Duel Monsters is a card game that was derived from Ancient Egypt. When Pegasus J. Crawford arrived in Egypt on an archaeological expedition, he discovered the large stone tablets with images of large monsters were carved into them. When Pegasus returned to his home, he was inspired by what he had seen, and he decided to paint the monsters that he had seen on the stone tablets.
Later on, Pegasus used his paintings as the artistic basis for a variety of cards in a game he created called 'Duel Monsters' (Magic and Wizards in the first arc of the manga) on several of the cards he made. The game was released a few months later in Japan and several other countries (including the United States of America, Australia, Germany, and China) and soon became very popular.
In the Toei anime, Yuugi says that the game was introduced when he was in 3rd grade (Elementary school, 3rd year), or seven years prior to the start of the Toei series, which features the main characters in 10th grade (High School, 1st year). If this is to be taken literally, and Pegasus' age at the beginning of the Yu-Gi-Oh! Duel Monsters animation is taken into account, that means he introduced the game at age 17. This would imply that the death of Pegasus' wife Cyndia and his subsequent journey to Egypt in search of necromancy techniques all happened within the course of a year.
In the manga (Volume 2; Duel 9: "The Cards With Teeth"), Sugoroku Mutou doesn't mention anything about when the game Magic and Wizards was created, or by whom, but he does say that it is wildly popular in the United States of America and has only a 'small following' in Japan. Furthermore, he adds that his prized Blue-Eyes White Dragon card was so 'overpowered' that production was stopped, rather than Pegasus having intentionally stopped production of the card after approximately five copies were made. By Volume 8 (Duel 60: "Challenge"/Yu-Gi-Oh!: Duelist Volume 1, Duel 1), the game's name changes to Duel Monsters, but the cards and basic gameplay are the same. The game has also become a great deal more popular in Japan, warranting a technology-sharing agreement between Kaiba Corporation and Pegasus' company, Industrial Illusions for the purpose of a Japanese national tournament, which is televised for all to see.