Alley Cat (1984)

Okay, my first game is not random at all, but one that i played a lot when we had our first 286 PC in 1990:

You are a male cat, searching for love. On your way you have to face various dangers like thrown out boots, angry pitbull-dogs and zappy eel. Every level consists of three challenges:

Try to enter a window from the alley
Win one of five random minigames
Climb the heart level to reach the cat-girl

Developer: Synapse Software Corporation
Publisher: IBM