Playing With History Project Reflection
Probability has a couple definitions, some of them being the likelihood of something happening or the mathematical definition, the likelihood of an aspect happening, often written in a fraction, percentage, or decimal. This is exactly what we’ve learned, what probability is and how to calculate it. Before this I had never liked fractions or percentages, they weren’t really something that I enjoyed learning in math. This year, I am glad to say that I don’t have as much trouble with them anymore. At the beginning we did assignments like Game of Pig to help us begin to learn probability. These assignments really helped as it combined things that we had previously known and slowly made it more complex. From there we learned different types of probability to help us better understand it, theoretical probability, conditional, and observed. Through learning this we were able to differentiate the different types of probability and how they were each different. After learning that, we started working with multiple events which let us work with multiple steps, making the problems more complex. Some of the most helpful tools that we received this semester however, would probably be the two-way tables and tree diagrams. These were a huge help in solving for the probability because they helped us map out the problem and walk us through the problem. Then, with expected value, joint probability, and marginal probability we started working the probability into equations which was complicated at first, but easy to get the hang of. Throughout the whole process we learned so much on this subject and had a lot of fun with the projects and assignments on the way.
The game that I made was based on the game Knucklebones that was created and played around the time of the Renaissance. The game’s origin has not been determined, but is said to have been started in either Egypt or Lydia. After that, the Greeks and Romans adopted the game and it was played by people of all ages. The game could be played in several ways, but the pieces never changed. They were oddly shaped small pieces that had sides that were all different. Some children played it in a similar way to how we play the game of jacks, which was the most popular way of playing. It was also played my men and women to determine luck depending on how the pieces landed on the back of their hand. It was played especially by women to determine their love life. This game is known because it had been depicted in many paintings and sculptures. I chose this game because of how it had evolved and adapted. I liked how there were several different ways that it was played and how it was played by everyone. It was very interesting to learn about and I had a lot of fun adapting it into the game that I created. I liked how the game was originally, but I changed it a little to make it more interesting to play. I made pieces and a board to play with and included the aspect of throwing the sticks into the air and catching them on the back of your hand. The chance aspect of this game is the sticks. They have a symbol on each side, one has a star, and one has a circle. This makes it so that it doesn’t rely too heavily on skill and more on the chance of what side each stick will land on. The rules of the game are this; first, you throw your set of sticks into the air. Then, try to catch them on the back of your hand. If you catch one on the back of your hand that’s a star, go forward two spaces. If the stick lands on the board on the star side, then it only counts for one space. The circles don’t count for any spaces moved, unless you catch it on the back of your hand on the circle side, in which case it would be worth one space. There are also extra bonus squares that give you extra spaces or have you move backwards. After adding up how many spaces you move, take your piece and move it, then give the next person their turn.
What is the probability that you will get all stars when throwing four sticks into the air?
The probability of getting a star or a circle on each individual stick is .5 because there only two sides with two options. Considering this, we can make a tree with the probability of .5 for every stick. In order to find the probability for getting all stars, we would multiply the probabilities by each other to get one joint probability. In this case you would do: ½ * ½ * ½ * ½ which equals .0625. This can also be used to find any combination of results. For example, if you wanted to find the probability of you getting three stars and one circle, since the probability number of each outcome is the same you would get the same answer. The only thing that would make it change in this situation is if you had an unfair one or if you added more sticks. This would cause the results to be different than previously calculated.
During this project I enjoyed learning about different games and how they have evolved and changed. All of them had a very interesting origin or history and it was very interesting to learn about some of them before settling on the game of knucklebones. Although it took me a little longer than expected to come up with an adaptation idea, I eventually came up with something and it was fun to create. I especially enjoyed the aspect of turning the game into something different and adapting it, still keeping it’s original guidelines. Coming up with ideas to adapt it was a little challenging at first, but I liked the amount of freedom that we had with it and enjoyed creating something new.
Probability has a couple definitions, some of them being the likelihood of something happening or the mathematical definition, the likelihood of an aspect happening, often written in a fraction, percentage, or decimal. This is exactly what we’ve learned, what probability is and how to calculate it. Before this I had never liked fractions or percentages, they weren’t really something that I enjoyed learning in math. This year, I am glad to say that I don’t have as much trouble with them anymore. At the beginning we did assignments like Game of Pig to help us begin to learn probability. These assignments really helped as it combined things that we had previously known and slowly made it more complex. From there we learned different types of probability to help us better understand it, theoretical probability, conditional, and observed. Through learning this we were able to differentiate the different types of probability and how they were each different. After learning that, we started working with multiple events which let us work with multiple steps, making the problems more complex. Some of the most helpful tools that we received this semester however, would probably be the two-way tables and tree diagrams. These were a huge help in solving for the probability because they helped us map out the problem and walk us through the problem. Then, with expected value, joint probability, and marginal probability we started working the probability into equations which was complicated at first, but easy to get the hang of. Throughout the whole process we learned so much on this subject and had a lot of fun with the projects and assignments on the way.
The game that I made was based on the game Knucklebones that was created and played around the time of the Renaissance. The game’s origin has not been determined, but is said to have been started in either Egypt or Lydia. After that, the Greeks and Romans adopted the game and it was played by people of all ages. The game could be played in several ways, but the pieces never changed. They were oddly shaped small pieces that had sides that were all different. Some children played it in a similar way to how we play the game of jacks, which was the most popular way of playing. It was also played my men and women to determine luck depending on how the pieces landed on the back of their hand. It was played especially by women to determine their love life. This game is known because it had been depicted in many paintings and sculptures. I chose this game because of how it had evolved and adapted. I liked how there were several different ways that it was played and how it was played by everyone. It was very interesting to learn about and I had a lot of fun adapting it into the game that I created. I liked how the game was originally, but I changed it a little to make it more interesting to play. I made pieces and a board to play with and included the aspect of throwing the sticks into the air and catching them on the back of your hand. The chance aspect of this game is the sticks. They have a symbol on each side, one has a star, and one has a circle. This makes it so that it doesn’t rely too heavily on skill and more on the chance of what side each stick will land on. The rules of the game are this; first, you throw your set of sticks into the air. Then, try to catch them on the back of your hand. If you catch one on the back of your hand that’s a star, go forward two spaces. If the stick lands on the board on the star side, then it only counts for one space. The circles don’t count for any spaces moved, unless you catch it on the back of your hand on the circle side, in which case it would be worth one space. There are also extra bonus squares that give you extra spaces or have you move backwards. After adding up how many spaces you move, take your piece and move it, then give the next person their turn.
What is the probability that you will get all stars when throwing four sticks into the air?
The probability of getting a star or a circle on each individual stick is .5 because there only two sides with two options. Considering this, we can make a tree with the probability of .5 for every stick. In order to find the probability for getting all stars, we would multiply the probabilities by each other to get one joint probability. In this case you would do: ½ * ½ * ½ * ½ which equals .0625. This can also be used to find any combination of results. For example, if you wanted to find the probability of you getting three stars and one circle, since the probability number of each outcome is the same you would get the same answer. The only thing that would make it change in this situation is if you had an unfair one or if you added more sticks. This would cause the results to be different than previously calculated.
During this project I enjoyed learning about different games and how they have evolved and changed. All of them had a very interesting origin or history and it was very interesting to learn about some of them before settling on the game of knucklebones. Although it took me a little longer than expected to come up with an adaptation idea, I eventually came up with something and it was fun to create. I especially enjoyed the aspect of turning the game into something different and adapting it, still keeping it’s original guidelines. Coming up with ideas to adapt it was a little challenging at first, but I liked the amount of freedom that we had with it and enjoyed creating something new.