Terence has a checkerboard with 10 rows and 10 columns, a single checker at the bottom-left corner, and a spinner with the numbers 1,2, and 3. There is an equal chance of each number being spun.

He first spins the spinner and moves the checker from the bottom-left corner up the number of spaces spun. He then spins the spinner again, this time moving the checker right the number of spaces spun.

He repeats this process twice more, thus spinning the spinner for a total of six times from the outset.

Determine the probability that the checker will land on the same color as the square on which it started.