[1] Though early in his life he worked as a computer programmer with the IBM 360 assembly language, he began designing games in the 1950s.

[5][6] Abbott also invented logic mazes, the first of which appeared in Martin Gardner's Mathematical Games column in the October 1962 issue of Scientific American.

[7][8][9] One of the more prominent of these is Theseus and the Minotaur, which was originally published in the book Mad Mazes.

In 1965, he moved back to New York, where he continued to work as a computer programmer, mostly with the IBM 360 assembly language.

[1] Abbott created all of his card games during the 1950s, starting with Babel in 1951,[2] and ending with Auction in 1956.

In 1963, the book Abbott's New Card Games was published by Sol Stein of Stein and Day, containing the rules for all eight of his card games and the rules for his chess variant, Baroque chess.

This was the first logic maze to be published, appearing in Gardner's Mathematical Games column.

[22][7][9] A logic maze has a set of rules, ranging from the basic (such as "you cannot make left turns") to the extremely complicated.

[28] However, the publisher, Sol Stein, preferred the name "Ultima," so that is the title that was used in the book.

[16] Eleusis is probably Abbott's most prominent game, due to its metaphors and its suitability for use as a teaching tool.

[5] Martin Gardner wrote about it in his Mathematical Games column in the June 1959 issue of Scientific American.

[14] Basically, the gameplay consists of the dealer choosing a secret rule dictating how cards are to be played, and the players playing cards in an attempt to figure out the rule through inductive reasoning.

Martin Gardner wrote about this version in the October 1977 issue of Scientific American.

[29] Abbott also self-published a pamphlet in 1977 with the rules for the improved version, titled The New Eleusis.

[21] The game was published in Germany by Franjos in 1992; Abbott was not satisfied with this version, however, due to several flaws in it.

His game Eleusis uses a similar idea, in that you do not know how cards are to be played at the beginning; George Brancaccio, someone Abbott worked with at the Bank of New York, commented on this, saying "In your game Eleusis, you don't know what cards can be played.