1. The problem asks for the theoretical probability of landing on a green square (not including the "end" square) when rolling a 6-sided die and moving along a path with 54 squares (excluding start and end). 2. The total number of squares you can land on after a roll is 54. 3. The number of green squares (excluding the end square) is given as 3. 4. The probability of landing on a green square is the ratio of green squares to total squares: $$\text{Probability} = \frac{\text{Number of green squares}}{\text{Total number of squares}} = \frac{3}{54}$$ 5. Simplify the fraction: $$\frac{3}{54} = \frac{1}{18}$$ 6. Therefore, the theoretical probability of landing on a green square (not including the end) is $\frac{1}{18}$. This means if you roll the die many times, about 1 out of every 18 moves will land you on a green square.