What's On Back?
For this POW, the game is called What’s on Back? This game consists of three cards. One card has an X on both sides. One card has an O on both sides. And the last card has an o on one side, and an X on the other side. The situation of this problem was someone picks up a card and based on what they see, guesses on what symbol they think is on the back of the card.
What this problem wanted was for us to figure out the probability of a strategy used to play this game. Some strategies that we were suggested to investigate were always guess an X, always guess the same symbol as you pick up, and to always guess the opposite symbol of what you pick up.
What I first did was play the game with a friend. I guessed the symbol that I picked up every time for 30 times, getting 19 guesses right and 11 guesses wrong. The friend, Allison Hopkins, was guessing X the entire time as her strategy for another 30 times, getting 18 right and 12 wrong. I was more successful in my strategy, although it was a tiny difference: 1.
I listed my outcomes of the experimentation of strategies above. After this point, I realized that picking a number like 30 was not the best idea. Since you can multiply 30 by roughly 3.33 to get 100 for a percentage, I multiplied the number 19. This percentage represents the percentage of right answers you should get based on the data I collected for the strategy of picking the symbol that I originally picked up. When rounded, this percentage is 63% of correct answers. I repeated the same process for the next strategy, multiplying 18 by 3.33 to get a rounded number of 60%. This is all my experimental results based on data.
Next, I looked at a theoretical set of data. Once you have picked up a card, there are only two symbols to choose from, giving the idea that each theoretical percentage of winning would be at 50% for both strategies.
To find a more common ground, I averaged the 63% and 50% to get 57%. Then I did the same thing with 60% and 50%, getting 55%. So, in conclusion, I would say that based on data and theoretical situations, the strategy that I worked with, picking the symbol that you originally picked up, would have a higher chance of winning than Allison’s.
For this problem, I think that I deserve an 8.5/10. I understood all of the ideas that were shown to me with this probability problem, my only flaw being that I only got data from 30 times. I feel that I should have gotten a little more data, but I still did all of the math to get the probabilities and I am proud of that. Even though I didn’t get a lot of data, I would still use persistence as a skill that I used when working through this problem. I had a little bit of a hard time with getting the difference between experimental and theoretical, and what to do with the percentages after that. I chose to average them and base my conclusion on the averaged amount, feeling that it would be much closer to what the percentage would look like if I had done more tests.
What this problem wanted was for us to figure out the probability of a strategy used to play this game. Some strategies that we were suggested to investigate were always guess an X, always guess the same symbol as you pick up, and to always guess the opposite symbol of what you pick up.
What I first did was play the game with a friend. I guessed the symbol that I picked up every time for 30 times, getting 19 guesses right and 11 guesses wrong. The friend, Allison Hopkins, was guessing X the entire time as her strategy for another 30 times, getting 18 right and 12 wrong. I was more successful in my strategy, although it was a tiny difference: 1.
I listed my outcomes of the experimentation of strategies above. After this point, I realized that picking a number like 30 was not the best idea. Since you can multiply 30 by roughly 3.33 to get 100 for a percentage, I multiplied the number 19. This percentage represents the percentage of right answers you should get based on the data I collected for the strategy of picking the symbol that I originally picked up. When rounded, this percentage is 63% of correct answers. I repeated the same process for the next strategy, multiplying 18 by 3.33 to get a rounded number of 60%. This is all my experimental results based on data.
Next, I looked at a theoretical set of data. Once you have picked up a card, there are only two symbols to choose from, giving the idea that each theoretical percentage of winning would be at 50% for both strategies.
To find a more common ground, I averaged the 63% and 50% to get 57%. Then I did the same thing with 60% and 50%, getting 55%. So, in conclusion, I would say that based on data and theoretical situations, the strategy that I worked with, picking the symbol that you originally picked up, would have a higher chance of winning than Allison’s.
For this problem, I think that I deserve an 8.5/10. I understood all of the ideas that were shown to me with this probability problem, my only flaw being that I only got data from 30 times. I feel that I should have gotten a little more data, but I still did all of the math to get the probabilities and I am proud of that. Even though I didn’t get a lot of data, I would still use persistence as a skill that I used when working through this problem. I had a little bit of a hard time with getting the difference between experimental and theoretical, and what to do with the percentages after that. I chose to average them and base my conclusion on the averaged amount, feeling that it would be much closer to what the percentage would look like if I had done more tests.