for dice/sorensen metric, your example of "night", "natch" you are showing a value of .60, however according to the algorith the expected answer for the same two strings is .25

could you please elaborate on how you got .60?

links for reference:
https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient

http://www.gutenberg.us/articles/eng/S%C3%B8rensen_similarity_index

http://wooorm.com/dice-coefficient/