Combinatorial Game Suite has been used to calculate exact values of positions in Fox and Geese well beyond what is feasible by hand. A description of Fox and Geese appears in Winning Ways, vol. 3, by Berlekamp, Conway, and Guy. Also in that volume are Elwyn Berlekamp's comprehensive strategies for winning the sum of a Fox and Geese position and an arbitrary Hackenbush string.

This page is intended primarily for those who have read through Berlekamp's analysis and are interested in the details of CGSuite's output, such as the "museum" that appears in WW in abbreviated form.

All of the output is in plain-text format, but it is nonetheless quite
readable. For easiest viewing, make sure that word wrap is turned *off*
in your text editor. The symbol `^`

is used for ↑ and `v`

for ↓.
`^5`

is ↑↑↑↑↑, etc. As always,
"height" refers to the sum of the ranks of all four geese.

Aaron SiegelLast modified: 14 May 2003 08:02:08 PM |