Are all combinatorial games equivalent to Blue-Red-Green Hackenbush?

Question

Given a combinatorial game, is there guaranteed to be a Blue-Red-Green Hackenbush game, finite or infinite, that's equivalent to it?

Answer 1

Hmm. I think so.

Not a great answer, but "Winning Ways" is a hard book to look something up in.

For the previous answerer, this is combinatorial game theory. Best references are "On Numbers and Games" by Conway and the "Winning Ways" by Berlekamp, Conway and Somebodyerother.

I do know that all finite impartial games are equivalent to a single pile game of nim.

I think you can prove it simply for finite games, but as I think about it I am getting lost.

Sorry

Answer 2

I think that we used some other games to find different values that you could not find in hackenbush. For example, I don't remember the value star poping up in hackenbush. It did pop up in the map coloring game. Also, we did not see the values up, down, or switches in the game Hackenbush.

Answer 3

Dude, what kind of Math is that.