All Questions
Tagged with combinatorial-game-theory nim
14 questions
1
vote
1
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141
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Is there a solution to this subtraction game with extra rules. (combinatorial game theory, CGT, nim like)
All of the rules are as follows:
There is only 1 pile with $n$ objects.
The players can at max pick $m$ objects.
The players cant take the same amount as what the opposite player taken last turn and ...
- 13
1
vote
2
answers
291
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Do restricted Nim-like games have winning strategies?
Considering a Nim-like game to be:
There are three piles $A,B,C$, and the amount of their elements are $|A|=2, |B|=5, |C|=6$;
There are 2 players. Each time a player can either take $x (1\leq x \leq ...
2
votes
0
answers
309
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Combining a Nim-variation and Wyrthoff's game. How to find a winning strategy? [closed]
Wythoff's game is a variation of the classical Nim - There are two heaps and the players take turns either taking any amount from one heap, or the same amount of both heaps. The winner is the one ...
9
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1
answer
389
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Ordered Nim game
Consider the following variant of Nim:
There are two players and $n$ piles of stones, with sizes $a_1,\dots,a_n$, such that $a_i\leq a_j$ for any $i<j$.
A move consists of removing a positive ...
- 91
3
votes
1
answer
640
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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 ...
- 31
3
votes
0
answers
715
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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 ...
- 1,129
5
votes
0
answers
306
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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 ...
- 1,129
15
votes
3
answers
2k
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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 ...
- 1,129
5
votes
0
answers
216
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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 $n$,...
- 151
6
votes
1
answer
330
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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 ...
- 6,403
11
votes
2
answers
634
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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 ...
- 211
2
votes
2
answers
1k
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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 ...
- 37
2
votes
7
answers
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 ...
- 163
3
votes
1
answer
3k
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The game of "nimble" with no stacking
The game of Nimble is played as follows. You have a game board consisting of a line of squares labelled by the nonnegative integers. A finite number of coins are placed on the squares, with possibly ...
- 14k