Overview:
Throughout this project, we used our studies of the Renaissance era to reproduce/adapt a Renaissance game to involve a form of "chance". This project mainly revolved around probability. Probability is the measure of the likelihood that an event will occur. We started off this project with The Game of Pig where we tried the find the "best strategy" to win the game. This game is played with one dice, you roll the dice and accumulate points as your role, but if you roll a 1 then all the points you have been accumulating disappear. As we were playing the game we had to come up with a strategy for winning. A Mathematical Strategy is a complete plan of action to carry out a plan to achieve a goal. After playing the game I had it clear we were going to be learning about probability. I had learned about probability in previous years but I was excited to learn even more and it would be a good refresher. I learned many new probability concepts and I also go to revisit concepts that I had not worked with in a while. My main goal for this project was to keep an open mind of what we were learning because even though we have previously learned probability, I wanted to keep in mind that we were going to learn new things. I also wanted to improve in using the habits of a mathematician. In each worksheet we did throughout this unit I learned something new or I got to practice using a concept.
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Concepts learned:• Observed Probability - is the probability being observed, the probability that actually happened.
• Theoretical Probability - is based on reasoning and is written as a ratio of the number of favorable outcomes to the number of possible outcomes. • Conditional Probability - the probability of an event occurring based on the previous event • The probability of Multiple Events - is used to find the probability of multiple events that occur for an experiment. • Expected Value - is the return you can expect for some kind of action • Two-Way Tables - Organizes data in two categorical variables, • Tree Diagram - shows all the possible outcomes of an event • Joint Probability - is "likelihood of two events occurring together and at the same time are calculated." • Marginal Probability - " gives the multiple values of the variables in the subset without reference to the other variables or their values." |
My Renaissance-Inspired Game:
The game we choose to recreate is Frussi also known as Primero. Primero is a 16th-century gambling card game of which the earliest reference dates back to 1526. Primero is closely related to the game of primo visto, if not the same. The game was known as the noblest of all card game, it was played commonly among the nobles. According to a poem that Francesco Berni wrote the game was most commonly played in Italy at the beginning of the 16th century. This game is still played in central Europe and Spain with Italian-suited cards under the names of Goffo or Bambara. Primero is similar to our modern day poker. I chose this game because of its similarity to modern poker because poker is a game I enjoy to play. Probability plays an important role in this game because the probability of pulling out a certain card from a 52 deck of cards in low. For example, a probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck.
How to play to Primero? |
How is the game played?
Types of Hands: -Chorus: four of a kind -Fluxus: all cards, same suit -Supremus: highest possible three flushes (ace, 6, 7 and unnecessary fourth card) -Primero: one card from each suit -Numerous: 2 - 3 cards same suit, higher beats out lower value cards. |
For our game, no building was really necessary since all that was needed was a deck of 52 cards. Our artifact that we were going to show on exhibition was a card that would have been used during the Renaissance era. That picture is located right next to My Renaissance-Inspired Game.
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Probability Analysis:
Disclaimer: for this game we did not create a deck of cards, we just used a regular deck, and we also took out some of the cards that we did not need to play the game.
Question: What is the probability of getting a chorus of 5, in the second hand dealt?
Analysis: There are 52 cards in a deck, but we remove the 8s, 9s, and 10s, so we will just be working with 40 cards. There are 4 of each card so we could just say 1/40.
How to solve: We started with drawing the tree diagram. The diagram shows the probability of getting dealt a four of kind for all the ones. As we were solving our question we found it easier to find the probability of one of the card group and then multiplying that probability by 10 to find the total probability of getting dealt a Chorus for all card groups. Our work and tree diagram are down in the image below.
Question: What is the probability of getting a chorus of 5, in the second hand dealt?
Analysis: There are 52 cards in a deck, but we remove the 8s, 9s, and 10s, so we will just be working with 40 cards. There are 4 of each card so we could just say 1/40.
How to solve: We started with drawing the tree diagram. The diagram shows the probability of getting dealt a four of kind for all the ones. As we were solving our question we found it easier to find the probability of one of the card group and then multiplying that probability by 10 to find the total probability of getting dealt a Chorus for all card groups. Our work and tree diagram are down in the image below.
Reflection:
Throughout this project, I grew a lot as a mathematician. This is because I was able to become stronger with using the habits of a mathematician. For example, a challenge I faced throughout this project was the probability trees. When working on the probability trees I would get really unorganized and my probability trees would get messing and confusing. A habit of mathematician I really got to improve on for this unit was Staying Organized, this is because after I realized that it was my fault that the probability trees were not making sense I started slowing down when working on them or doing them twice so they came out neater. A success I had in this project was understanding the two-way tables, at first glance I thought I was not going to understand them because they looked too hard. When we did the “Dr.Drew the dog ate my homework” worksheet and we went over how to fill out the two-way table I understood how to fill it out. I was able to explain it to my classmates who didn't understand. Thanks to my understanding of the two-way table I was able to help others. Overall the project really helped me grow as a mathematician and improve my habits of a mathematician, and that will come in useful in future projects.