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Sprouts
Sprouts is a pencil-and-paper game invented in 1967 by mathematicians John Conway and Michael Paterson at Cambridge. Despite needing only a few starting dots, it draws on graph theory and topology, and the number of possible moves is strictly limited, guaranteeing the game always ends.
Sprouts Rules
Begin by drawing a few spots on paper — two or three is typical for a first game. On your turn you draw a curved or straight line connecting one spot to another, or a spot back to itself, then place a new spot somewhere along that line.
Two rules constrain every move: a line may not cross itself, any other line, or any spot, and no spot may ever have more than three lines meeting at it. A spot with three connections is dead and cannot be used again.
Players alternate turns. The game ends when no legal line can be drawn. In the standard version the player who makes the last possible move wins; in the misère version that player loses.
Sprouts Strategy & Tips
Count the move ceiling
A game starting with n spots lasts at most 3n−1 moves and at least 2n. Knowing the parity of the total move count tells you whether you want to be the first or second player.
Watch the survivors
Track how many spots still have a free connection (one or two lines). Lines between live spots keep options open, while connecting a spot to itself burns two of its three slots at once.
Wall off regions
Each curve divides the page into separate regions. Trapping live spots in different regions from your opponent's playable spots can leave them stranded with no legal move.
Plan the parity early
Because the game length is bounded, the winner is often decided by who controls whether the final move count is odd or even. Steer toward self-loops or long connections to nudge the total.
Frequently Asked Questions
Who invented Sprouts?
John Horton Conway and Michael Stewart Paterson created Sprouts at Cambridge in 1967. Conway later popularized it through Martin Gardner's column in Scientific American.
Does Sprouts always end?
Yes. Each move adds at most one new spot but uses up connection slots, so a game starting with n spots can run for at most 3n−1 moves before no legal line remains.
How many starting dots should I use?
Two or three spots make a good first game. With perfect play the first player wins from games of 3, 4, or 5 spots, so experiment to find a fair challenge.
What is the difference between normal and misère Sprouts?
In normal play the player who makes the last move wins. In the misère variant the player who makes the last move loses, which changes the winning strategy completely.