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Some games with relatively small [[game tree]]s have been proven to be first or second-player wins. For example, the game of [[nim]] with the classic 3–4–5 starting position is a first-player-win game. However, Nim with the 1-3-5-7 starting position is a second-player-win. The classic game of [[Connect Four]] has been mathematically proven to be first-player-win.
With perfect play, [[English draughts|checkers]] has been determined to be a draw; neither player can force a win.<ref>{{cite journal|url=http://www.sciencemag.org/cgi/content/abstract/1144079 |title=Checkers Is Solved |access-date=2008-11-24 |doi=10.1126/science.1144079 |pmid=17641166 |volume=317 |issue=5844 |journal=Science |pages=1518–1522|year=2007 |last1=Schaeffer |first1=J. |last2=Burch |first2=N. |last3=Bjornsson |first3=Y. |last4=Kishimoto |first4=A. |last5=Muller |first5=M. |last6=Lake |first6=R. |last7=Lu |first7=P. |last8=Sutphen |first8=S. |s2cid=10274228 }}</ref> Another example of a game which leads to a draw with perfect play is [[tic-tac-toe]], and this includes play from any opening move.
Significant theory has been completed in the effort to [[Solving chess|solve chess]]. It has been speculated that there may be [[First-move advantage in chess|first-move advantage]] which can be detected when the game is played imperfectly (such as with all humans and all current [[chess engine]]s). However, with perfect play, it remains unsolved as to whether the game is a first-player win (White), a second player win (Black), or a forced draw.<ref>J.W.H.M. Uiterwijk, H.J. van den Herik. [https://web.archive.org/web/20180109064212/https://pdfs.semanticscholar.org/55dd/2fee1f0981fbfabd4b158a6584eefaacbcea.pdf "The Advantage of the Initiative]". (August 1999).</ref><ref>{{cite journal
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