Logging Game

Logging can be a very mundane job, but Alice and Bob have devised a game to help them pass the time. They take turns choosing a log, and cutting it into 2 smaller logs. The sum of the lengths of the 2 logs equals the length of the original log. The only restriction is that neither of the resulting logs may be shorter than 1 meter in length (but exactly 1 meter is fine). In other words, non-integer