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

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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.

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Week 7: What You Can Do From Here

The topic for this seventh and final week is Where to go from here.

- Dr. Tom MorleyProfessor

School of Mathematics

[MUSIC].

cut. [MUSIC].

Wrong class. This is games without chance.

Tom Morley. this is week seven.

Where do we go from here? Our first little piece is infinite and

loopy games. Now previously we looked at hack and bush

games. And if they were red blue they were

mostly numbers. And if they had green stalks in them.

They were these weird mean things and the.

aton, and all kinds of good stuff. Now you can actually do infinite numbers

in this same way take a hack and bush all blue, all the way up, and keep on going

forever. And that's the number which

mathematicians call omega. Now, that's infinity, but there's one

more, one larger than that, then we take an infinite stalk.

That's, goes up like this. The stocks are getting shorter and

shorter but there's still infinitely many of them and they keep going on like that.

And then put another blue stock on top of them and that's omega plus one.

And you can take infinite stock getting smaller and smaller, and smaller but

still infinite, keep on going forever. And put another infinite stalk on top of

it. Keep on going forever and another

infinite stalk. Keep on going forever and that's three

omega. And you can look at omega, omega and

omega, omega, omega. And you can get larger and larger and

larger. All of these these are what mathmaticians

call ordinal numbers but these together with real numbers stood inside a number

system called the surreal numbers. Which was includes the numbers that we

talked about in games. The infinite numbers, and if you want to

know more about this, there's a famous book by Donald Knuth called Surreal

Numbers. And that's what I want to say about

infinite games and loopy games. Take care.

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