Develop an Unbeatable Strategy!

Consider a two player coin game where each player gets turn one by one. There is a row of even number of coins, and a player on his/her turn can pick a coin from any of the two corners of the row. The player that collects coins with more value wins the game. 

Develop a strategy for the player making the first turn, such he/she never looses the game.

Note : The strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.

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Example :

  18 20 15 30 10 14


First Player picks 18, now row of coins is
  20 15 30 10 14


Second player picks 20, now row of coins is
  15 30 10 14


First Player picks 15, now row of coins is
  30 10 14


Second player picks 30, now row of coins is
  10 14


First Player picks 14, now row of coins is
  10 


Second player picks 10, game over.



Develop an Unbeatable Strategy!

The total value collected by second player is more (20 +
30 + 10) compared to first player (18 + 15 + 14).
So the second player wins.

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This is the unbeatable strategy! 

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