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Tag Archives: partial games
Combinatorial Game Theory XI
Lesson 11 In this lesson, we will cover more on canonical forms. First recall that for m↑ + (*n) with m > 0, this game is positive except when (m, n) = (1, 1). Let’s consider the canonical forms of … Continue reading
Combinatorial Game Theory X
Lesson 10 In lesson 7, we learnt that if A, B are Left’s options in a game with A ≥ B, then we can drop B from the list of options and the game remains equal. In this lesson, we will … Continue reading
Combinatorial Game Theory Quiz 2
This quiz lasts 70 minutes and covers materials from lessons 19. Use the simplicity rule to compute the values of the following games. (10 points) {1/2  } {1/4  } {1/8  3/8} {0  7/8} {1/8  9/16} … Continue reading
Posted in Homework
Tagged combinatorial game theory, computer science, game numbers, intermediate, partial games, up game
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Combinatorial Game Theory IX
Lesson 9 Typically, at the end of a Domineering game, the board is divided into disjoint components, so the overall game is the (game) sum of the individual components. Suppose we have the following 6 components: How should the next … Continue reading
Combinatorial Game Theory VIII
Lesson 8 In this lesson, we will further familiarise ourselves with games involving numbers. At the end of the lesson, we will encounter our first positive infinitesimal: the “up” ↑. Here, an infinitesimal is a value which is strictly between –r and r … Continue reading
Combinatorial Game Theory VII
Lesson 7 [ Warning: another long post ahead. One of the proofs will also require mathematical induction. ] In this lesson, we will see how some games can be represented by numbers (which can be integers or fractions). We will also … Continue reading
Posted in Notes
Tagged combinatorial game theory, computer science, game numbers, hackenbush, intermediate, partial games, programming
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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