Teeko is an abstract strategy game invented by John Scarne in 1937 and rereleased in refined form in 1952 and again in the 1960s. Teeko was marketed by Scarne's company, John Scarne Games Inc.; its quirky name, he said, borrowed letters from Tic-tac-toe, Chess, Checkers, and Bingo. 
The Teeko board consists of twenty-five spaces arranged in a five-by-five grid. There are eight markers in a Teeko game, four black and four red. One player, "Black" plays the black markers, and the other, "Red", plays the red. Black moves first, and places one marker on any space on the board. Red then places a marker on any unoccupied space; black does the same; and so on until all eight markers are on the board. The object of the game is for either player to win by having his markers situated in a straight line (vertical, horizontal, or diagonal) or square of four adjacent spaces. (Adjacency is horizontal, vertical, or diagonal, but does not wrap around the edges of the board.) If neither player has won after the "drop" (when the eight pieces are put on the board), then it's attempted via the following method: The players alternate moving pieces one at a time, with Black playing first. A piece can only be moved to an adjacent space.
The rules, as summarized above, are very simple, but the strategy is complicated enough to fill a book, Scarne on Teeko, by Scarne (1955). Nonetheless, Guy Steele solved the game (i.e., showed what must occur if both players play wisely) via computer in 1998: he found that neither player can force a win.
There are sixteen variations of Teeko, such as Advanced Teeko, which have slightly different rules. All sixteen are outlined in Scarne on Teeko; the rules above are for "Standard Teeko" (or "Teeko"). Steele showed that Advanced Teeko is a win for Black (assuming, again, that both players play perfectly), as is one other variation, but the other fourteen are draws.
- Eskin, Blake. "A world of games: Cards and gambling authority John Scarne claimed to have invented one of the greatest board games of all time. Was he bluffing?" Washington Post, July 15, 2001, p. W18.
- Scarne, John (1955). Scarne on Teeko. New York: Crown Publishers.
- Epstein, Richard A. (2012) The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, p. 341.