Editing Sprouts (game) (section)

===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]].<ref>{{cite web|url=https://www.cs.cmu.edu/~sleator/papers/Sprouts.htm |title=David Applegate, Guy Jacobson, and Daniel Sleator, ''Computer Analysis of Sprouts'', 1991 |publisher=Cs.cmu.edu |access-date=2012-09-26}}</ref> 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 [[conjecture]]d 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.

{| border="1" cellspacing="0"
|-
|&thinsp;'''Spots'''
|&thinsp;0
|&thinsp;1
|&thinsp;2
|&thinsp;3
|&thinsp;4
|&thinsp;5
|&thinsp;6
|&thinsp;7
|&thinsp;8
|&thinsp;9
|&thinsp;10
|&thinsp;11
|&thinsp;...
|-
|&thinsp;'''Normal Outcome'''&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Loss&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;Win&thinsp;
|&thinsp;...&thinsp;
|}

In 2001, Riccardo Focardi and Flamina Luccio described a method to prove by hand that the normal 7-spot game is a loss.<ref>{{cite web| first1 = Riccardo |last1 = Focardi | first2 = Flamina | last2 = Luccio | title = A new analysis technique for the Sprouts Game | date = 2001| citeseerx = 10.1.1.21.212|s2cid = 18947864 }}</ref>

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 [[nimber]]s to accelerate the computation, reaching up to 32 spots.<ref>{{cite arXiv|first1=Lemoine|last1=Julien|first2= Viennot|last2=Simon|title=Computer analysis of Sprouts with nimbers|year=2010|eprint=1008.2320 |class=math.CO}}</ref> They have extended the computation up to 44 spots in 2011, and three isolated starting positions, with 46, 47 and 53 spots.<ref name="sproutsWiki">[http://sprouts.tuxfamily.org/wiki/doku.php?id=records Computation records of normal and misère Sprouts], Julien Lemoine and Simon Viennot web site</ref>

The normal-play results so far are all consistent with the conjecture of Applegate, Jacobson, and Sleator.