Monthly Archives: August 2012

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

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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

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Combinatorial Game Theory Quiz 1

This quiz lasts 70 minutes and covers materials from lessons 1-4. For A-C, determine whether the following Nim games are first or second-player wins. There is no need to find the winning move. (10 points) (10, 15, 17, 19) (7, … Continue reading

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Combinatorial Game Theory IV

Lesson 4 In this lesson, we will work on a large class of games, known as take-and-break games. First consider a simple example. Kayles Kayles is an example of a take-and-break game: Start with a few heaps of contiguous bottles, … Continue reading

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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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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

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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

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