Not to be confused with Mystery Crate games.
You can either start the mystery game from the pop-up you will see when you load the game, from a panel in the build menu, or by navigating to Specials and then the name of the latest holiday/season and selecting the mystery game. Click on "Play Now" (or "Play") to open the Mystery Game menu.
Click on one of the many presents moving across the screen. Prizes are purely random, so the color or shelf the present is on doesn't affect anything. Your first turn is free, but if you want to play again you have to spend Cash for every try. The amount has varied from 20-30 Cash.
It is possible to win the same item more than once. All items won will be placed in your inventory. Removing these items will return them back to your inventory.