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.

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

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

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

available for blue and there more or less the same.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

right is. And the best opening move for right is

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

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

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

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

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

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

Right's turn is 3. Right cuts that.

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

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

This says that if right goes first, right loses.

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

for, for yourself. It.

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

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

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

Take care.

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