How many effectively unique keys does the playfair cipher have?

Hi, I would say it is more than 120

It is. If my reasoning is correct, there are 360,000 unique ciphers. My reasoning is this: when i/j is counted as one letter and repetition is not allowed (as in Playfair), there are 25*24 = 600 possible digrams. Since each digram corresponds to one of those unique digrams, there are 600^2 = 360,000 unique Playfair ciphers (one should probably actually use 359,999 because one of the "ciphers" maps each digram to itself).