An Ante Duel is a Duel where both players stake cards of equal value, and the winner of the duel claims both cards. This is the only way to become the Owner of a card in a duel. These Duels are completely optional but are forbidden in most official tournaments.
In the anime and manga, these duels were more common. In the manga, ante is said to be a common rule in trading card games, and ante duels were required in the Battle City tournament. In Yu-Gi-Oh! GX, however Duel Academy's policy forbids ante duels between students.
Players that play with an ante usually bet a rare card that isn't a part of their Deck, as many players tend to be afraid of losing cards from a Deck they spent time building and balancing.