I find that the more pins I use at once the better rewards I get, instead of going up at intervals.
For the mermaid magic, I used around 600 altogether. First lot I used 120 and didn't get anything good, next lot was 130 and I got the Mary Poppins pin. I was a bit down after that, but decided to keep riding and saved up 278 pins 15 mins before the mermaid magic was originally going to be finished. I used them all in one shot, got another Mary Poppins and finally a mermaid! Then again, a person before me used 230 pins in one shot and got 2 mermaids (and he already had 4 and used 700 altogether in different pullings).
Before the mermaid magic, I was 100 in one lots and got a pegasus and mary poppins pin, a few nights later I used another 100 and got both again.
I really don't know how it works, but in my experience (and I am definitely not as lucky as the person who used 700 pins and got 6 mermaids, when I used 600 and got 1) pulling in larger quantities helps me a whole heap more even if it is still a bit dismal compared to others.