This course will cover the mathematical theory and analysis of simple games without chance moves.

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From the course by Georgia Institute of Technology

Games without Chance: Combinatorial Game Theory

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This course will cover the mathematical theory and analysis of simple games without chance moves.

From the lesson

Week 1: What is a Combinatorial Game?

Hello and welcome to Games Without Chance: Combinatorial Game Theory! The topic for this first week is Let's play a game: Students will learn what a combinatorial game is, and play simple games.

- Dr. Tom MorleyProfessor

School of Mathematics

Alright, so you want to look at the solution of this.

Â So let's, let's try to solve it. This is not the only possible argument.

Â But let's say, let's try to see what's going on.

Â So if blue goes first that's left. Then, then there's only two edges

Â available for blue and there more or less the same.

Â So blue will cut this. Now if you think about it and therefore

Â thi, this right edge, this red edge up here is, floats off.

Â Right can either do this or this. But right's best move is to move here,

Â because, if right doesn't cut this now, then blue will cut down the blue below it

Â next time. And then right will, will be without a

Â move. So right that's the best move for right

Â after blue does this. So let, let, let's label these 1 2.

Â Then, then blue left only has 1 move left. So that's got to be this one 3.

Â And then right only has 1 move left so that's get cut, that's 4.

Â And now it's blue's turn. It's left's turn.

Â No moves available, so left loses. So if left goes first then left loses.

Â Alright, let's take a look and try to see what happens if right moves first.

Â Right moves first. Again, you can either look at all possible

Â cases or you can look at it and try to figure out what the best opening move for

Â right is. And the best opening move for right is

Â either this one or this one. Because, because of this, this threat

Â from, from left to chop down below and, and get rid of that right move, right may

Â as well take this move while, while he or she can.

Â Now, left at this point might as well chop down a right and so that happens.

Â And now this right is unavailable. This all flows up off the page.

Â Let's see if now left. It's now rights turn so this was 1, 2.

Â Right's turn is 3. Right cuts that.

Â And now left cuts this. And now, well, it's rights turn and

Â there's no moves, so right loses. Going back to the original picture.

Â This says that if right goes first, right loses.

Â Okay, so if you got this, great. Make up other things and, and try them out

Â for, for yourself. It.

Â If you have some difficulty with that let us know what, what the problems were.

Â Go through the solutions carefully, and see if you can't fi, pizz, puzzle it out.

Â And, and we'll see you all next time, with week two.

Â Take care.

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