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Robot tries to get to (0,0) or (1,0)

Source: SMO Open 2019 Q3

July 6, 2019
combinatoricsgameilostthegameCombinatorial games

Problem Statement

A robot is placed at point PP on the xx-axis but different from (0,0)(0,0) and (1,0)(1,0) and can only move along the axis either to the left or to the right. Two players play the following game. Player AA gives a distance and BB gives a direction and the robot will move the indicated distance along the indicated direction. Player AA aims to move the robot to either (0,0)(0,0) or (1,0)(1,0). Player BB's aim is to stop AA from achieving his aim. For which PP can AA win?
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