A game is played with identical coins according to the following rule.  In each by round, the player with the most coins gives one coin each to the other $$2$$ players and also places one coin into the discard pile. The game ends when one player runs out of coins. Players $$X$$, $$Y$$ and $$Z$$ start with $$20$$, $$19$$ and $$18$$ coins, respectively. How many rounds will the game last? 
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