or k+1 with other possibilities being quite unlikely. One player tries to create enclosed regions containing survivors (thus reducing the total number of moves that will be played) and the other tries to create pharisees (thus increasing the number of moves that will be played). Winning strategies Since Sprouts is a finite game where no draw is possible, a perfect strategy exists either for the first or the second player, depending on the number of initial spots. The main question about a given starting position is then to determine which player can force a win if they play perfectly. When the winning strategy is for the first player, it is said that the outcome of the position is a "win", and when the winning strategy is for the second player, it is said that the outcome of the position is a "loss" (because it is a loss from the point of view of the first player). The outcome is determined by developing the game tree of the starting position. This can be done by hand only for a small number of spots, and all the new results since 1990 have been obtained by extensive search with computers. Normal version Winning Ways for your Mathematical Plays reports that the 6-spot normal game was proved to be a win for the second player by Denis Mollison, with a hand-made analysis of 47 pages. It stood as the record for a long time, until the first computer analysis, which was done at Carnegie Mellon University, in 1990, by David Applegate, Guy Jacobson, and Daniel Sleator. They reached up to 11 spots with some of the best hardware available at the time. Applegate, Jacobson and Sleator observed a pattern in their results, and conjectured that the first player has a winning strategy when the number of spots divided by six leaves a remainder of three, four, or five. This is a mathematical way of saying that the pattern displayed by the outcome in the table below repeats itself indefinitely, with a period of six spots. In 2001, Riccardo Focardi and Flamina Luccio described a method to prove by hand that the normal 7-spot game is a Loss. Then, the computation results were extended in 2006 by Josh Jordan up to 14 spots. In 2007, Julien Lemoine and Simon Viennot introduced an algorithm based on the concept of nimbers to accelerate the computation, reaching up