The first person only needs to remove 1 and leave 12.

When the second person takes 1, the first person takes 2.

When the second person takes 2, the first person takes 1.

The purpose is to ensure that multiples of 3 are taken away.

In this way, the first person can guarantee to take a multiple of 3, and will definitely take the remaining 12, that is, the original 13 and the last one.

So, the first person must win.

Just take away, 1, 4, 7, 10, 13.