This project was about the renaissance and the many figures during this time, but for math we focused on games that were played. Our entire math portion was focused on probability of outcomes in life, and anywhere in math. Each student had to study one game from the renaissance and remake it, or add a modern twist to the game. This first part is defining the vocabulary we used during the project.
PART 1 Vocab Definitions:
• Probability (definition) -The chance that something can occur, 100% probability means it will for surely happen, and it can’t go over 100%. It can also be in a fraction form.
• Observed Probability- It’s the probability from your experiment that you did and observed.
• Theoretical Probability- It’s the probability before the experiment, what the math says could happen in the perfect world.
• Conditional Probability- The probability something will happen to object A, given that object B’s occurrence happen
• Probability of Multiple Events- Probability of Multiple events is the probability of 2 or more event happening.
• Expected Values- Expected value is 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- Two way tables show joint and marginal probabilities along with totals.
• Tree Diagram- A tree diagram is a way of looking at all the possible outcomes and probabilities in an equation, it shows both the joint and conditional probabilities.
• Joint Probability- Joint possibility is a statistical measure where the likelihood of two events occurring together and the same point in time are calculated. It is the probability of event y happening at the same time as event x.
• Marginal Probability- It’s the probability of a specific event happening in part of a probability equation.
PART 2 History and Tutorial of Our Game:
For most of its lifespan As-Nas existed with Ganjifa cards. As-Nas date back to the 17th century, (originated in Persia) and at that time a 25 card pack was used, with 5 suits, each suit having one court card and four numeral cards. Cards from the 19th century with the classic As-Nas designs can be found in various museum collections. By 1877 As-Nas cards were gradually falling into disuse, being replaced by European types. The game of As-Nas largely fell out of fashion by around 1945. However, As-Nas may have persisted a little longer in rural areas, some traditions have stayed in place and the cards are still used. The cards may have influenced today's modern westernized cards with standard suit symbols (hearts, clubs, spades and diamonds). Âs Nas is played with a set of five subjects, all courts, each of which is repeated either four or five times, for a total number of 20 or 25 cards. Therefore, there are no pip cards, nor suits, as well. Usually As-Nas cards were hand-painted on cardboard, and then lacquered.
PART 1 Vocab Definitions:
• Probability (definition) -The chance that something can occur, 100% probability means it will for surely happen, and it can’t go over 100%. It can also be in a fraction form.
• Observed Probability- It’s the probability from your experiment that you did and observed.
• Theoretical Probability- It’s the probability before the experiment, what the math says could happen in the perfect world.
• Conditional Probability- The probability something will happen to object A, given that object B’s occurrence happen
• Probability of Multiple Events- Probability of Multiple events is the probability of 2 or more event happening.
• Expected Values- Expected value is 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- Two way tables show joint and marginal probabilities along with totals.
• Tree Diagram- A tree diagram is a way of looking at all the possible outcomes and probabilities in an equation, it shows both the joint and conditional probabilities.
• Joint Probability- Joint possibility is a statistical measure where the likelihood of two events occurring together and the same point in time are calculated. It is the probability of event y happening at the same time as event x.
• Marginal Probability- It’s the probability of a specific event happening in part of a probability equation.
PART 2 History and Tutorial of Our Game:
For most of its lifespan As-Nas existed with Ganjifa cards. As-Nas date back to the 17th century, (originated in Persia) and at that time a 25 card pack was used, with 5 suits, each suit having one court card and four numeral cards. Cards from the 19th century with the classic As-Nas designs can be found in various museum collections. By 1877 As-Nas cards were gradually falling into disuse, being replaced by European types. The game of As-Nas largely fell out of fashion by around 1945. However, As-Nas may have persisted a little longer in rural areas, some traditions have stayed in place and the cards are still used. The cards may have influenced today's modern westernized cards with standard suit symbols (hearts, clubs, spades and diamonds). Âs Nas is played with a set of five subjects, all courts, each of which is repeated either four or five times, for a total number of 20 or 25 cards. Therefore, there are no pip cards, nor suits, as well. Usually As-Nas cards were hand-painted on cardboard, and then lacquered.
PART 3 Probability Analysis of Our Game:
Throughout this project I used many different habits of a mathematician, but the one that stood out in our game was problem solving, for the longest time we weren’t sure how to make our game, if we were going to print it or hand make it. Then we finally settled on printing it and spread out the work. Another Habit of a mathematician that we displayed during this project was taking apart and putting back together problems. We used this skill when we were learning how to make probability analysis's. To understand the final probability of each equation I took apart each section of our probability trees, then looked at the outcomes of those.
IN THIS IMAGE: The problem I was solving here is, What is the probability that you get two or more cards of the same suit two rounds in a row. At the top we have the chance of getting no combos, then we have that number minus one. This finds the probability of getting the two in a row which is 36%. Then below we have a tree showing how the first round chances could work if you got the right combos.
Throughout this project I used many different habits of a mathematician, but the one that stood out in our game was problem solving, for the longest time we weren’t sure how to make our game, if we were going to print it or hand make it. Then we finally settled on printing it and spread out the work. Another Habit of a mathematician that we displayed during this project was taking apart and putting back together problems. We used this skill when we were learning how to make probability analysis's. To understand the final probability of each equation I took apart each section of our probability trees, then looked at the outcomes of those.
IN THIS IMAGE: The problem I was solving here is, What is the probability that you get two or more cards of the same suit two rounds in a row. At the top we have the chance of getting no combos, then we have that number minus one. This finds the probability of getting the two in a row which is 36%. Then below we have a tree showing how the first round chances could work if you got the right combos.
Part 4 Reflection:
I’m going to start with the challenges I faced throughout this project, my biggest challenge was formatting the probability equations. This was a struggle because it was new to me and it continued to affect me from beginning to end. Each equation we answered had to be Pr [A]= x%. This was also difficult because some of the equation had to variables, and the equations to solve these variables took the same format. My biggest success during this project was easily my game. We took time and researched our game, found out how to play it, what it looked like originally, and even how it’s been changed modernly. The struggle with our game was finding a way to change how it’s played with a form of probability. We soon realized that the answer was right in front of us and was what we’d been using the whole time, coin flips. This project started with simple coin probabilities and patterns and we didn’t even think that this could be a tie breaker for too long. This year I plan to continue growing in the way I set up my notebook and math equations in general. Usually my notes and set ups for equations are just scattered and have the answer somewhere in there circled. If I go in order I think it’ll help me grow in any state or unit we’re in at the time.
I’m going to start with the challenges I faced throughout this project, my biggest challenge was formatting the probability equations. This was a struggle because it was new to me and it continued to affect me from beginning to end. Each equation we answered had to be Pr [A]= x%. This was also difficult because some of the equation had to variables, and the equations to solve these variables took the same format. My biggest success during this project was easily my game. We took time and researched our game, found out how to play it, what it looked like originally, and even how it’s been changed modernly. The struggle with our game was finding a way to change how it’s played with a form of probability. We soon realized that the answer was right in front of us and was what we’d been using the whole time, coin flips. This project started with simple coin probabilities and patterns and we didn’t even think that this could be a tie breaker for too long. This year I plan to continue growing in the way I set up my notebook and math equations in general. Usually my notes and set ups for equations are just scattered and have the answer somewhere in there circled. If I go in order I think it’ll help me grow in any state or unit we’re in at the time.