As previously stated, the strategy for this game is to
pop one balloon.
You will win, because
Your opponent's only move is to pop a single balloon. Repeat, and you will eventually pop the last.
This is not correct BTW - but I will leave it as an exercise to the reader as to why. Cheaters can look at the comments!
$N$ is odd
Use the same strategy as the $99$ balloon case: go first and pop one balloon.
$N$ is even
In this case, you must
On the clown's turn, he will do one of the following:
- Pop half or more balloons.
- Pop an odd number of balloons less than half
- Pop an even number of balloons less than half.
Pops half or more
You win easily by popping the rest.
Pops an odd number of balloons
It is now your turn in an "$N$ is odd" case. So, pop 1 and let the game play out.
Pops an even number of balloons
On your turn, simply pop $2$ balloons.
You win because the clown again has an even number of balloons and he is in the same prediciment as before. Only now his options are limited to popping $2$ (and leaving it even) or $1$ (and making it odd). The moment he pops $1$ you win. Otherwise, you will eventually be left with the last $2$ balloons and get to pop them both to win.