All Questions
8 questions
1
vote
2
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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
views
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
votes
1
answer
389
views
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
0
answers
715
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 ...
- 1,129
5
votes
0
answers
306
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 ...
- 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
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 ...
- 6,403
2
votes
2
answers
1k
views
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 ...
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