combined Shannon's Hex-playing herustic with alpha-beta search. On the subject of early Computer Hex, notable early implementations include Dolphin Microware's Hexmaster, published in the early 1980s for Atari 8-bit computers. Until 2019, humans remained better than computers at least on big boards such as 19x19, but on Oct 30, 2019 the program Mootwo won against the human player with the best Elo rank on LittleGolem, also winner of various tournaments (the game is available here). This program was based on Polygames (an open-source project, initially developed by Facebook Artificial Intelligence Research and several universities) using a mix of: zero-learning as in AlphaZero boardsize invariance thanks to fully convolutional neural networks (as in U-Net) and pooling and growing architectures (the program can learn on a small board, and then extrapolate on a big board, as opposed to justified popular claims about earlier artificial intelligence methods such as the original AlphaGo). Strategy Although it is known that the first player (without the swap rule) has a theoretical winning strategy, it is not known what that strategy is, except for very small boards. However, there are a large number of useful tactical and strategic concepts available to Hex players. Virtual connections and templates A set of stones of one color is said to be virtually connected if the stones' owner can guarantee to connect them, no matter what the opponent does. The simplest example of a virtual connection is a bridge, shown in diagram 1. Although the bridge's two red stones are not adjacent, Red can guarantee to connect them: if Blue plays in one of the bridge's empty cells, then Red can play in the other. Note that the virtual connection requires not just the two red stones, but also the two empty cells of the bridge. The cells (empty or otherwise) that are part of the virtual connection are called the carrier of the virtual connection. A template is a pattern of stones and empty cells that is virtually connected and minimal (i.e., removing any stone or empty cell from the carrier would break the virtual connection). Templates can be characterized as interior templates (guaranteeing a connection between two or more stones) and edge templates (guaranteeing a connection between one or more stones and a board edge of the same color). Some examples of interior templates and edge templates are shown in diagrams 1 and 2, respectively. Mathematical theory Determinacy It