Leibniz & Games

“Human beings are never more ingenious than in the invention of games.”

  — Gottfried Wilhelm Leibniz

“I strongly approve the study of games of reason, not for their own sake, but because they help to perfect the art of thinking.”

  — Gottfried Wilhelm Leibniz

“A different—and perhaps better—analogy is provided by certain games, in which all the places on the board are supposed to be filled in accordance with certain rules; towards the end of such a game a player may find that he has to use some trick if he is to fill certain places that he wants to fill. If he succeeds in filling them, but only by resorting special measures, he has achieved a maximal result but not with minimal means. In contrast with this, there is a certain procedure through which he can most easily fill the board, thus getting the same result but with minimal ‘cost’.”

— Leibniz, “The Ultimate Origin of Things,” translated by Jonathan Bennett

“In practical affairs one always follows the decision rule in accordance with which one ought to seek the maximum or the minimum; namely, one prefers the maximum effect at the minimum cost, so to speak. And in this context time, place, or in a word the receptivity or capacity of the world, could be taken for the cost of the plot of ground on which the most pleasing building possible is to be built . . . the situation is like that in certain games, in which all places on the board are supposed to be filled in accordance with certain rules, where at the end, blocked by certain spaces, you will be forced to leave more places empty than you could have or wanted to.”

— Leibniz; see Markku Roinila, “Leibniz on Rational Decision-Making”

Gottfried Wilhelm Leibnitz on go

"On Certain Games" (in Dutch, German, Latin, French)

English translation by Robert de Neufville (from the French and German versions)

Peg Solitaire

“The game called Solitaire pleases me much. I take it in reverse order. That is to say that instead of making a configuration according to the rules of the game, which is to jump to an empty place and remove the piece which one has jumped, I thought it was better to reconstruct what had been demolished, by filling an empty hole over which one has leaped.”

— Leibniz

Reverse Solitaire

Xinyu Sun's Result on Peg Solitaire

Match Three

A Brief History of Match Three by Baldwin Brown-Canning IV

(I have not seen this information anywhere else. — RD)