We started with the Game of Pig and learned about the chance aspect behind probability. We then started to transfer to the concept behind probability by talking about the background and explanation about all the Math behind it. We started to learn about probability trees and the aspect on how they are formed and solved. But before that we were talking and experimented with coins and with that we solved simple probability questions. But the main part of this project was based around creating our own Renaissance board game and creating a probability question, then solving it. We also many different methods to find the different probabilities, such as:
Probability (definition) - Is the chance that something will happen, how likely it is that some event will occur or play out. The extent to which something is probable
Observed Probability - Observation, or observed value, of a random variable is the value that is actually observed
Theoretical Probability - Theory behind probability, using your knowledge of a situation and using your logical reasoning to calculate the even happening.
Conditional Probability - The probability of an event ( A ), given that another ( B ) has already occurred. Probability of Multiple Events -As it sounds, the probability of two or more events happening
Expected Value -A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
Two-Way Tables - Organizes data collected about two categories with variables.
Tree Diagram - A diagram with multiple branches, representing different processes and relationships.
Joint Probability - A statistical measure where the likelihood of two events occurring together and at the same point in time are calculated. Is the probability of event variables Y occurring at the same time as event X occurs.
Marginal Probability - “The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.”
Backgammon is estimated to be created about 5,000 years ago and may well have originated in what today is Iraq previously, Mesopotamia. This game was found when the early dice was discovered in the area. The name “Backgammon” is most likely derived from “back” and Middle English “gammon”, meaning “game” or play. Discovers have shown that a board race game existed there around 3000 BC. The artifacts include two dice and 60 checkers, and the set is believed to be 100 to 200 years older than Royal Game of Ur. The game of backgammon is first mentioned in Bhartrihari's Vairagya Satakam. There is definitely changes the game has had, there has been improvements in Backgammon. Since the 19th century there has been many additions to the game. Such as doubling cube, gambling and creating strategies. Other than that the game still has the same setup and concept. I chose this game to exhibit because it was created in early existence and itś interesting to learn about games they played in the earlier centuries. I also chose Backgammon because it was a strategy, but also chance game so that sounded extremely interesting to get to know more about.
How Its Played: It is a two player game where playing pieces are moved according to the role of the dice, and a player wins by removing all of their pieces from the board before their opponent does. Each side of the board has a track of 12 long triangles, called points. The points form a continuous track in the shape of a horseshoe, and are numbered from 1 to 24. In the most commonly used setup, each player begins with fifteen checkers, two are placed on their 24-point, three on their 8-point, and five each on their 13-point and their 6-point. The two players move their checkers in opposing directions, from the 24-point towards the 1-point. Points 1 through 6 are called the home board or inner board, and points 7 through 12 are called the outer board. The 7-point is referred to as the bar point, and the 13-point as the midpoint
After rolling the dice, players must, if possible, move their checkers according to the number shown on each die. For example, if the player rolls a 6 and a 3, the player must move one checker six points forward, and another or the same checker three points forward. The same checker may be moved twice, as long as the two moves can be made separately and legally: six and then three, or three and then six. If a player rolls two of the same number, called doubles, that player must play each die twice. The objective is to get all your pieces to your home board, once you have done so everytime you roll you are able to start taking your pieces off the board.
Chance and probability play a role in my game because the whole point of the game is based around the dice rolling. It is also a strategy game, but the main part is about the chance and getting the higher number on the dice roll.
Probability Analysis - Work Displayed In Images Questions: Whats the probability of rolling 2 dice and getting doubles? The probability of getting doubles with 2 dice is 6/36 or 1/6 = 16.7% Whats the probability of rolling 2 dice and getting a number of 6 or higher? The probability of rolling a 6 or higher is 26/36 or 13/18 = 72% Whats the probability of rolling 2 dice and getting a number below 6? The probability of rolling below a 6 is 10/36 or 5/18 = 27%
I chose these questions because getting doubles is a large part to the game and could effect your chances of winning and losing. Also in Backgammon the higher number you roll the more opportunity you have cause you are allowed to then move your pieces multiple times or a farther distance. Habit Of Mathematician: We used multiple habits of a mathematician when creating our game, and our probability analysis, such as collaborate/listening and stay organized. These three habits of a mathematician are very important because without these skills I wouldn’t be able to finish and complete my work in this project. Staying Organized was important in this project making sure everything was in order and your deadlines was set and met. Without this I would get lost very quickly and struggle with learning the concept of probability. Collaborating and listening is important when we worked with our peers when we had questions or needed help with our work. Listening was vital when we were beginners at learning probability questions etc.
Part 4: Reflection The Probability project was overall a decent project, it was easy to understand the concept of probability at first when we did simple chance and probability questions. But once we started to get deeper and learn about probability trees that's when it began to be a challenge. It was then explained more with worksheets and explanations and that's when I begun to have success. My most memorable part of this project was being able to actually create my final product. I had many success when creating my board game such as time management, problem solving and building. I worked solo for this project so it made me an increased workload, so I had to be focused throughout the project. Which then transitioned to my publish worthy final product. If I could change something about this project or process I would display the games better during exhibition days. Cause it was unorganized and many of the games weren’t even displayed.