This is something I did as a child. I also used to (and still sometimes do), dump boiled eggs.
Step 1: Egg dumping
Competition happens in pairs.
Toss a coin to see who goes "bottoms" and who goes "tops".
"Bottoms" holds their egg in their fist, blunt end upwards. "Tops" hold their egg in one hand, with the pointed end sticking out.
"Tops" rap their egg sharply on "bottoms", once and once only.
If one of the eggs cracks, they lose. Eat the loser.
If neither egg cracks, change ends - "tops" becomes "bottoms" and vice versa.
Repeat until one egg cracks.
If you have several friends together at once, a knockout competition can be held, survivors battling survivors.
In UK pubs, egg dumping is an Easter charity event - competitors buy a pre-boiled egg for a pound, half the money goes in the pot for the winner, the rest goes to charity.
(Since first drafting this Instructable, I have found that egg-dumping was an Anlgo-Saxon tradition, and is also known as "jarping". Apparently some Geordies are under the false impression that they invented it, but we know better, don't we?)