The Game of Set
Friday, February 27
Set Overview
Set is a card game in which the players try to find a set of three cards. In order for it to be a set, each category (color, number, pattern, shape) must be all the same or all different. For shape, cards could either be all of the same certain shape (all waves, all diamonds, or all ovals), or all different (one wave, one diamond, and one oval). In the number category, either all cards must have the same number of shapes (all with one, all with two, or all with three) or one card with one, one card with two and one card with three. For pattern, cards could all have the same pattern (all solid, all open, or all striped) or you could have a set where one card is solid, one is striped, and one is open. There are three colors, red, purple, and green, so you could have a set with all red, all green or all purple, or you could have a set with one of each red green and purple.
A set must contain cards that are all the same or all different in each of the four categories outlined above. So, you could not have a set if two of the cards are purple and one is green, or if two of the cards are solid and one is striped.
A set must contain cards that are all the same or all different in each of the four categories outlined above. So, you could not have a set if two of the cards are purple and one is green, or if two of the cards are solid and one is striped.
Set Thought
I noticed that most of my sets had different numbers (one card with one picture, one with two pictures, and one with three pictures). I think it is easiest for me to see these sets because when I play set I first find a 'one' card then look for a 'two' card that is the same shape, then look for a 'three' card to match. This is probably why 4/6 of my sets were the same shape with different numbers. The other two sets were both the same number with different colors.
To become a better set player, I think I need to focus more on the sets that are different in more categories. Based on the sets I found, I think I am better at finding similar cards than I am different ones. Also, I found that I tend to think about color first, which might make it hard for my brain to see cards that are different in all categories. All of the sets I found in round 1 are the same in at least one category (number), usually two (color, shape). |
Set Trends
While playing this game, I was wondering if there was a way to have a certain number of cards so that there will always be a set. Because I really like this other game called 'spot it' and there are cards that each have about 9 different pictures on it, and you have to put two cards down and the first person to spot the one that they have in common wins. It is cool because every two cards has a picture in common, no matter which two cards it is. I wonder if something similar can happen with set, like is there a way to ensure that a set is always on the table?
I wonder how hard set would be if you added a fourth choice to each category, like add yellow, square, polka dots, and four picture cards. Then, all sets would contain four cards instead of three. I think if a fourth category was added, it would make it a lot harder for me to find sets that are all different. Or, how easy would set be if you took away a choice from each category, so each set would only have two cards instead of three.
I wonder how hard set would be if you added a fourth choice to each category, like add yellow, square, polka dots, and four picture cards. Then, all sets would contain four cards instead of three. I think if a fourth category was added, it would make it a lot harder for me to find sets that are all different. Or, how easy would set be if you took away a choice from each category, so each set would only have two cards instead of three.
Set Thoughts
Can we still play set if we only used the cards of one color?
We wanted to see if it was still possible to play the game of set only using cards of a single color. We predicted that it might be easier, because you would not have to worry about color as a requirement for a set, because all cards would be the same color.
We tested our hypothesis by splitting the set deck into three, one stack for each color (green, red, and purple). We randomly selected purple as our test deck. Then, we set out a normal set deck but using only the purple cards. One person from our group timed while the rest of us tried to find sets. When we found a set we marked the time it took us to find it. We repeated this four times with the purple deck. Then, we repeated this with a regular set deck that contained all three colors.
We had an interesting data set. All of the numbers from the purple group were lower, except one which we eliminated because it was an unsolvable deck. We also eliminated the longest time from the regular deck, to make it fair. Then we took an average of the purple times and an average of the regular deck times. The average time to find a set from the purple deck was substantially shorter than the average time to find a set from the standard deck. This confirmed our hypothesis that set would be easier if you only used a single color card.
However, it was interesting that one of the times (out of only four) we played with the purple deck we couldn't find a set. We would need to conduct more testing, but maybe an unsolvable set occurs more often when only using one color? It could be true because there seem to be less possible sets when only using one color.
We tested our hypothesis by splitting the set deck into three, one stack for each color (green, red, and purple). We randomly selected purple as our test deck. Then, we set out a normal set deck but using only the purple cards. One person from our group timed while the rest of us tried to find sets. When we found a set we marked the time it took us to find it. We repeated this four times with the purple deck. Then, we repeated this with a regular set deck that contained all three colors.
We had an interesting data set. All of the numbers from the purple group were lower, except one which we eliminated because it was an unsolvable deck. We also eliminated the longest time from the regular deck, to make it fair. Then we took an average of the purple times and an average of the regular deck times. The average time to find a set from the purple deck was substantially shorter than the average time to find a set from the standard deck. This confirmed our hypothesis that set would be easier if you only used a single color card.
However, it was interesting that one of the times (out of only four) we played with the purple deck we couldn't find a set. We would need to conduct more testing, but maybe an unsolvable set occurs more often when only using one color? It could be true because there seem to be less possible sets when only using one color.