Playing with HIstory - CORA'S DP

Project Overview
When we started the Playing with History project, we were introduced by a game called "The Game of Pig." In this game, 2 or more people receive two dice to share. Whoever reaches the sum of 50 first out of the players wins that round. This is a game of chance and that is because someone could either roll the die many times and risk losing, but getting lots of tallies or they could roll for a short number of times, and not risk getting so many points or losing. We were expected to learn probability and chances.

Probability definition
"The extent to which something is probable; the likelihood of something happening or being the case."

Observed Probability
"In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself is the process dictating how the observation comes about."
Theoretical
Theoretical probability: probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes. See also: Probability. Experimental Probability.

Conditional
"The probability of an event (A) given that another (B) has already occurred."

Probability of Multiple Events
To find the probability of two independent events that occur in sequence, find the probability of each event occurring separately, and then multiply the probabilities. This multiplication rule is defined symbolically below.

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
A two-way table of counts organizes data about two categorical variables.

Tree Diagram
A thing that has a branching structure resembling that of a tree.

Joint Probability
A joint probability is a statistical measure where the likelihood of two events occurring together and at the same point in time are calculated. Joint probability is the probability of event Y occurring at the same time as event X occurs.

Marginal Probability
In probability theory and statistics, the marginal distribution of a subset of a collection of random variable is the probability of the variables contained in the subset.

Renaissance Game
The board game Fox and Geese was said to be created in 1697. The design on the board looks complex with squares, rectangles, and diagonal lines in the small squares. In this game, it requires two players. There are 33 points on the board to move the game piece(s) to. One player is the fox which could move in every direction of the board: forward, backwards, and side to side. The fox can also use any lines in the board which includes the diagonal lines that leads to the points. The other player receives 15, 17, or 18 game pieces which are the geese. The geese can only move forward, diagonally forward, and side to side. The geese can prevent the fox from being able to move and win if they surround the fox in all directions with more than one behind the other. This is because if there's one space behind the geese then the fox can jump across that geese and the other player loses that game piece. If the fox captures every goose on the board, then it wins. This is a game of inequality, so the players have to take chances to try to win.

Probability Analysis
A few questions I had to consider for my probability analysis were: Is this game a concept of probability? How can I include probability to this? And what question will I have based on probability? I also had to solve this problem and show how it works. This is a habit of a mathematician, simply problem solving.
Fox and Geese is a game is inequality and strategy. I included probability to this game by having a coin toss to determine which player out of the two takes the first turn.
The question is, what is the probability of one player out of two going first on at least one game?
Pr [Go 1st on 1 game] = 1/2 (One out of 2 chances)

Reflection
For this project, I succeeded in finding a fun game from the Renaissance time called Fox and Geese. Luckily the game was a game of chance since there was a little unfairness in the game. I also felt that I did well with the research of the game. Unfortunately though, I didn't get to create the full game because I was out sick for the building days, but I know the game, how it works, and the time it was originally created.
For probability, we did a lot of assignments showing us to use the proper equation to figure out the probability of real-world problems and learned to really focus on the question and what it's asking because if the words are switched around even just a little bit, it could have a whole new meaning. We learned and created Tree Diagrams to make it simpler to find out the probability. One assignment in which we used these was the marble problem. I feel that I should've asked questions more for this project because at some points I got confused.