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

Loading...

From the course by Georgia Institute of Technology

Games without Chance: Combinatorial Game Theory

105 ratings

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

From the lesson

Week 2: Playing Multiple Games

The topics for this second week is Playing several games at once, adding games, the negative of a game. Student will be able to add simple games and analyze them.

- Dr. Tom MorleyProfessor

School of Mathematics

>> So here what I want to do just is, is to show you what I think the answers are.

And we'll come back next time and, and do this in more detail based on what, what

feedback we get. A plus b.

Left going first. Lefts, best move going first is to remove

2 of these to ignore these edges over here.

Remove 2 of these in which case left can now, force a win.

So left going first, left wins and the best opening move, the winning opening

move is to remove 2, 2 quarters from the nim heap of side 3.

C plus F, is a 0 gain, and, so if left moves first, left loses.

E plus F, left moves first, let's see. Left moves first, the only move is to cut

down the, the left move over here, now right has to move over here.

Now left has no moves so left move, loses on here.

Four is the more complicated one, which we'll probably take a look at, at some

point. But it turns out that this is also a zero

gain and it turns out that if left, whatever move left starts with Left loses.

So, there's, there's some hints, It tells you what to shoot for.

Try, try, try, see if you can get the same answers as we.

Note that not. We want, just, not, not just the answers.

You should be able to explain, why it is that either left wins or right wins.

So we'll see you all next week. Take care.

Coursera provides universal access to the world’s best education,
partnering with top universities and organizations to offer courses online.