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A Beautiful Mind
   

The 2001 movie [ext] A Beautiful Mind, directed by Ron Howard and starring Russell Crowe, tells of the life of John Forbes Nash Jr., winner of the Nobel Prize for his work on game theory in economics.

Someone want to detail the Go references in this movie? I've yet to see it, but many new players I've taught have mentioned they first saw the game there. -- Bignose

Working from memory here (minor spoilers for those who have not yet seen the movie):

  • Nash, while in Princeton, is lured to play by some of his friends-to-be. He loses, much to his amazement, as he says: "I had the first move advantage, and my play was perfect." According to the game theory, in a complete knowledge game, he should've won, or at least achieved a draw.
  • Later on in the movie, as Nash returns to Princeton to try and fight his... problem, his old friend points at a goban while they're walking in the park, and invites him to an another game.

That's it - not too much really.

--JanneJalkanen


AvatarDJFlux I haven't seen the movie, but I've been reading Nash' biography by Sylvia Nasar (A Beautiful Mind, Faber & Faber, 1998) from which the movie was inspired.
Go is mentioned six times in 388 pages, and of course there's no trace of the scenes above described.
Even if they are true, it is just ridicolous that anyone could pretend to play "perfectly" at go... even top professionals, at their stratospherical level, admit to make some mistakes every now and then.... ;-)

dnerra: Of course this is ridicolous, and in the movie this episode is meant to characterize Nash: how he mistakenly believes he could understand the world (uhm, just Go here :-) ) "perfectly" just from abstract mathematical analysis.[1] This in contrast to his more successful attempt of modelling reality with his Nash equilibrium.
Btw, if you haven't seen the movie yet -- well, it was nice, but nothing extraordinary I'd say, so no need rush to the theatre :-)


Of course, even if he played perfectly, game theory does not state that he should have won. True that go is a complete knowledge game, so (assuming perfect play from both sides) what the theory says is that: either the 1st player cannot but always win, or he cannot but always lose (or cannot but draw). And at the moment we don't know which (most likely we never will). Even if anyone was that naive to belive his plays to be perfect, he still could not conclude that he is garanteed to win.

Side note: taking in account komi, I would not bet on either possibility (w or b always win in a perfect game). Draw is unlikely.

As a comparison, in chess also the perfect game is either a perpetual black victory, or a perpetual white victory or a perpetual draw and we don't know which, but in that case the most likely situation is that a perfect game always draws.

Marco Tarini

In go, if the winning party were always white, then black should start with a pass move. This forces either a draw (white passes) or a black win (since black now moves second). With an non-integer komi, draws are impossible. Hence, the best possible result for white after a black pass is to pass himself to gain a draw. Thus white can never win, assuming that both parties play a perfect game. The result of the perfect game must thus be either a draw or black win. Does my logic compute? :-) --JanneJalkanen

Dieter: No. You are assuming that komi switches sides after a pass, which is not the case.

JanneJalkanen: Actually, I thought that two passes would mean a draw, with no stones on board, komi or no komi. Then I started wondering: If both players pass immediately, what is the result? Are all points on board dame or would they have to be played out? Or would both players passing be a loss to both players? The result probably varies according to the rule set used, yes?

Dieter: I was referring to Hence, the best possible result for white after a black pass is to pass himself to gain a draw. This is not true, because White now has the advantage of komi AND moving first. You seemed to apply symmetry where there was none. Probably I don't understand the point.

Illich: No, the point JanneJalkanen made was correct. Maybe I can rephrase it (with my not so good english):

What we want to proove: "In no komi Go game, black either wins or draws."

Proof by contradiction:
(1) Contradiction: Assume that after perfect play white wins
(2) Now, if black knows this, he passes in his first move.
(3) This leeds to two follow-ups:
(3a) White also passes, the game is draw.
(3b) White plays. Then black can use white's perfect strategy from point 1 and so he wins.

Both 3a and 3b are contradictory of 1. So the original sentence is proved.
For games with komi, it cannot be proven - it is simple a matter of the size of komi: if it is bigger than certain amount, white will win after perfect play.


One thing I did not like about the Go in the movie is that, at the end of the game, Nash's opponent slams the stone down and the move is greeted by a lot of ooh's and aah's from the audience, and the game immediately is over at that point. (He captured a single stone if I remember correctly) I was expecting him to say 'checkmate!', just like in movies where chess is depicted, but luckily that didn't happen. Of course, the 'perfect play' statement made up for it. --Garf

It appeared to me as if Nash's opponent had managed to catch Nash in Damezumari and pick off a good sized group of stones. --StormCrow


My favorite Go-related moment in the film takes place when Nash is challenged to a game. 'Scared?' his opponent asks him.

'Terrified,' he responds, 'Petrified, mortified, and stupefied... of you!'

--Regyt


[1] Now that I read this again, immediately a certain Go player comes to my mind, not living too far away from where I live... Am I the only one? :-). Dieter: hmmm, would that be the one chasing the "pen of God" with which he will write the perfect Go book ?


I think that the game they played was taken from a 1971 game between Rin Kaiho and Ishida Yoshio (1971-06-10.sgf from GoGoD). Looks like they tried to finish off the game badly...

[Diagram]
Diag.: Moves 218 to 218


This is a copy of the living page "A Beautiful Mind" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.