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In some two-player sequential games with complete information, one player may be tempted, when possible, to mirror the opponent's moves. When this gives one player a winning strategy, the game loses all interest unless the rules are changed to avoid this pitfall.
What role does chance play in a board game? It can vary widely, ranging from total dominance, where players have no say at all, to complete absence. Between the two extremes, the strategies of many games rely on optimizing probabilistic principles.
Blaise Pascal had a gift for illuminating all manner of situations through sound, precise analysis, pinpointing the difficulties and explaining himself with unsurpassable clarity. One of the most famous questions in probability—the problem of points—was a case in point.
In a board game, it is fairly common, partway through a match, to feel that you are ahead of (or behind) your opponent. Through the example of Domineering, this article invites you to discover how John Conway formalized this notion.
