Fox and Geese

[cjsmith]

Anybody here good at the game of Fox and Geese? Total beginner wonders how a game is ever anything but a draw. Seems too easy for either side to force the draw.

Comments

[hitchhiker.livejournal.com]

I think one of the Winning Ways (http://www.amazon.com/exec/obidos/tg/detail/-/0120911027/102-9551075-3836957?vi=glance) books had a section on it. Not sure now - it's been a while since I read them.

How do you draw a game, anyway? It's monotonic wrt the geese, innit?

[cjsmith.livejournal.com]

Tis. Here are my thoughts, potentially very confused.

Since the geese must corner the fox to win, they cannot win if there are fewer than (my best guess) six of them. Since the geese cannot move backwards, if the fox ever gets behind the line of geese and decides to stay there he cannot be cornered. Since the fox must eat all the geese to win, he cannot win if two or three geese are on the far end of the board, because they are stuck in such a way that they cannot be eaten. So I am guessing that any game with fewer than six geese AND two geese in the end row, or any game with the fox past all the geese AND two geese in the end row, seems like a draw.

Thanks for the book pointer!

[hitchhiker.livejournal.com]

Ah - I'm talking about another variant, in which the geese try to force the fox to the top edge of the board and trap it there, and the fox tries to break free and hit the bottom edge. No capturing involved.