**Introduction**

An overview of my entire project would start with the beginning where I was trying to figure out what kind of game I wanted to create. So I first went to the drawing board and eventually joined Michael and Alex in a group to recreate a game called Thirty-One. We started to learn about Probability and what the probability was to get a certain number of the types of cards, I was mainly expecting to learn a lot about how much games have changed and how different things are now a days with card games as well as probability and of course the math portion of it about your chances and the risk you are taking while playing these games.

Once we figured out what kind of game that we wanted to create "Thirty-One" we needed to learn how the game worked. The game was all about probability or chance of getting a higher number than everyone else before someone else beats you to it. Each card had a certain number, for example the number cards had the number they presented and card such as, jack's ,king's ,queen's or ace's had their own special number. Once we played the game alittle bit we then eventually decided to recreate what the cards would look like back then and document them on card stock to show anyone that decided to check it out. The process over all was pretty fun and I think I learned a lot of different ways of finding the probability for something to happen.

**Definitions**

**Probability**

**Observed Probability**

**Theoretical Probability**

**Probability of Mutiple Events**

**Expected Value**

**Two-Way Tables**

**Tree Diagram**

**Joint Probability**

**Marginal Probability**

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Renaissance-Inspired GameBackground The game Thirty-one" orginated in the 15th century. It has always been a popular game but nobody really knows when it orginated although it does have muitiple names and similar versions such as Big Tonka, Nickel Nock, Blitz, and more. Who played it during the Renaissance?The people that played it during the time were the French and known for being played around the world in the 15th century. Is there a Modern version?The game is also played now adays except it has many different names in many other countries such as, south Louisiana, Mississippi, Pennsylvania, Central Indiana, and more. Why did you choose this game?We choosed this game because of the easy to learn concept and easy to teach. It was also a unique game that seemed fun to learn about. How is the game played?The game is played by having from two to seven people where the players need to attempt to get to the number 31 before everyone else and win the game. Each card resembles a number and every turn the played has a option of keeping the cards they have or discard one of the onces they have to choose a new card out of the deck. The game lasts around 10 minutes and it all about luck of getting the better hand when the game starts. |

**Probability Analysis**

Questions One:

Questions One:

The question I am going to use is what is the probability of getting a perfect set of thirty-one on your deck at the beginning of the game. The two out comes are yes you get a perfect set of thirty-one at the beginning of the game and the second out come is not getting a deck of below thirty-one. If you get a perfect deck you then have the opportunity of getting either keeping the perfect deck when you draw your next card or losing your prefect deck when you choose a new card, or end up having a bad deck below thirty-one to getting a perfect deck or having a bad deck of below thirty-one to keeping a bad deck of thirty-one. To simplify this instead of caculating every single number possible Im just going to focus on the decks being a whole

**Calculations**

So you have six possible outcome

**Yes Perfect Deck:**

Keep Thirty-one

Lost Thirty-one

**No Perfect Deck:**

Still no Thirty-One

Gained Thirty-One

**How many possible outcomes?**

You Totally have a 50 50 chance for yes and no and totally have a 1/6 (16.67%) chance of getting one

of the outcomes. If it is yes you have a 1/2 chance and if its no you have a 1/2 chance. Pretty Simple

**Questions Two**

Now alittle more difficult question. What is the possibility of getting a queen or a king in the 5 decks you draw at the beginning of the game

Now this will be similar to questions one except alittle more complicated.

**Caculations**

*(The Outcomes are)*

Card 1, Card 2, Card, 3, Card 4, Then King or Queen.

*Google Doc Link to all of the possilbe Outcomes*

docs.google.com/document/d/19KMzldM560CaMKL1MP8qdJr5c7MsA-VJLZ1w30ww8yQ/edit?usp=sharing

There are 7776 outcomes and I didnt do this on my own instead I used a Combinations Caculator to find all of the

Possible Combinations you can get from getting a Queen or King including 4 other cards in your deck. Now your chances of getting a king of queen in

all of those numbers are huge and would take forever to count so instead Im going to estimate and say 3000 of the 7776 were queen's or kings. Now if 3000 of the cards were queens or kings that would mean the rest of the 4000 are Random Cards and your Outcome for how many kings of queens would be 3000/7776 38.5802469136% of getting a king or queen in your deck of course with that estimation. I was able to use

**Conjecture and Test**to say what if the outcome is 3000 out of 7776 and used a specific number to find out the outcome of the total estimate percent. I started small and ended up with around 7776 outcomes. I also ended up using

**Describe and Articulate**when creating the tree diagram.

**Reflection**

I quite enjoyed this project, is was one of my favorites projects this year. Playing old card games and learning about how they worked and how you find the probability or chance was intresting. At the beginning I did have trouble finding a game to do with my partners but we eventually figured out that we were gonna do a game called Thirty-one. Creating the recreations of renaissance cards games were enjoyable but they also took a good good chunk of time to create. It was amusing to learn on how the game worked and eventually playing it to over and over againn to get a better look on how the game works. I enjoyed presenting the game and just overall I think this was a great project and should be used again in the future.