You are playing a game against a casino called Five-Card Battle.

For each round, both you and the dealer have the five cards above (aces are worth 1). You and the dealer each choose a card secretly, and then reveal the choices simultaneously. If the sum of the cards is even, then the casino wins $1. If the sum of the cards is odd, then you win $1. Note that 13 out of the 25 possible sums are even, so if both you and the dealer pick randomly the casino has an advantage in the long run.

Suppose you know the dealer's protocol is to randomly and independently pick a card every round. Is there a strategy for you to have an advantage in the long run?

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