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Unlimited time off is the strangest and most confusing shit I ever heard of.
Honestly, If my contract didn't contain a law given number of hours, I would be completelly lost about what is a correct number days off.
I get the idea, but it muddies the entire concept too much. 
I would be almost happier, if I had an option to request UNPAID time off, because there would be an understanding, that it is not a parasitic relationship with the employer.