Sprouts+

Sprouts is a mathematical game invented in 1967 by John H. Conway and Michael S. Paterson. The rules are simple. Two players start with a certain number of Dots. They take turns drawing a Line connecting any two Dots or connecting a Dot back onto itself. After each Line is drawn an additional Dot is added along the newly drawn Line. No Line can cross another Line. A Dot can have up to three Lines connected to it. The players take turns drawing a Line until no additional Lines can be drawn. The player who drew the last Line wins the game. The app color codes each Dot to indicate if it has three lines connected to it, is reachable by another Dot or is blocked by lines and cannot be reached.

The strategy of the game is to divide the Dots into M groups by encircling Dots so that Lines cannot be connected to them from Dots in the other groups. M starts at 1 and increases as the players draw Lines that encircle Dots to form additional groups. Note that each time a Line is drawn, it fills two connections on preexisting Dots and it creates a new Dot that has one additional connection so the total number of connections is decreased by one (i.e. -2 + 1 = -1) for each new Line drawn. Note also that the last Line drawn in each encircled group will always generate a new Dot with one unfilled connection. If the game starts with N Dots that represents 3*N unfilled connections and there can therefore be 3*N Lines drawn minus one Line for each of the M groups formed during the game. This number will be even if N-M is even (2*N is always even) and odd if N-M is odd. To be the last player to draw a Line, the player who plays first will want to form M groups such that N-M is odd while the player who plays second will want to form M' groups such that N-M' is even.

The app allows you to play with 2, 3, 4, 5, 6 or 7 Dots. Two Dot games are unlimited. Other games require a Token. The game comes with 20 Tokens. Additional Tokens can be purchased through an IAP: 25 Tokens for $1, 100 Tokens for $2 (approximately).

The game can be played on one device or on two connected devices connected through local WiFi or the Game Center. Using the Game Center you can invite friends and use SharePlay to incorporate a FaceTime window and voice communication. Alternatively you can play with a random player at a matching skill level.