That is the awesomest idea ever, Rev. I am going to steal it.
When/ if I ever get a job.
No. It is the second most awesomest idea. I shall betray a deep, dark secret. Normally it is reserved only for those that have mastered the dark arts of crypto. But you have an honest face, so I shall trust you with it. Guard it with your life.
The most awesomest idea is to optimized quasi-random operand conditioning. What is that? Either madness or genius. You can do it on paper or automate it. The point is to give a random gift. Completely without reason. Ah, but you have to use pseudorandomness for the full effect. No more often than 16 days and no less than every 36 days.
If one was so inclined (and lazy), you could generate a set of random numbers between 0 and 20, add 16. Then plug it into a reminder service or calendar software. When you get a reminder, you give a random gift.
For accurate randomness of gifts, I recommend categorizing them. Use another random numbers seed to select the category. And another random number seed to select the item from the category.
Now atmospheric noise is the NSA gold standard recommended source of randomness, but you can find your own random number generator. Just make sure it's really random, or you're using poor cryptological techniques and that'd make a crypto analysist sad.