Ethan Song and Bryan Guo are playing an unfair game of rock-paper-scissors. In any game, Ethan has a \( \frac{2}{5} \) chance to win, \( \frac{2}{5} \) chance to tie, and \( \frac{1}{5} \) chance to lose. How many games is Ethan expected to win before losing?

Let's think step by step and output the final answer within \boxed{}.
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