Solution:

Note that if you make a turn and there is 1 counter left, you have won since the other player must pick up that counter.

If you make a turn and there are 7 counters left, you can win: if your opponent picks up 1, 2, 3, 4, or 5 of them, you can respectively take $5, 4, 3, 2$, or $1$ of them to leave $1$.

Likewise, if you play and there are $13$ counters left, you can in the same way play to leave $7$ on your next turn.

Continuing in this way, we see that the first player can win by removing $1$ counter, leaving $49$, and then playing on the succeeding turns to leave $43, 37, 31, 25, 19, 13, 7$, and $1$.