Zermelo's theorem
In a finite two-player game of perfect information with no chance, either one player can force a win or both can force at least a draw.
In a finite two-player game of perfect information with no chance, either one player can force a win or both can force at least a draw.
Often misread asTaking the theorem to mean chess is solved, or that it shows the first player wins because moving first is an advantage.
How to see it
In chess, one of the three results is already settled
In a finite two-player game of perfect information with no chance, exactly one of these holds: the first player can force a win, the second can, or each can force at least a draw. Which of the three it is, the theorem does not say.
The checkIt says the value exists, not what it is; for chess nobody knows which of the three cases holds.
Try itSay which of the three outcomes the theorem delivers for noughts and crosses, and which for chess. If you can do the first and not the second, you have understood it correctly.
Games that show it
Know these first
When it stops being true
- Perfect information
- finite-horizon
Easily confused with
Sources
- Zermelo, E. (1913). Proceedings of the Fifth International Congress of Mathematicians, Volume 2, Cambridge University Press, 501-504.
- Osborne, M. & Rubinstein, A. (1994). MIT Press.