# Questions tagged [nim]

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### A "semi-genetic" definition of addition and multiplication in the field $\operatorname{On}_p$?

Let $+,\cdot$ denote multiplication in $\mathbb{N}_0$. The addition and multiplication in $\operatorname{On}_p$ are denoted $\oplus, \otimes$. Recursive definition of addition: x \oplus y := ((x+y) \...
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1 vote
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### Misere nim variant

Is there a name (and strategy) for this nim variant? There are $n$ lists of objects, say $L_1,\ldots,L_n$ where $L_i = \{a_{i,1},a_{i,2},\ldots,a_{i,n_i}\}$. Players take turns choosing a list and ...
691 views

### Nimbers and Surreal Numbers [closed]

I have been researching Combinatorial Game Theory. One common theme is the assignment of values to games in order to classify the game as a win for a specific player. One such way is class of surreal ...
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299 views

### Generalization of Sprague-Grundy Theorem

In my research on Combinatorial Game Theory, I used a certain theorem that is essentially a generalization of the Sprague-Grundy theorem. Because the result hinges too much on the work of others to be ...
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### Why does the bitxor function appear in Nim?

I am conducting research in Combinatorial Game Theory (CGT). Although I have done a considerable amount of reading, I do not completely understand why the bit-xor function also known as the nim-sum ...
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211 views

### Analysis of Nim-Like Game? [closed]

There are a finite number of heaps, each with a finite number of counters. Two players take turns; on each move, they may remove exactly one counter from any heap, and also, if the heap is of size $n$,...
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318 views

### Anything known about the Grundy Ordinal of Sylver's Coinage

Sylver's coinage is an example of an unbounded finite (if slightly modified) combinatorial impartial game. Quoth wikipedia: The two players take turns naming positive integers that are not the sum of ...
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623 views

### Nim and the Sierpinski Gasket

(I discovered this in high school, sent it off to a journal, never heard back, and forgot about it. I've never found anyone else who appeared to know about it; the combinatorial game theorists I've ...
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### Generalized Sprague-Grundy Theorem

Hey, I know what is Sprague-Grundy theorem, but I want to know about generalized Sprague-Grundy (GSG) theorem ( which is used for games with cycles ). Apparently there seems to be very less ...
2k views

### Nim-like(?) game winning strategy?

I have the following Nim-like game (at least, it seems Nim-like to me). There are $2k$ tokens in a row, $k \in \mathbb{N}$. Each token $a_i$ has a value $v_i \in \mathbb{N}$ All this information ...
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