6 ms·
Transfinite NIM (the game, not the programming language)
- lblume 2y agoNim is, in fact, a proper subset of Hackenbush, a game extensively studied by Conway. I found the following video extremely useful and well-visualized: https://www.youtube.com/watch?v=ZYj4NkeGPdM https://www.youtube.com/watch?v=ZYj4NkeGPdM
- zem 2y agomore like hackenbush is a generalisation of nim; the latter is ancient and the former was invented by conway.
- ykonstant 2y agoThe author's previous post on winning strategies for regular Nim may be more interesting to people here: https://jdh.hamkins.org/win-at-nim-the-secret-mathematical-strategy/ https://jdh.hamkins.org/win-at-nim-the-secret-mathematical-s...
- demaga 2y agoYes, thank you! I had a lot of fun playing around with Nim and other mathematical games after I watched [talk on surreal numbers by Tom Hall](https://www.youtube.com/watch?v=xpXoluxBYw0 https://www.youtube.com/watch?v=xpXoluxBYw0). But the transfinite version went completely over my head. Also, I find it funny that reading about Nim is how I learned the term misère, even though I played lots of misère games before without realizing!
- 998244353 2y agoHere's another (seemingly finite) problem being analyzed with the same "Nim but with ordinal numbers" approach: https://codeforces.com/blog/entry/85984 https://codeforces.com/blog/entry/85984
- klik99 2y agoMy grandpa was a fan of Nim, and at restaurants we’d play with sugar packets while waiting for food. It’s a great game to entertain kids. He also invented Dr. Nim which some gray beards may be familiar with. Turing Tumble is an evolution of Dr. Nim/DigiComp II.
- ColinWright 2y agoI am so familiar with Dr Nim ... your grandpa invented that ?!? Kudos ...
- klik99 2y agoThanks, but I didn't do anything! He did a lot in his life, wish I realized that earlier and wrote more of it down. I have his original prototype: https://youtu.be/X_IUoFDMhZ8 https://youtu.be/X_IUoFDMhZ8 Also was recently reading this about the history of ESR which is interesting: https://retrocmp.com/attachments/article/302/Duerig.PDF https://retrocmp.com/attachments/article/302/Duerig.PDF
- ColinWright 2y agoIt's worth mentioning that Dr NIM[0] did not play the NIM[1] studied by Combinatorial Game Theorists ... there are two things called "NIM". One is as played by Dr NIM, where you have a single heap, and on each turn you can take 1, 2, or 3 tokens. Then the person taking the last token wins (in normal play), or loses in Misère play. This is now known as "The Subtraction Game". The version of NIM that Game Theorists study has multiple heaps, and on each turn you choose a heap and take one or more from that heap, including possibly taking all of them. Again, as before, the winner is the person taking the last token (in normal play). But Dr NIM is awesome. Did he also have something to do with DigiComp II [2] ?? (Edit: Checking Wikipedia, I'm guessing he did. I played with an early version at Cliff Stoll's house last year ... so much fun.) [0] https://en.wikipedia.org/wiki/Dr._Nim https://en.wikipedia.org/wiki/Dr._Nim [1] https://en.wikipedia.org/wiki/Nim https://en.wikipedia.org/wiki/Nim [2] https://en.wikipedia.org/wiki/Digi-Comp_II https://en.wikipedia.org/wiki/Digi-Comp_II
- dang 2y ago[stub for offtopicness]
- pmarreck 2y agoFWIW, Nim (the programming language) is certainly interesting and possibly underrated. https://nim-lang.org/ https://nim-lang.org/
- hugs 2y agoSaving a few clicks, this is about the math game called Nim, not the programming language called Nim. (Also, today I learned there's a math game called Nim.)
- rubenvanwyk 2y agoCame here and thought this going to be about the Nim programming language.
- ColinWright 2y agoOK, I've edited the title to make it clearer that this is about the mathematical game and not the programming language.
- dvh 2y ago
- graycat 2y agoAs I recall, the Nim strategy is in Courant, 'What is Mathematics'.