The Game in "Last Year at Marienbad"

[Lionel Mandrake]

If you have seen the movie "Last Year at Marienbad" (1961), you will remember a certain game.

"In a spacious baroque castle, that is run as a modern luxury hotel for an upper-class clientele, one of the guests (Giorgio Albertazzi) tries to persuade a woman (Delphine Seyrig) that they have had something like an affair the previous year, and that this year she ought to elope with him to a new life outside the geometric architecture and highly formal society of the establishment--away also from the man who seems to be watching over her (Sacha Pitoeff), and who may be her husband. In the course of various encounters and conversations the protagonist gradually succeeds in bending the woman to his will, and at the end of the movie the two seem to be ready to leave the splendid world of the hotel for an unknown destination.
...
"Much of the guests' time is spent with typical leisure activities and games--marksmanship competitions, ballroom dancing, dominoes, poker, and a game without a name in which the apparent husband of the woman invariably excels. This nameless game is played repeatedly throughout the film.

"It is played by placing cards or other suitable objects in the following order:

ooooooo
ooooo
ooo
o

"Two players then take turns in removing as many cards from a row as they wish--with the restriction that the cards have to be taken from one row only each time. ...

"X and M, the two rivals for the woman, play the game several times. M always wins. "Can you ever lose?" X asks him at one point. "I can lose," M replies, "but I always win."

read more:
http://faculty.frostburg.edu/phil/forum/Marienbad.htm

Several characters in the movie speculate about the best strategy for playing this game, and they argue whether the first player should win or lose. For a definitive answer, browse:
http://www.plambeck.org/oldhtml/mathematics/games/misere/03R/index.htm

[struggle4progress]

1. All short impartial games are actually nim in disguise!

[Lionel Mandrake]

2. Not exactly.

You are alluding to the Sprague–Grundy theorem, which states that

"every impartial game under the normal play convention is equivalent to a nimber"

http://www.facebook.com/pages/Sprague-Grundy-theorem/133495113357300

But the game under consideration (misere) violates the normal play convention, and the theorem does not apply.

[struggle4progress]

3. Fair enough.