Project Overview
This project was about how board games have always been around and have evolved. The project focused on learning about probability and we did that by looking into what probability and all of the technicalities. This unit has helped me to grasp a true understanding for what probability is. I think that the best part of this unit was all of the challenge options. They really pushed your thinking and helped to make you actually understand why all of this is useful.
Probability Key:
~Probability~
Probability is the likelihood of something happening or being the case.
~Observed Probability~
Observed probability is the probability given based on observed data.
~Theoretical Probability~
Theoretical Probability is the probability of something happening based not on data, but on algebraic thinking.
~Conditional Probability~
Conditional Probability is the probability of something given something else. I.E. What is the probability that you will roll a 6 given that you have a unfair die.
~Probability of Multiple Events~
The Probability of Multiple Events is the sum of individual events.
~Expected Value~
The Expected Value is the value that is predicted. EV= n * Pr[A]
~Two-Way Tables~
Two way tables are a way of separating multiple events to see the bigger picture. They are very easy to look at and understand.
~Tree Diagram~
Unlike the Two way table a tree diagram shows more including the branch probabilities. Also known as the probability of a specific event happening.
~Joint Probability~
Joint Probability is the probability of two or more things happening. I.E. What is the probability that you roll a die 2 times and you roll a 2 then a 3.
~Marginal Probability~
Marginal Probability is the probability of one event when you are given multiple.
Probability is the likelihood of something happening or being the case.
~Observed Probability~
Observed probability is the probability given based on observed data.
~Theoretical Probability~
Theoretical Probability is the probability of something happening based not on data, but on algebraic thinking.
~Conditional Probability~
Conditional Probability is the probability of something given something else. I.E. What is the probability that you will roll a 6 given that you have a unfair die.
~Probability of Multiple Events~
The Probability of Multiple Events is the sum of individual events.
~Expected Value~
The Expected Value is the value that is predicted. EV= n * Pr[A]
~Two-Way Tables~
Two way tables are a way of separating multiple events to see the bigger picture. They are very easy to look at and understand.
~Tree Diagram~
Unlike the Two way table a tree diagram shows more including the branch probabilities. Also known as the probability of a specific event happening.
~Joint Probability~
Joint Probability is the probability of two or more things happening. I.E. What is the probability that you roll a die 2 times and you roll a 2 then a 3.
~Marginal Probability~
Marginal Probability is the probability of one event when you are given multiple.
My Renaissance Game:
Mancala
History of Mancala and How we changed it:The oldest game of Mancala was found in the 6th - 7th Century. There is over 800 names for this game and many different variations of mancala. During the renaissance this game was called Aware. It was most commonly found in Southern Europe and Africa. because it could be played with anything even rocks and sand/dirt. The game is played where you take one of the slots of marbles and you move then and drop one in each slot until you run out always going counter clockwise. The goal is to get the most in your end slot each players is on the right. Don't forget to skip the other persons end slot because you don't want to give them points. We changed this game by adding probability into it. If you have played Mancala you would know that it is very thought based. What we did was make it so that there is no decision making. How we did that? We came up with the idea of numbering every slot on the board. We also added a dice so that depending on what you roll that is the slot you use. These are the rules/instructions:
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Probability Analysis:My probability question for my renaissance game was "What is the most amount of tokens you can get into your pot on your first turn?"
To find the highest amount of tokens you can get in your pot on the first turn you first need to find were you are taking from. There is a 1/6 probability to roll any number from 1-6. If we focus on the number 4 we can see that there is a total of 2 tokens in your pot. The way I calculated this probability was by drawing a chart out. In the chart we see that we started at hole #4 with 4 tokens, put a token in each hole (Including one in the pot) and ran out in the 1st hole on the opposite side. Continuing this sequence you will have 5 tokens and end in the 6th hole of the opposing side, then the 5th hole (your side), 3rd hole (opposing), and ending in the starting position. This was very challenging to calculate because Mancala is originally a logic game that was very hard to present in a probability chart/drawing. |
Exhibition Reflection:
This exhibition was very fun for me. I was able to display my game and get some great people to enjoy it. It was a great time to display our work. Although the time was short we were able to get the point across that we had learned a lot about probability. I think that in every way and for every class this was my best exhibition that I have done.