Tenzi Free Think Friday
Friday April 17
1) Previous memory of probability - I remember learning about probability and it being relatively simple in most cases but it can get way more challenging as you add more variables. I remember that probability is the number of 'correct' over the total. For example, the probability of rolling a one on a dice would be 1 (because there is one side of the dice with a 1) over 6 (because there are six different possible outcomes). The probability of rolling a one on two dice would be 2/12 because there are two possible ones and twelve total choices.
2) Today's work - Today my group focused on trying to play and understand the game, then we looked into the probability aspect of the game. At first we thought that you had to roll all of the dice until they were the same, but then we figured out that you are allowed to take some out and only roll the ones that are not the number you want. I am very glad we figured this out because we would probably have had to roll all ten dice like 10 million times before they all landed on the same number. After we figured out how to play, we played it two different ways and recorded how many rolls it took to get all of the same number. First, we all worked on our own with five dice. We recorded how many rolls it took each of us to get the dice to all be the same. Then we worked as two pairs, trying to get 10 of the same number. Looking back, I realized that it probably would have been better to study if we had counted how many dice we rolled each time, because we counted one 'roll' as 'roll all of the leftover dice that are not the correct number'. This was unscientific because the number of dice we rolled changed with each time.
3) What I want to know - I really want to understand better how there can ever be a probability of 100% (unless it is like the probability of picking a red ball out of a container containing 10 red balls). It just seems like there is always a super tiny chance that something crazy could happen, like you could roll 20 dice and get all ones. I would like to know when in probability it is okay to round and say there is no chance or there is a 100% chance. I would like to know how to calculate the chances of rolling two 2's on two dice or three 3's on three dice, etc. I know how to calculate the chances of rolling one 2 on two dice or one 3 on three dice, but I know that the chances of rolling two of the same number are lower than rolling one.
4) Collaboration - Today my group collaborated by working together to collect data for our study of Tenzi. At first we took turns, each person working by themselves to get 5 of the same (we only had enough dice for 5 each). The other people in the group counted rolls to make sure there weren't any mistakes. Then, we decided to work in pairs so that we would have ten dice and repeat the process, counting rolls until all dice were the same number. We did this because we could compare the number of rolls it took to get ten with the number of rolls it took to get five, and see if the probability changed. The number of rolls to get five the same were 16, 6, 12. The number of rolls to get ten of the same were 16, 11, 11, 17. So, the number of rolls to get ten were, on average, more than the number of rolls to get five, however our sample group is too small to have a definitive result. Also, it was smaller but not considerably smaller, and we included outliers in the data. In college I see myself collaborating a lot. I will be studying animal science for my undergraduate degree, and when working with animals it is very important to communicate to make sure the animal is safe and taken care of. In college I also see myself collaborating with my roommates because we will have to complete tasks such as cleaning and it will be a lot easier if we all chip in. Later on in my education, for vet school, I will need to collaborate effectively in order to help my patients. I will need to talk with the animals family, other doctors and technicians to make sure the animal is taken care of.
2) Today's work - Today my group focused on trying to play and understand the game, then we looked into the probability aspect of the game. At first we thought that you had to roll all of the dice until they were the same, but then we figured out that you are allowed to take some out and only roll the ones that are not the number you want. I am very glad we figured this out because we would probably have had to roll all ten dice like 10 million times before they all landed on the same number. After we figured out how to play, we played it two different ways and recorded how many rolls it took to get all of the same number. First, we all worked on our own with five dice. We recorded how many rolls it took each of us to get the dice to all be the same. Then we worked as two pairs, trying to get 10 of the same number. Looking back, I realized that it probably would have been better to study if we had counted how many dice we rolled each time, because we counted one 'roll' as 'roll all of the leftover dice that are not the correct number'. This was unscientific because the number of dice we rolled changed with each time.
3) What I want to know - I really want to understand better how there can ever be a probability of 100% (unless it is like the probability of picking a red ball out of a container containing 10 red balls). It just seems like there is always a super tiny chance that something crazy could happen, like you could roll 20 dice and get all ones. I would like to know when in probability it is okay to round and say there is no chance or there is a 100% chance. I would like to know how to calculate the chances of rolling two 2's on two dice or three 3's on three dice, etc. I know how to calculate the chances of rolling one 2 on two dice or one 3 on three dice, but I know that the chances of rolling two of the same number are lower than rolling one.
4) Collaboration - Today my group collaborated by working together to collect data for our study of Tenzi. At first we took turns, each person working by themselves to get 5 of the same (we only had enough dice for 5 each). The other people in the group counted rolls to make sure there weren't any mistakes. Then, we decided to work in pairs so that we would have ten dice and repeat the process, counting rolls until all dice were the same number. We did this because we could compare the number of rolls it took to get ten with the number of rolls it took to get five, and see if the probability changed. The number of rolls to get five the same were 16, 6, 12. The number of rolls to get ten of the same were 16, 11, 11, 17. So, the number of rolls to get ten were, on average, more than the number of rolls to get five, however our sample group is too small to have a definitive result. Also, it was smaller but not considerably smaller, and we included outliers in the data. In college I see myself collaborating a lot. I will be studying animal science for my undergraduate degree, and when working with animals it is very important to communicate to make sure the animal is safe and taken care of. In college I also see myself collaborating with my roommates because we will have to complete tasks such as cleaning and it will be a lot easier if we all chip in. Later on in my education, for vet school, I will need to collaborate effectively in order to help my patients. I will need to talk with the animals family, other doctors and technicians to make sure the animal is taken care of.
Friday, April 24 - 30
1) My favorite version of Tenzi was Pyramidzi. Pyramidzi is where you first roll all ten dice trying to get four 4's. After you get that you line them up on the desk and roll the remaining dice trying to get three 3's. When you get three 3's you put them on top of the fours vertically. Then you roll the remaining three dice and try to get two 2's, putting them on top of the row of 3's. Then you roll the last dice until you get a 1 and put it on the top of the pyramid. This one is my favorite because it is three dimensional and you can see how far along your competition is which challenges you to move faster. It is also fun because it is easy at first when you have more dice, but as you move up the pyramid it takes longer and longer to get the numbers you want.
Some strategies that might be useful would be moving faster, because then you could get more rolls (more chances) before your competitors which would make it more likely to get the numbers you want. Another strategy could be (I am not sure if this is against the rules) to roll all of the dice on the first move and pull out any 4's 3's 2's or 1's, saving them for later, that way it would go faster and you wouldn't have to re-roll numbers that you already had. A final strategy is making sure to set up your pyramid in the corner of the desk not the middle because once while playing I accidentally knocked over my pyramid with the other dice and had to start over.
2) Numerous scientific studies have been conducted regarding the impact of brain stimulating games on mental performance. One study, conducted by UCSF (a sub-link of the Psychology Today (https://www.psychologytoday.com/blog/the-athletes-way/201403/eight-habits-improve-cognitive-function) article: http://www.nature.com/news/gaming-improves-multitasking-skills-1.13674) was particularly interesting. This study used a specially designed 'driving' video game to see if it could improve the multitasking skills of aging people. First, they had a bunch of people of all different ages try the game and they got a score. The scores got progressively worse as age increased. Then, they took only the older group (60 - 80 years) and had them play a version of the game that got more difficult as skill improved. They played the game again, six months later, and their scores were better than the young people the first time. This study was trying to prove that games can increase multitasking skills, attention, and memory. It also proved that those skills were not temporary, they remained strong for over six months. While this article only focused on the one specific driving game, other studies have looked at the impacts of more general puzzle solving games.
An article (http://www.bigfishgames.com/blog/building-a-better-brain-one-game-at-a-time/) outlines the many ways problem solving games can help improve cognitive skills. One important way that playing Set and Tenzi can help improve cognitive function is through practicing pattern recognition and matching skills. This article claims "...intelligence is based on pattern recognition, matching and recognition." Maybe practicing matching cards of Set could help build pattern recognition skills, and therefore increase intelligence (if brain researcher Jeff Hawkins is correct). Games like Tenzi might help increase hand-eye coordination because it calls for quick reflexes when choosing which dice to re-roll each round. Tenzi also might help develop organizing skills because organizing dice faster gives a player a strong advantage in the game. Being able to recognize quickly and separate the dice that have the same number helps players build organizing skills. Overall, I personally think Set would build cognitive skills more effectively than classic Tenzi because it requires the player to recognize more complicated patterns, while in Tenzi players rely more on chance. However, playing any game helps people relieve stress. "Relieving stress through games is an excellent way to deal with pent-up emotions that may negatively affect performance in work, school and life in general," (Big Fish). Playing games allows people to connect with each other by providing a safe environment where learning can take place through trial and error.
Some strategies that might be useful would be moving faster, because then you could get more rolls (more chances) before your competitors which would make it more likely to get the numbers you want. Another strategy could be (I am not sure if this is against the rules) to roll all of the dice on the first move and pull out any 4's 3's 2's or 1's, saving them for later, that way it would go faster and you wouldn't have to re-roll numbers that you already had. A final strategy is making sure to set up your pyramid in the corner of the desk not the middle because once while playing I accidentally knocked over my pyramid with the other dice and had to start over.
2) Numerous scientific studies have been conducted regarding the impact of brain stimulating games on mental performance. One study, conducted by UCSF (a sub-link of the Psychology Today (https://www.psychologytoday.com/blog/the-athletes-way/201403/eight-habits-improve-cognitive-function) article: http://www.nature.com/news/gaming-improves-multitasking-skills-1.13674) was particularly interesting. This study used a specially designed 'driving' video game to see if it could improve the multitasking skills of aging people. First, they had a bunch of people of all different ages try the game and they got a score. The scores got progressively worse as age increased. Then, they took only the older group (60 - 80 years) and had them play a version of the game that got more difficult as skill improved. They played the game again, six months later, and their scores were better than the young people the first time. This study was trying to prove that games can increase multitasking skills, attention, and memory. It also proved that those skills were not temporary, they remained strong for over six months. While this article only focused on the one specific driving game, other studies have looked at the impacts of more general puzzle solving games.
An article (http://www.bigfishgames.com/blog/building-a-better-brain-one-game-at-a-time/) outlines the many ways problem solving games can help improve cognitive skills. One important way that playing Set and Tenzi can help improve cognitive function is through practicing pattern recognition and matching skills. This article claims "...intelligence is based on pattern recognition, matching and recognition." Maybe practicing matching cards of Set could help build pattern recognition skills, and therefore increase intelligence (if brain researcher Jeff Hawkins is correct). Games like Tenzi might help increase hand-eye coordination because it calls for quick reflexes when choosing which dice to re-roll each round. Tenzi also might help develop organizing skills because organizing dice faster gives a player a strong advantage in the game. Being able to recognize quickly and separate the dice that have the same number helps players build organizing skills. Overall, I personally think Set would build cognitive skills more effectively than classic Tenzi because it requires the player to recognize more complicated patterns, while in Tenzi players rely more on chance. However, playing any game helps people relieve stress. "Relieving stress through games is an excellent way to deal with pent-up emotions that may negatively affect performance in work, school and life in general," (Big Fish). Playing games allows people to connect with each other by providing a safe environment where learning can take place through trial and error.