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 of the time and Mr Pinata hits his target 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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1 solution
Firstly it's important to note that if Mr Pinata shoots at Mr smooth and he is successful then he most likely to lose against Mr Accurate when he gets the chance to shoot. It would seem then that Mr Pinata should shoot at Mr Accurate, however if he is successful then he will be in a head to head duel against the superior Mr Smooth so again, he is less likely to win. Now if Mr Pinata shoots in the air then Mr Smooth will shoot at Mr accurate, otherwise he will be defeated in the next round. Whoever wins the duel between Mr Accurate and Mr Smooth will have to face Mr Pinata in a 1-1 where Mr Pinata will a l w a y s have the 1st shot. Hence, it the best option for Mr Pinata.