If you think it in a way of dynamic programming it could help.
Imagine we have N pirats. Calculate probability of draw for single round (either all N pirats has the same gesture or there's a pirat for every possible gesture).

Then calculate average number of rounds to be played before someone lost (standard geometric sum).

Now someone is lost and we have the same game but with less pirats. So we can use DP-approach with probabilities.

Use doubles, it's enough to get AC.
You would be happy to implement this problem (my impl is 30 lines with i/o on c++).

the statement says "You should help him determine the expected value of prize in case of his victory"
but I believe it should be the case of anyone's victory.
can someone who solved the problem please clarify this?
thanks

Edit: I got accepted assuming the original statement is wrong

Edited by author 25.11.2016 17:53

Many AC codes input the n=100, output have many zero before the radix point, the relative error is not enough very much! Why did they accept?

Give me, please, first 10-15 answers.

http://en.wikipedia.org/wiki/Rock-paper-scissors

paper beats rock (by surrounding it)
rock beats scissors (by smashing them)
scissors beats paper (by cutting it)

:)