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Draw a tree diagram to get started.
You could also fill in a table for all possible outputs for, say, the first 5 letters produced to get a feel for the problem and which sequences will win first.
You can also read http://plus.maths.org/issue55/features/nishiyama/ which has answers to the required computations.
Ante Up
Age 16 to 18
Challenge Level 
Draw a tree diagram to get started.
You could also fill in a table for all possible outputs for, say, the first 5 letters produced to get a feel for the problem and which sequences will win first.
You can also read http://plus.maths.org/issue55/features/nishiyama/ which has answers to the required computations.
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