through simulations of your game. 3. Will you be able to answer all of the questions in Step Two for your game? 4. You are required to discuss your plans with Mr. Dal Forno. He must give you his stamp of approval by the date posted above before you continue. Part II: Development (20 points) Due Date: Thursday, April 23 1. Name your game 2. Describe the rules of your game clearly and concisely. These should be included in your project notebook as a separate, 3. 4. 5. 6. neatly typed and reproducible page. Be sure to include all betting and monetary rules. Buy-in for your game should not exceed $5 and your largest payout per play cannot exceed $30. Each team will have a total of $20 to play each other’s games. Each game will have a total of 10 minutes available for classmates to play on game day. Play your game, record the results, and determine the experimental probability of winning. “Playing of your game” may be done with the actual materials, or simulated with your calculator. Play a realistic number of times in order to feel somewhat confident about your experimental probability. Determine the theoretical probability of winning your game. This may be much more difficult than it sounds… so think about this aspect of your game as ideas grow. All work must be shown, of course! Determine the expected value of winnings. You should consider whether your game is a single pay-in or if the amount of the bet is determined by the player. (If amount bet is determined by the player, you should choose a couple of possibilities for calculation). Each game will have a starting pot of $100. Write up a detailed description of your strategy in developing your game. Create and/or gather any supplies necessary for playing your game. This may be limited by the current lockdown. Part III: Game On (15 points) Monday, April 27 (Prior to game day, you will receive a packet of descriptions of your peers’ games. You will have a couple of nights to read through these to determine your strategy for playing your classmates’ games. 1. Write a detailed description of your game-playing strategy knowing that you will have $20 to play games. You may choose any games that you want, but they will be slotted for play in a random order on game day. 2. On game day: record your results from playing your peers’ games on your game-playing worksheet. Tally how much money you have to finish. 3. On game day: record the results of your classmates playing your game. Tally how much money is left in your pot at the end. Part IV: After Party (10 points) Statistical Analysis due; Thursday, April 30 1. Examine your game-playing strategy. How did you do? What might you have done differently? How did your results compare to what you expected? 2. Examine your game development strategy. Are there any improvements or alterations that you think should be made to your game? How did the results compare to your calculations? All components of the project are to be turned in on Thursday, April 30. This includes your project notebook and any game-related materials. Project Calendar Sunday April Monday (1) Tuesday(2) Wednesday Thursday (3) Friday Saturday 12 13 Game Project Assigned 14 15 16 Present Proposal 17 18 19 20 Proposal acceptance 21 22 23 Game materials and rules due 24 25 26 27 Game day 28 29 30 Final write-up due May 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ...
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