Who will win a Rock, Paper, Scissors, Lizard, Spock game?
Python 3, 68 50 48 bytes



EDIT: Thanks to 3 tricks from Neil, and 2 from Mr. Xcoder

Each input string has a distinct fourth character, so I'm using that to distinguish them. If you arrange the elements in the cycle (scissors, paper, rock, lizard, spock), then each element beats the element directly after it and the element 3 spots to the right, cyclically. So we subtract the inputs' positions in the cycle. If that number is 0, it's a tie. If it's 1 or 3, it's a win for the first player. In my original solution, the cycle difference would index into the string "210100" to distinguish the results of the game. Neil somehow figured out this can be accomplished without indexing by adding 7 and taking the modulus by 3. Edit: Originally I used the second character to identify the string, but if you use the fourth and reverse the cycle, you get cake. And we could all use more cake.

lambda x,y,z="cake".find:(7+z(y[3])-z(x[3]))%5%3


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Older version:

lambda x,y,z="caoip".index:(7+z(y[1])-z(x[1]))%5%3


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Original version:

b="caoip"
def r(x,y):return"210100"[(b.index(y[1])-b.index(x[1]))%5]


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