Hello again! This week definitely wasn't as busy as the last week, but it was still pretty fun. As for research, I've been debugging some of my programs (I'm not very good at programming) and reading literature on other variations of nim. One interesting concept I was looking at was the idea of a Grundy Value.
A Grundy Value is a number that a certain position of an impartial game can be written as. Grundy Values are usually looked at only in impartial games, meaning that it's only looked at in games like nim (since most boardgames aren't technically impartial).
Using binary, the Grundy Values allow us to associate each nim game to a number. This binary representation also allows us to determine 'safe values' in nim. These safe values would be points that a certain player would be guaranteed a win at. Looking at safe values can also check whether a board game is impartial or not. Having a certain set of safe values for a game could mean that the game is not impartial.
My problem is applying all these concepts to nim with a handicap. Once the handicap is added, the game is no longer impartial. Either some of the terms I was learning about don't apply at all anymore or I need to modify them to still apply with the handicap. I'm still pretty lost, but hopefully I can translate some of the theorems for impartial games to nim with a handicap.
In terms of my math class at ASU, things have been going well. I've caught up with the material for the most part. I've really enjoyed the lectures so far too! As for the test...
I took the first midterm for the differential geometry class at ASU. I thought I knew the material, but I turned out to be wrong. There were five problems on the test (and an extra credit problem). I solved three of them. Then I got stuck on the fourth. After wasting a lot of time on the problem, I realized I had another problem to do. I moved on to the fifth, but I didn't know how to do that one either. The test was hard for me. It's a lot different in college apparently.
I'll study harder for the next one. The test was still fun despite me being bad at it. I don't have anything else to say...
Thanks for reading~
A Grundy Value is a number that a certain position of an impartial game can be written as. Grundy Values are usually looked at only in impartial games, meaning that it's only looked at in games like nim (since most boardgames aren't technically impartial).
Using binary, the Grundy Values allow us to associate each nim game to a number. This binary representation also allows us to determine 'safe values' in nim. These safe values would be points that a certain player would be guaranteed a win at. Looking at safe values can also check whether a board game is impartial or not. Having a certain set of safe values for a game could mean that the game is not impartial.
My problem is applying all these concepts to nim with a handicap. Once the handicap is added, the game is no longer impartial. Either some of the terms I was learning about don't apply at all anymore or I need to modify them to still apply with the handicap. I'm still pretty lost, but hopefully I can translate some of the theorems for impartial games to nim with a handicap.
In terms of my math class at ASU, things have been going well. I've caught up with the material for the most part. I've really enjoyed the lectures so far too! As for the test...
I took the first midterm for the differential geometry class at ASU. I thought I knew the material, but I turned out to be wrong. There were five problems on the test (and an extra credit problem). I solved three of them. Then I got stuck on the fourth. After wasting a lot of time on the problem, I realized I had another problem to do. I moved on to the fifth, but I didn't know how to do that one either. The test was hard for me. It's a lot different in college apparently.
I'll study harder for the next one. The test was still fun despite me being bad at it. I don't have anything else to say...
Thanks for reading~
Congratulations for getting through your test, even it was hard. I'm sure you did better than you think you did. How are you planning to approach modifying the concepts you are learning about so that you can apply them to nim with a handicap?
ReplyDeleteI want to see if the concepts still hold when the game is changed. I'll look at some of the proofs for the big theorems in nim and see if they'd still be applicable to different variations!
DeleteWell at least you were honest about how you did both on the test and in regards to advancing your project. Those Grundy Values seem like they would be pretty useful so I'm interested to see if you can find a way to implement them with the handicap like you mentioned.
ReplyDeleteYup! I'll definitely try to get them involved.
DeleteWell at least you were honest about how you did both on the test and in regards to advancing your project. Those Grundy Values seem like they would be pretty useful so I'm interested to see if you can find a way to implement them with the handicap like you mentioned.
ReplyDeleteI think I might have actually heard Grundy values referred to as nim values before; are they more often associated with nim than other similar impartial games or is that just a coincidence?
ReplyDeleteThey are mostly associated with nim! Totally not a coincidence.
DeleteAre there any specific computer programs that you are using to do your research? I do not have much (okay any) background in this type of math so any diagrams/pictures/screen shots you can provide would be really helpful!
ReplyDeleteI just use python to write algorithms for giving win probabilities! I'll try to graph some of my results so you guys can see it soon!
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