Wild West Shootout!

Three men: Mr Accurate, Mr Smooth and Mr Pinata are in a 'truel' (a shootout between 3 people where a player wins if the other 2 players have been shot). Mr Accurate hits his target 100% of the time, Mr Smooth hits his target \(\frac{2}{3}\) of the time and Mr Pinata hits his target \(\frac{1}{3}\) of the time. However, Mr Pinata shoots 1st, Mr Smooth shoots 2nd and Mr Accurate shoots 3rd. Who should Mr Pinata shoot at, in his 1st shot, if he is to have the greatest chance (probability) of winning?

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