My tamagotchi started playing hide and seek earlier. Where I am, the time was 11:40, and my tamagotchi is just 1 minute slower. I reckon hide and seek is just another randomly chosen thing when you leave your tamagotchi alone for a while, like tv or rolling around?
P.S. Right now I am defining it plays hide and seek as when your tamagotchi comes closer and closer to you until all you can see is it's face, then it goes back to normal size and repeats.