During the Playing with History project, we took inspiration from renaissance games, and made our own versions of the originals. We did a lot of mini probability activities leading up to this project, like playing a "game of pig" with dice, and a few other ones as well. We also used a lot of different methods to find the different probabilities, such as:
My game was called Wari, and it was basically an even older version of mancala. Wari originated in Africa, and some parts of East Asia. The official name of the time, "Oware", means he/she marries. The legend said that a man and a woman had played the game endlessly, and to keep the game going, they got married. The game was also often played as a way of meeting others. It was a very social and inviting game that people would join just when walking by. The modern version of this game is mancala, although mancala was around near the same time as Wari. Mancala was just played in other areas. My group and I chose to play this game because we all really enjoyed the game of mancala, and it was interesting to learn how other cultures had played the game. To give the game chance, my group and I added a dice aspect to the game, where you roll before each turn. You roll 2 dice before each turn, If you roll above a seven, your turn is skipped. If you roll above a seven twice in a row, you go on your next turn no matter what. To speed up the game, we also made a rule that if you roll a double (2 of the same number) your instantly out of the game.
Probability Analysis:
Our Question: What is the probability that your turn will be skipped, or that you'll roll a double?
Chance your turn is skipped (rolling over a 7): 15/36
Chance that the game is over and you lose (rolling a double): 6/36
We used multiple habits of a mathematician when creating our game, and our probability analysis, like staying organized and seeking why and proving it. These two habits of a mathematician are very important because without organization, we would get lost very quickly. And if we didn't seek why and prove, everyone in the group would be on completely different pages, and we would be doing three different things.
Overall I thought that this was a really good project, and all of the classes blended very nicely. I had a few struggles at the beginning, like choosing a game to pursue. At first it was tough to choose because we either couldn't get our hands on the materials, or the game was to complex for exhibition. Once we found Wari, we figured it could work perfectly if it just incorporated chance. That was yet another struggle we had, not being able to figure out how to add chance. We solved this problem by figuring out a way to incorporate dice, and even incorporated a step where if rolled correctly, you could instantly lose or win the game. Little things like this made the game go a lot quicker, thus letting more people play on the night of exhibition. We also had a lot of success when making our game, like our team work and collaboration. I feel like we all collaborated very well and split the work nice and even. I think that without my group members, I wouldn't have gotten to the game where it was the night of exhibition, and vice versa if my group didn't have me. If we were to do this project again, I think I would keep it all the same, except for the way we presented our games at exhbition. At least in my case, it was all kind of a mess, and I had to set up my game on a table near the back where not many people came. I think If we had moved our game to a different room or booth this would have helped, but we were told there would be space. All in all, this was a really good project and I enjoyed it. I think that the concept was really good, and it all blended together really nicely.
- Probability
- the extent to which something is probable
- Observed Probability
- The value that is actually observed
- Theoretical Probability
- based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes
- Conditional Probability
- the probability of an event,, given that another has already occurred.
- Probability of Multiple Events
- As it sounds, the probability of two or more events happening
- 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 table that has an x and y axis, displaying information on a certain topic
- Tree Diagram
- There are two "branches" (Heads and Tails) The probability of each branch is written on the branch. The outcome is written at the end of the branch.
- Joint Probability
- 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 happening at the same time as event X
- Marginal Probability
- he marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.
My game was called Wari, and it was basically an even older version of mancala. Wari originated in Africa, and some parts of East Asia. The official name of the time, "Oware", means he/she marries. The legend said that a man and a woman had played the game endlessly, and to keep the game going, they got married. The game was also often played as a way of meeting others. It was a very social and inviting game that people would join just when walking by. The modern version of this game is mancala, although mancala was around near the same time as Wari. Mancala was just played in other areas. My group and I chose to play this game because we all really enjoyed the game of mancala, and it was interesting to learn how other cultures had played the game. To give the game chance, my group and I added a dice aspect to the game, where you roll before each turn. You roll 2 dice before each turn, If you roll above a seven, your turn is skipped. If you roll above a seven twice in a row, you go on your next turn no matter what. To speed up the game, we also made a rule that if you roll a double (2 of the same number) your instantly out of the game.
Probability Analysis:
Our Question: What is the probability that your turn will be skipped, or that you'll roll a double?
Chance your turn is skipped (rolling over a 7): 15/36
Chance that the game is over and you lose (rolling a double): 6/36
We used multiple habits of a mathematician when creating our game, and our probability analysis, like staying organized and seeking why and proving it. These two habits of a mathematician are very important because without organization, we would get lost very quickly. And if we didn't seek why and prove, everyone in the group would be on completely different pages, and we would be doing three different things.
Overall I thought that this was a really good project, and all of the classes blended very nicely. I had a few struggles at the beginning, like choosing a game to pursue. At first it was tough to choose because we either couldn't get our hands on the materials, or the game was to complex for exhibition. Once we found Wari, we figured it could work perfectly if it just incorporated chance. That was yet another struggle we had, not being able to figure out how to add chance. We solved this problem by figuring out a way to incorporate dice, and even incorporated a step where if rolled correctly, you could instantly lose or win the game. Little things like this made the game go a lot quicker, thus letting more people play on the night of exhibition. We also had a lot of success when making our game, like our team work and collaboration. I feel like we all collaborated very well and split the work nice and even. I think that without my group members, I wouldn't have gotten to the game where it was the night of exhibition, and vice versa if my group didn't have me. If we were to do this project again, I think I would keep it all the same, except for the way we presented our games at exhbition. At least in my case, it was all kind of a mess, and I had to set up my game on a table near the back where not many people came. I think If we had moved our game to a different room or booth this would have helped, but we were told there would be space. All in all, this was a really good project and I enjoyed it. I think that the concept was really good, and it all blended together really nicely.