We want to
find strategies to win in various games. It is possible that
there is a systematic way to find such strategies for all games, but we
will first explore specific games.

For the first game, you can play against the computer

here
or against a human

here
and figure out the rules, or read this:

Chomp
Start with an m by n rectangle. The 1st player picks a box
and remove the boxes above and to the right of it including
itself. The 2nd player does the same. Repeat until
a player is forced to pick the (poison) box in the lower-left corner,
in which case he loses.