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Tag Archives: impartial games
Combinatorial Game Theory Quiz 3
The quiz lasts 75 minutes and covers everything from lessons 112. For each of the following Nim games, find one good move for the first player, if any. (10 points) [ Note : exactly one of the games is a … Continue reading
Combinatorial Game Theory XII
Lesson 12 Recall the following Domineering configuration in lesson 10: The above game has a nice theory behind it. Definition : For any game G, the game –G (called miny–G) is defined to be: The game +G (called tiny–G) is defined … Continue reading
Posted in Notes
Tagged combinatorial game theory, computer science, domineering, game infinitesimals, impartial games, intermediate, minies, tinies, toads and frogs
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Combinatorial Game Theory VI
Lesson 6 General Combinatorial Game Theory [ Warning: the following lesson is significantly longer than the previous ones. ] Starting from this lesson, we will look at a more rigourous, complete and general theory. Prior to this, in any game configuration both … Continue reading
Combinatorial Game Theory V
Lesson 5 We did mention in the first lesson that CGT covers games without draws. Here, we’ll break this rule and look at loopy games, i.e. games with possible draws. [ To be specific, loopy games are those where it’s … Continue reading
Posted in Notes
Tagged basic, combinatorial game theory, computer science, impartial games, loopy games, nim values, programming
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Combinatorial Game Theory Quiz 1
This quiz lasts 70 minutes and covers materials from lessons 14. For AC, determine whether the following Nim games are first or secondplayer wins. There is no need to find the winning move. (10 points) (10, 15, 17, 19) (7, … Continue reading
Posted in Homework
Tagged basic, combinatorial game theory, computer science, impartial games, nim, nim values
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Combinatorial Game Theory IV
Lesson 4 In this lesson, we will work on a large class of games, known as takeandbreak games. First consider a simple example. Kayles Kayles is an example of a takeandbreak game: Start with a few heaps of contiguous bottles, … Continue reading
Posted in Notes
Tagged basic, combinatorial game theory, computer science, impartial games, nim values
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Combinatorial Game Theory III
Lesson 3 We’ve learnt Nim and we’ve learnt the Square Game. Now, let’s combine them and consider the following game, which we shall name Nim Square. Start with r heaps of stones, of sizes . Play alternates between two players: at … Continue reading
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Tagged basic, combinatorial game theory, computer science, impartial games, nim values, programming
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Combinatorial Game Theory II
Lesson 2 In this lesson, we will focus on a special type of game called Nim. Although it’s only one out of infinitely many possible games, understanding it in depth will be very beneficial in analysing a much larger class … Continue reading
Posted in Notes
Tagged basic, combinatorial game theory, computer science, impartial games, nim, programming
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Combinatorial Game Theory I
[ Prerequisites required: none for now. ] In the middle of 2000, I was waiting to go to graduate school and had a bit of free time on my hands. So I decided to prepare a website which teaches combinatorial … Continue reading
Posted in Notes
Tagged basic, combinatorial game theory, computer science, impartial games, programming
2 Comments