| SPROUTS DATA | |||
| NUMBER OF STARTINFG DOTS | WINNER 1 | WINNER 2 | WINNER 3 |
| 3 | PLAYER 1 | PLAYER 1 | PLAYER 2 |
| 4 | PLAYER 2 | PLAYER 2 | PLAYER 1 |
| 5 | PLAYER 1 | PLAYER 2 | PLAYER 2 |
I enjoyed this project because I learned it in the form of a game. Above is some of the data I collected analyzing the game, and trying to figure out strategy. Math is often evolved in games. I took on this project because I was interested in the strategy, and I enjoyed a break from trig and functions.
This is an example of trigonometry notes. Trigonometry was a subject that I found very difficult. I didn’t understand many of my class or homework assignments in this area. However I did overcome this struggle and eventually learn what I needed to know by getting whatever extra help I could. This meant that I spent many hours afterschool until I understood what I was being taught.
I am proud of this work because these are equations that I have had to come back to many times. I wrote thorough notes so that I could understand whatever is that I didn’t before reading these notes. If I hadn’t done as well on these notes, it would have been more difficult to take whatever information I needed from these notes.
Sprouts
In this project I have examined the game “Sprouts.” The game starts with a certain number of dots. The first player must draw a curve connecting two of the dots, or loop back on to the original, and then add a dot on to their own curve. The next player does the same. No curves can cross, and no dot can have more than three lines connected to it. The last player to draw a curve wins. Before I started to examine the game, I found out some interesting facts that compelled me to take this on as a project. One of the most important details is that the first player has an advantage of winning if the game begins with three to five dots, and each player were to play a perfect game. Computers have determined the winner of a perfect game for up to 32 dots. No strategy for a perfect game has been completed, because of how unpredictable, and difficult to analyze the game is. The other reason I became so interested in this game was that I would have expected for this game to go on forever because of the constantly growing amount of dots. The only way to figure out how it ever came to a stop was to play the game, and from there I adopted the game as my project.
For my project I decided to expand on some of these facts. I began by playing 3 dot games, and worked up to five. I used red marker for each dot, a blue marker for player one, and a green marker for player two. The results were as I suspected, blue won the majority of the games, just like it had been discovered by those who’ve analyzed the game before me. However, I found that green won more times in a four-dot game than a three-dot game, and more in a five-dot game than in a four-dot game. From this information I came to the conclusion that from three to five-dot games, the higher amount of dots at the beginning of the game, the better chance at winning green (player two) has. Another way to put this might be that the higher amount of dots in a three to five-dot game, the more difficult it is for blue (player one) to win. The game becomes even more complex after five dots, so my conclusion has been confined to five dots, however I will still enjoy further examination of this game with others in the future.
