Xavier, Yvonne and Zac are playing a game with standard coins. Initially, Xavier has 50 coins, Yvonne has 30 coins and Zac has 22 coins. At each turn, they all simultaneously toss just one of their coins. If all the coins come up heads or all the coins come up tails, each player takes back his/her coin. However, if one of the coins shows a different symbol to the other 2, the tosser of that coin takes all 3 coins. The game ends when someone has 0 coins. What is the expected length (in number of turns) of this game?

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