First-player and second-player win: Difference between revisions

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In [[game theory]], a two-player [[turn-based game]] is a '''first-player-win''' if a [[optimal play|perfect player]] who plays first can always force a win.

Similarly, a game is '''second-player-win''' if a perfect player who plays second can always force a win.

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 ana examplefirst-player-win ofgame. However, Nim with the 1-3-5-7 starting position is a firstsecond-player-win game.

The classic game of [[Connect Four]] has been mathematically proven to be first-player-win.

It remains a matter of conjecture as to whether other games such as [[chess]] are first-player-wins; see the article [[first-move advantage in chess]] for more on this. The first player in [[English draughts|Checkers]], however, can only guarantee themselves a draw under perfect play.<ref>{{cite web|url=http://www.sciencemag.org/cgi/content/abstract/1144079 |title=Checkers Is Solved - Schaeffer et al. 317 (5844): 1518 - Science |publisher=Sciencemag.org |date= |accessdate=2008-11-24}}</ref>

==See also==

*[[Strategy-stealing argument]]

*[[Second player win]]

*[[Forced draw]]

*[[Zugzwang]]