The lottery for the Endorse Your Heart Out event is open to everyone who has endorsed more than 90% of all WA nations. There are 98 of these nations as of the last update, and each of them have the same chance of winning. That means you have a roughly 1% chance of winning each day, and about a 14% chance of winning through the duration of the event. So there's a 86% chance you wouldn't get anything. Understand?
The regular card lottery is a different matter. There are over 550 nations eligible for it, and even though certain factors will boost your chances, such as high number of endorsements given, the overall chance is still quite minimal.