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Name: Dan Sallitt
Location: New York, New York, United States

Wednesday, January 23, 2008

Marienbad: The Game

After I first saw Last Year at Marienbad, I spent a long evening in my college dorm analyzing the card game that Sacha Pitoëff uses to establish dominance over Giorgio Albertazzi. (Quick: name another Albertazzi movie. He played for Losey a few times...but it's odd that his prominent role in Marienbad didn't lead to more of an art-film career.) By the early morning hours I had devised a set of rules for responding to every possible card configuration. I taught the strategy to my 12-year-old brother, so he could beat his teachers at school.

But I'm writing to make a contribution to film scholarship, not because I think my blog needs some human interest. Revisiting the film as a perfect player, I realized that Pitoëff made a mistake in his second game! Albertazzi could have beaten him, but didn't see the opening; and Pitoëff regained control immediately. Whatever system Pitoëff uses is flawed. Revise your opinions of the film accordingly.

At the time, I hoped that I could decode the film as easily as I did the game. Over the years I grew comfortable with the way that Resnais and Robbe-Grillet throw wrenches in the works of any story interpretation that I can come up with. These days, I enjoy thinking of Marienbad as being about the writing process, with Seyrig as a fictional character who has to be brought in line with Albertazzi's aesthetic concept. Leave it to Robbe-Grillet to equate writing (or anything else, for that matter) with sexual domination.



Anonymous Anonymous said...

Hi Dan! I had almost the same experience, was fascinated by the game and became an instant champion at it even before watching "Marienbad" for the second time. However, if I remember rightly, there was no mistake in Pitoëff's move. Only the need to take a chance, in order not to repeat always the same first move, or because your opponent's starter forces you to risk a second-best move, which is dangerous.
Really, there is only ONE way of making a first move (specially if you don't start the game; it's yet harder if you do) that will lead safely to victory, and ONLY if you never make a mistake. It's easy if the other player is a newcomer, but after that it becomes very difficult to win. The first one who wanders loses. All other starts are risky, and can become fatal if the other player plays consistently well. You can have a favourable configuration which includes another which may make you lose. And if your contender sees it, you lost. It's a good game, you can play it anywhere, with coins, matchsticks, pieces of paper, cards, whatever.
P.S. I continue to consider "L'Année dernière à Marienbad" a very good movie, still so new I wonder if, even in France, it would have been possible to make today.
So long,

January 24, 2008 10:09 AM  
Blogger Dan Sallitt said...

Miguel - we need to find an online game of Marienbad (or Nim, as it is also called) to test our respective systems! I feel confident that I could have beaten Pitoëff in that second game. I can't remember the exact sequence of moves, but I believe that Albertazzi presented Pitoëff with a 0-2-5-6 state, and Pitoëff responded with 0-2-5-4 instead of making the correct move (which would be 0-2-4-6). If Albertazzi had responded with 0-1-5-4, he would have been in command.

My belief is that the person who starts the game will always lose against a perfect player. How would you make a winning first move?

I just looked for web-based Nim games. I found one where the computer program was easy to beat, and another where the program seemed to be a perfect player, and I could beat it only by making it go first.

January 24, 2008 10:56 AM  
Anonymous Mike Grost said...

There is a complete mathematical analysis of Nim in Martin Gardner's book, "The Scientific American Book of Mathematical Puzzles and Diversions" (1959). The game was analyzed by Harvard math prof Charles Leonard Bouton in 1901.

January 24, 2008 11:02 AM  
Anonymous Daniel said...

So is it possible to explain the game system in a few sentences, or is winning every time a far more complex process?

January 24, 2008 4:23 PM  
Blogger Dan Sallitt said...

Daniel - you can find some sites that describe a mathematical approach to winning. My solution was a brute-force evaluation of every possible state, and it resulted in a two-step method, which I'll try to give briefly. Assume the opponent starts first.

Step 1: Early game

If the opponent takes more than one card from a row, go to step 2.

However, if the opponent takes one card, then you should take one card from an untouched row.

If, after that, the opponent does anything other than take one card from an as-yet untouched row, go to step 2.

But if the opponent continues the pattern and takes one card from an untouched row, you should take one card from the final untouched row. Then go to step 2.

To summarize the above: as soon as more than one card has been removed from any row, go to step 2. Otherwise, keep deflowering new rows by taking one card from them.

Step 2: Good states

After the opponent's move, you must look for a move that will create one of the following six states. There will always be one and only one move that will bring you to one of these states.

State 1: 1-2-3
State 2: 1-4-5
State 3: n-n (where n > 1)
State 4: 1-n-n-1 (where n > 1)
State 5: 1-1-1
State 6: 1 (i.e., victory)

It doesn't matter which order the quantities are in. In other words, 1-3-2 is the same as 1-2-3.

Starting first

If you start first, you are advised to play slowly to give the opponent a chance to make a mistake. If the opponent doesn't make a mistake, you can't win. But, as soon as the opponent does something you wouldn't do in his or her place, you are in charge of the game again: just look for one of the six good states.

Does this make sense?

January 24, 2008 11:35 PM  
Anonymous Daniel said...

It does! But I'm going to have to practice to learn Step 2. Thanks Dan!

January 25, 2008 11:23 AM  
Blogger Dan Sallitt said...

Sorry to drag this out (some readers may actually be here for film discussion), but I made a mistake in my description of Step 2 when I said "There will always be one and only one move that will bring you to one of these states." There will always be at least one good move, but in some cases there may be more than one good move. For instance, if you are confronted with a 1-3-3 state, you can win by going either to 3-3 or to 1-2-3.

January 25, 2008 11:41 AM  
Anonymous Anonymous said...

Hallo Dan!

I'm writing, because I've also noticed that 'M' made a mistake in the second game.

The game went on as follows:

1) Oponent: 7530 M: 7520
2) 6520 6420
3) 6320 5320 (and here it is! - the correct move would be 1320 instead of 5320)
4) 5310 2310
5) 2210 2200
6) 1200 1000 .

But what is really interesting in here is the fact that in the original script by Robbe-Grillet there was no mistake! Istead of 6320 - 5320 there was 6410 - 5410.

I wonder if Resnais did it deliberately or it was just a mistake. In the first case the question is why? Maybe this is the key to the solution of Marienbad's mystery?

If you (or anybody else) would like to talk about the film, write me: .

Best regards,

November 13, 2008 12:22 PM  
Blogger Dan Sallitt said...

Dziękuję, Lech. The thing that really surprises me is that the Nim moves were specified in the script! In Hollywood, there'd have been a credit for a "Nim Adviser."

If Robbe-Grillet cared so much about getting the games right that he choreographed them in the script, how could he and Resnais (who allegedly had a close collaboration) allow a mistake to creep in? The most likely explanation is that Pitoëff just goofed up on the set, and it was too late to fix the mistake when it was discovered. If I were Robbe-Grillet, I would have been devastated, insisted on a reshoot.

November 13, 2008 12:57 PM  
Anonymous Anonymous said...

In fact Resnais shot the film without Robbe-Grillet and that's why he could have changed something on his own. But maybe you are right, maybe it's just a mistake (but not Pitoëff's one in fact - he probably just took one match from the last row as he should do without noticing that his oponent have played 6320 istead of 6410).


November 14, 2008 1:39 AM  
Anonymous Patrick Foley said...

@Dan Salitt, you should add (0,2,4,6) to your winning solutions, it is easy to get to I know but if you get the other player to go with a board of (0,2,4,6), there is no combination of things they can take away to bring the board back into their favor, allowing you to win. :)

April 1, 2009 8:09 PM  
Blogger Dan Sallitt said...

Patrick - of course you are right, but 0-2-4-6 is covered under the "Early Game" instructions. I broke my instructions into two phases in an attempt to make them easier to remember - otherwise I would have had to list another seven winning patterns.

April 2, 2009 12:19 AM  
Blogger R said...

From what I understood in the movie, they played the misere version: that is who takes the last card, loses. Thus the algorithm presented above will not work

October 11, 2009 12:23 PM  
Blogger Dan Sallitt said...

They certainly used the version of the game in which the person who takes the last card loses. But what's wrong with the process I described?

October 11, 2009 12:44 PM  

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