getting rich by counting the coins

On a table is a row of fifty coins, of various denominations. Alice picks a coin from one of the ends and puts it in her pocket; then Bob chooses a coin from one of the (remaining) ends, and the alternation continues until Bob pockets the last coin.

Prove that Alice can play so as to guarantee as much money as Bob.

The implication of the game is mind-blowing. This is a seemingly fair game that is rigged for the first player. No matter how the second player arranges the coins, it is impossible for him to end up with more money.

Why is this the case?


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