Assume you have a pair number of coins $2n$ with possibly different values, ordered in a line. Let us enumerate the coins as $x_1,x_2,\ldots,x_{2n}$. The coins are not ordered in any particular way.

The game has two players and the first player has to take one coin from the extreme points (either $x_1$ or $x_{2n}$). Then, the second player has to take one coin from the extremes and so on until there are no more coins. The winner is the one who ends up with more money.

It is clear that if $n=1$ then the first player wins or draws. If $n=2$ with a little more work you can prove that the first player has a winning (or draw) strategy and the same with $n=3$.

Does the first player have a winning strategy always?

What is the *optimal* strategy to maximize the profit?