I'm not a numerologist, but there's something about fairy tales and the number 3. From the 3 little pigs to Goldilocks and the 3 bears, the number 3 turns up all the time in these stories. It's actually a neat little narrative trick. The first incident (the first little pig with his house of straw) initiates the pattern. The second incident (the second little pig with his house of sticks) confirms the pattern, creating an expectation in the reader's mind. The third incident (the third little pig with his house of bricks) either fulfills or breaks the pattern in a climactic way (the Big Bad Wolf can't blow down the house of bricks and climbs down the chimney into the fireplace).
The story The Wonderful Wizard of Oz uses the number 3, but not in the traditional fairytale manner. Dorothy's adventures often break down into blocks of 3.
Upon starting on her journey, Dorothy makes 3 friends (Scarecrow, Tin Woodman, and Cowardly Lion). Before arriving in the Emerald City, the party faces 3 dangers (the river crossing, the Kalidahs and the Poppy Field). On their journey to the castle of the Wicked Witch of the West, the friends must face 3 waves of creatures sent by the Witch to destroy them. Once the Witch is defeated, Dorothy gains the Golden Cap, which allows her to command the Winged Monkeys (you guessed it!) 3 times. Not surprisingly, the ritual to summon the Winged Monkeys has 3 steps.
There is a little flexing of this pattern in the final leg of Dorothy's adventure. It looks very much like Dorothy and company have 4 encounters in this part of the story (the Fighting Trees, the Dark Forest, the China Country, and the Hammerheads). If I were to force it to fit the pattern, I would do so by not counting the Dark Forest. It was much more about the Cowardly Lion and giving him a place to rule, like Tin Woodman had the Winkie Country and Scarecrow had the Emerald City, than it was about the group having an adventure.
Both of these "Rules of 3" can be useful when preparing a story for an RPG. A fairy tale-style story can be easily created by setting up 3 simple scenes, each echoing a single theme or incident.
One of my players often makes the joke that the distance between any two places in my RPG worlds is "3 random encounters." (Even though I never use random encounters.) But it's not a bad idea. If you wanted to set up a list of random encounters for the characters to face, or just plan them into your story, it would make the land of Oz a bit more alive and interesting.