Thane asks for << a way to make tic-tac-toe, or something like it, into an interesting game Here are a number of tic-tac-toe-like games which are all more sophisticated and fun than your basic always-can-draw game. 1. Go-moku. This is played on a theoretically infinite square grid (a large piece of graph paper, or the beach, will do nicely). Each player marks any unoccupied square with their mark (X or O), marks are unchangeable, and the first player to get 5 in a row of their mark (vertically, diagonally, or horizontally) wins. (There are numerous variants. Cf. <http://project.blink-182.org/seb/spec.html> . However, be warned that most websites explaining the rules of the game seem to be written by sub-imbeciles.) 2. 3D tic-tac-toe. This is usually played on a 4x4x4 cube-shaped structure with four transparent 4x4 squares arranged one above the other with space to insert either of 2 kinds of markers. It's often available commercially, or you can build your own. First player to get 4 in a row right-left, front-back, up-down, in a planar diagonal, or in a main diagonal of the 4x4x4 cube wins. 3. 4x4 toral tic-tac-toe. Just like regular tic-tac-toe but played on a 4x4 board, and it takes 4 in a row in a straight line or diagonal to win. The main difference (besides 4 replacing 3) is that the winning line may wrap around, as though the game board has its opposite edges identified to make a torus. This means that instead of the expected 10 winning lines, there are now 6 more kinds of "diagonals" making 16 winning lines in all. (These 2 patterns, flipped and rotated, give all 6 new "diagonals".) ___________ | X | | X | | X | | X | ------------------- ___________ | X | | X | | X | |X | ------------------ 3.5 Of course 2. and 3. could be combined to get 3D toral tic-tac-toe -- but only for the advanced player! 4. Set. This commercial card game is somewhat like tic-tac-toe conceptually, but not mechanically. Each card has a graphic with 4 properties (C=color, N=number, S=shape, and L=line-style). The deck of 81 cards has one of every possible combination. The dealer shuffles the deck and not-too-quickly turns one card after another over and places it on the table (or floor). A "set" is any 3 cards having the following property: For each property P (= C, N, S, or L), either all 3 possibilities for P occur among the 3 cards, or else only 1 of the 3 possibilities occur. Any number 0 <= k <= 4 of the 4 properties can occur in all 3 possibilities, and then the remaining 4-k properties must each be constant among the 3 cards in the "set". (This may sound complicated at first, but it is easy to get used to on a gut level. (A set is really an affine line in the vector space (Z_3)^4, in case you really wanted to know -- and that's why it's like tic-tac-toe.) Anyhow, the first one to recognize a "set" among the face-up cards, yells "Set!" and collects the cards as a triple, over the course of the game stacking up the harvested "sets" so they can be counted when the deck has been all turned over (at which point there will be some unsettable collection of cards left). The one with the most "sets" wins. Set can be quite addictive. (An interesting problem discussed here some years ago and solved by Rich is this: What is the largest possible number of cards from the Set deck which has no "set" among them ?) --Dan