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boooeee
30th July 2008, 10:35 PM
Stumbled across this conspiracy theory after reading several wikipedia chess articles. The conspiracy is that IBM used a human grandmaster to "assist" Deep Blue during crucial parts of the game.

Link (http://chess.about.com/library/weekly/aa05f04.htm)

Basically, the conspiracy theory is based on the following:

- Kasparov was convinced that certain moves Deep Blue made could not possibly made by a computer (see link for one of the moves in question).
- IBM initially refused to publish Deep Blue's logs from the matches (they eventually provided them)
- IBM retired Deep Blue after defeating Kasparov.
- IBM received a lot of favorable publicity after the match, and saw a boost in its stock price.

Is this even plausible? Any chess experts here have any thoughts on Kasparov's claim that certain moves couldn't have been made by a computer?

Pato2747
31st July 2008, 10:49 AM
The link states a bunch of fallacies. "Kasparov said that Deep blue couldn't make those moves, so THERE WAS A HUMAN HELPING IT". It's drawing to conclusions based on simple speculation.

grmcdorman
31st July 2008, 11:15 AM
Indeed. Although I haven't RTFA*, I don't see how one can definitively say that a given move couldn't have been made by a computer. For that matter, the reverse probably doesn't hold either (computers and humans can make bonehead moves).

* Read The Fine Article: an acronym often seen on Slashdot. (http://www.slashdot.org)

ETA: Refusing to publish the logs: they may have felt they contained proprietary information; and the machine was special purpose and probably expensive to support and run.

Bob Klase
31st July 2008, 11:21 AM
The link states a bunch of fallacies. "Kasparov said that Deep blue couldn't make those moves, so THERE WAS A HUMAN HELPING IT". It's drawing to conclusions based on simple speculation.

You'd also have to consider the relatively small number of humans who would have a chance of winning against Kasparov.

madurobob
31st July 2008, 11:51 AM
Doesn't seem very likely to me. Kasparov was smugly overconfident and was demoralized by his first quick defeat in the six game match. He never got a chance to recover.

He never really had much of a chance. DeepBlue had access to a database of games Kasparov had played over several years and could analyze not just expected moves - but expected Kasparov moves. On the other hand, kasparov had access to only the few games he and DeepBlue played together.

Kasparov and DeepBlue also only played a hurried six games. When Spasky and Fisher played their storied match in the 70s they played 21 games - enough for them to get a feel for each other's strengths and weaknesses.

So, in a sense, Kasparov was playing with odds against him. In a more "fair" setting he may have done better.

madurobob
31st July 2008, 12:19 PM
From the article:
IBM retired Deep Blue without a rematch. Conclusion: IBM had something to hide.
That only makes sense if you have no head for business and no knowledge of IBM.

Once they beat Kasparov the deed was done. There would be little to gain in beating him again, and much to lose in a defeat.

Plus IBM in '97 was run by Lou Gerstner; famous for an intense focus on cutting spending that didn't drive revenue. The research arm of IBM always had a lot of leeway in how they spent money, but DeepBlue was never meant to be a revenue generator. It was a gimmick, a test to see what they could do. IBM got a little mileage out of it only because marketing took the idea and ran with it. Once the DeepBlue team proved what they could do it was time to get back to the real work of generating those billion dollar breakthroughs they're famous for.

The bottom line is that chess-playing computers is simply not IBM's core business and there is really no money to be made there.

epeos76
31st July 2008, 02:07 PM
There is a movie about this called, I think, Game Over. It includes some clips from the coverage of the matches.

The movie evidence goes something like this:

Kasparov crushed deep blue in the first game.

In the second game, the computer played very similarly with the exception
of one move that turned the game.

The IBM staff included a grandmaster who was very smug about beating
Kasparov - Means, motive, and opportunity

IBM controlled all access to the computer and refused to turn over the
"logs" for game two.

IBM refused a rematch and scuttled DeepBlue.

From the movie, it looked like Kasparov psyched himself out. Apparently, he could even have forced a draw after the critical move in game two. The only part that is at all suspicious to me is that IBM didn't seize the opportunity to dispel any doubt by turning over the logs from the second game after the match.

dudalb
31st July 2008, 06:00 PM
Look, I have no doubt that IBM consulted Grand Masters to help program Deep Blue. Who the hell else would it make sense to consult when building a chess program?
But as for evidence that there was some Grand Master sitting behind the scenes during the actual game.........that is CT kookiness.
"Pay No Attention To the Grand Master Behind the Curtain......"

moon1969
31st July 2008, 06:42 PM
Nah it can"t be true because Kasparov is a joo. rothschilds, zionists and the State of Israel would never let deep blue cheat. But Kasparov hates other joos like Roman Abramovich or Boris Berezovsky. Still to anti-semites it doesn"t matter that Vladimir Putins best friends Roman Abramovich is a joo. Maybe the nazi nashi youth thinks that Roman Abramovich is a good joo?

madurobob
31st July 2008, 07:52 PM
Nah it can"t be true because Kasparov is a joo. rothschilds, zionists and the State of Israel would never let deep blue cheat. But Kasparov hates other joos like Roman Abramovich or Boris Berezovsky. Still to anti-semites it doesn"t matter that Vladimir Putins best friends Roman Abramovich is a joo. Maybe the nazi nashi youth thinks that Roman Abramovich is a good joo?

Um, yeah... and much of the IBM empire was built on profits from doing business with nazi Germany. Somehow that figures into all this as well :rolleyes:

CFLarsen
1st August 2008, 01:14 AM
Whatever a human can do, a computer can do even worse.

SezMe
1st August 2008, 02:45 AM
Kasparov was smugly overconfident and was demoralized by his first quick defeat in the six game match. He never got a chance to recover.

There is a movie about this called, I think, Game Over. It includes some clips from the coverage of the matches.

The movie evidence goes something like this:

Kasparov crushed deep blue in the first game.
Sounds like that movie is a work of fiction and not to be relied upon as evidence of anything.

CptColumbo
1st August 2008, 04:00 AM
IIRC from the articles at the time of the last match, Kasparov's major complaint was that the computer was able to have every match Kasparov had ever played entered into it and Kasparov had to go into the match without any history on the comp's strategy. He felt that gave "Big Blue" an unfair advantage.

~enigma~
1st August 2008, 08:21 AM
Look, I have no doubt that IBM consulted Grand Masters to help program Deep Blue. Who the hell else would it make sense to consult when building a chess program?You don't need to be an expert at chess in order to write a successful program. Do you think all chess programs can be outplayed by the people who wrote the algorithms for them?

Jimbo07
1st August 2008, 08:37 AM
Does it matter? Computers were bound to get more powerful and be able to analyze games to deeper levels of moves, so even if Kasparov felt that particular match to be unfair, he would have been smart enough to know that the writing was now on the wall for chess...

madurobob
1st August 2008, 08:39 AM
Sounds like that movie is a work of fiction and not to be relied upon as evidence of anything.

My bad - poor wording on my part. He won the first game, lost the second. It was the loss in the second game - his first loss - that seemed to shake him.

http://www.research.ibm.com/deepblue/watch/html/c.shtml

Kasparov was stunned by his defeat and left the playing area at great speed without comment

Cuddles
1st August 2008, 09:19 AM
The bottom line is that chess-playing computers is simply not IBM's core business and there is really no money to be made there.

Another point is that making a computer beat a human at chess just isn't that impressive. Chess is a relatively simple game, and once computers were invented there was never really any doubt that they would one day be able to beat us, since even without clever programing it would be possible to just use brute force. Deep Blue was an interesting test to see if we had reached that point yet, with the conclusion that we have just about, but it's still in the realm of supercomputers and is by no means certain. There's really nothing to be gained by showing that computers can still beat people at chess.

On the other hand, a computer that could beat a master at something like Go would be a serious achievement, and is something that no-one is sure would be possible no matter how powerful computers get, since the amount of calculations required to brute force it are so many orders of magnitude higher.

As for the conspiracy, how can anyone possibly claim that a computer could not have made a particular move? A computer can make any move a human can. Neither I nor Kasparov have access to Deep Blue's program, so we can't comment on how likely it was to make a particular move, but there would certainly be nothing ruling out any move completely.

dudalb
1st August 2008, 02:01 PM
You don't need to be an expert at chess in order to write a successful program. Do you think all chess programs can be outplayed by the people who wrote the algorithms for them?

Yes, but if nothing else a Grand master would be good to test the program against.
And if it was a chess program for sale, having a Grand master involved would certainly be a good marketing move.

madurobob
1st August 2008, 02:24 PM
Yes, but if nothing else a Grand master would be good to test the program against.
A necessity, I suppose.
And if it was a chess program for sale, having a Grand master involved would certainly be a good marketing move.
Perhaps, but thats unrelated to DeepBlue. IBM had no intention of makrting a chess program. They were tinkering with AI to use in business modeling solutions and with linking unimpressive processors to generate impressive processing power. The lessons learned from DeepBlue can be seen applied in the kickazz BlueGene (http://en.wikipedia.org/wiki/Bluegene) line super computers.

Also, FWIW, DeepBlue was over 10 years ago. With todays computers and AI I'd wager a new computer-human match would end with the computer undefeated.

PixyMisa
1st August 2008, 10:05 PM
Another point is that making a computer beat a human at chess just isn't that impressive. Chess is a relatively simple game, and once computers were invented there was never really any doubt that they would one day be able to beat us, since even without clever programing it would be possible to just use brute force.
Actually, there was a lot of doubt expressed about this. There were plenty of confident predictions that computers could never beat top-ranking human chess players. All wrong, of course.

On the other hand, a computer that could beat a master at something like Go would be a serious achievement, and is something that no-one is sure would be possible no matter how powerful computers get, since the amount of calculations required to brute force it are so many orders of magnitude higher.
I give it five years.

Oliver
2nd August 2008, 12:14 AM
Funny thing is: The Computer didn't even know that it did win or not - or what chess is about, or what a human is, or IBM, or a computer...

epeos76
4th August 2008, 09:46 AM
Sounds like that movie is a work of fiction and not to be relied upon as evidence of anything.

It does, if you read it too quickly. In fact, Kasparov's "first quick defeat" happened in game two. (http://http://www.research.ibm.com/deepblue/watch/html/c.shtml)

He never recovered. As I said earlier, I think the "points" made in the movie are highly dubious, with the exception of IBM's refusal to publish the conclusive proof that there had been no human intervention in game two.

More likely than not, the corporation just didn't care enough to do this after the match. Still, it seems a little churlish..

Cuddles
4th August 2008, 09:55 AM
I give it five years.

If I were a betting person, I'd bet against it. Unless we actually manage to develop quantum computers, we won't have the computing power to brute force Go in the forseeable future. Programming is another matter and it's certainly possible someone will come up with a clever way of doing it. However, I really doubt it will be in the next five years, if at all. Not least because there are very few people even trying, Go just doesn't have the popularity chess does.

He never recovered. As I said earlier, I think the "points" made in the movie are highly dubious, with the exception of IBM's refusal to publish the conclusive proof that there had been no human intervention in game two.

More likely than not, the corporation just didn't care enough to do this after the match. Still, it seems a little churlish..

The most obvious answer is that they may not have had a way to do so. Deep Blue will certainly have logs, but I doubt they are so easily accessable that they can just be opened up straight after a game. Even if they were, they would not be in a form that a layperson would understand. The people who claim conspiracy would just say the people who translated them, presumably the same ones who did the programing in the first place and part of the conspiracy, lied.

epeos76
4th August 2008, 12:34 PM
That could well be, though I think Kasparov and other interested parties could probably have found people with the know-how to do the translation. There's some evidence the the logs were available and would have been useful.

Kasparov (somewhat unreasonably) wanted the logs during the match, so presumably he thought he could do something with them. IBM denied him the logs during the match on the grounds that it would give him unfair insight into DeepBlue's decision making process.

At one point, IBM actually agreed to provide the logs after the match in order to get Kasparov to keep playing. Why didn't it do as it promised? Well, post match the special team IBM put together to create DeepBlue dissolved. I suspect there probably wasn't any single human being left with both the authority and the motive to make it happen. It's telling, or at least irritating, that the film makers didn't ask any of the IBM people they interviewed that question.

btw I'm a big fan of Go. I got into the habit of using "epeos76" playing online.

madurobob
4th August 2008, 12:49 PM
On the other hand, a computer that could beat a master at something like Go would be a serious achievement, and is something that no-one is sure would be possible no matter how powerful computers get, since the amount of calculations required to brute force it are so many orders of magnitude higher.
Interestingly, my father had a Go playing computer while a psych prof at UNC in the late 70s. It played a modified version of the game (limited due the capability of the computers of the day) with other computers around the world. IIRC they lost in the championship round to a team from Toronto.

My gut feeling is that the best computers today (like the BlueGene I linked to earlier) have the processing power to easily dominate a human Go master. But, what is lacking is the programming.

Beerina
8th August 2008, 12:10 PM
The link states a bunch of fallacies. "Kasparov said that Deep blue couldn't make those moves, so THERE WAS A HUMAN HELPING IT". It's drawing to conclusions based on simple speculation.

I assume that whether Kasparov actually said that or not is a matter of record.

Whether it indicates there was probably a human doing it, I don't know.



Oh, wait. Yes I do. I've studied AI in detail and at the graduate level and programmed it professionally for years.

In layman's terms, basically when a guy like Kasparov says there's no way a computer could make such a move, he means the move is too clever for computers, which are little more than efficient game tree search machines.

See, there's this thing called the "horizon" effect, which basically means that, no matter how far you plan ahead, there could be something just further out you can't quite see that'll trash all your plans.

In simplest terms, it's setting your opponent up for a trap that they don't see, not because they're stupid, but because, in analyzing, "if I do this, then they do this, then I do this", and so on, the trap gets irrevocably entered into 3 more exchanges deep than you planned for.

Kasparov, who knows how computers and chess and chess algorithms work, would thus know there are certain moves a computer could not make precisely because they're too many moves deep. Indeed, chess grandmasters have long used this fact to beat chess computers, by setting up deep traps for the computer!

It's true programs are getting more clever, with larger tables of opening and closing moves, and various "deep plunge" algorithms, but the chess masters are very aware of all this, too*. In any case, there still is no solution anything significantly better than "try all possibilities".



So, yes, when he says it had a human feel to it, it would be a good thing to check out.






* After all, who the heck do you think are the primary domain experts on the construction of these computers!?!?

Beerina
8th August 2008, 12:28 PM
From the article:

That only makes sense if you have no head for business and no knowledge of IBM.

Once they beat Kasparov the deed was done. There would be little to gain in beating him again, and much to lose in a defeat.

Plus IBM in '97 was run by Lou Gerstner; famous for an intense focus on cutting spending that didn't drive revenue. The research arm of IBM always had a lot of leeway in how they spent money, but DeepBlue was never meant to be a revenue generator. It was a gimmick

I.e. a revenue generator! :)


Maybe not directly, as gigantic computers with lots of chess hardwiring aren't a particularly big market. But that's not the only way to generate money.

As mentioned, it helped gain recognition and thus the stock went up. And, I'm sure, by many times what the whole DeepBlue program cost.


Now, because, with a rematch, they'd "have little to gain and much to lose" gets much closer.

A. If they won again, it doesn't prove much other than that it wasn't a fluke.

B. If they lost, they get some press, but in an unfavorable, if light-hearted, light.

C. In the event of B., a third rematch, if they won, would receive far less press than A. did, and would be thus of much less value, stock-wise. And if they lost again, forget it.


When Kasparov said this, and I do remember him thinking there was a human in there overriding some decisions (some other human-computer matches allowed for 1 or more humans to override particularly stupid computer decisions as part of the rules, so it isn't unknown) I did wonder, as the AI issues w.r.t. chess playing and computers are well-known, and well-studied.

The long and the short of it, though, is he shouldn't have lead with his chin and rushed it.


My favorite quote of his, "The best chess computers can beat mundane Grandmasters. But not me and Karpov!"

Daald
8th August 2008, 01:58 PM
I was actually reading about this recently. I thought Kasparov was just being a sore loser. At later interviews he admitted that today's programs seem to have a personality of their own. I've read a lot about Kasparov lately and I noticed that he is very paranoid. A lot of chess champions seem to be.

For example, during Krammik's match his opponent thought he was going to the bathroom too much so he wanted controls placed. If you look at Kasparov and Karpov history you will see similar things.

Here is an interview with one of Deep Blue's engineers. Answers some questions raised here.

http://www.wired.com/science/discoveries/news/2007/05/murraycampbell_qa

TheDaver
10th August 2008, 06:19 AM
It’s definitely a believable conspiracy theory, if any of you have ever heard of The TurkWP (http://en.wikipedia.org/wiki/The_Turk) (not the one from The Sarah Connor Chronicles).

But of course that doesn’t necessarily make it true.

Beerina
15th August 2008, 10:09 AM
The Turk from the Sarah Connor Chronicles (AKA Terminator, The TV Show) was named after the old mechanical Turk, and deliberately so, as mentioned in the show itself.

Confuseling
16th August 2008, 08:47 AM
...As for the conspiracy, how can anyone possibly claim that a computer could not have made a particular move? A computer can make any move a human can. Neither I nor Kasparov have access to Deep Blue's program, so we can't comment on how likely it was to make a particular move, but there would certainly be nothing ruling out any move completely.

Computers can make any move a human can, but that doesn't mean a computer running a specific program can make any given move in some situation. A decision tree is a form of finite state machine (someone correct me, I'm no expert...), and as far as I know they're by definition predictable, so it's distinctly possible that with the logs someone could have ruled out the computer making a particular decision.

Maybe Kasparov could recognise particular patterns in its 'thought', and spotted this as an aberration. More likely, in my mind, he's as crazy as... well... a professional chess player.

huw-l
16th August 2008, 09:23 AM
If I were a betting person, I'd bet against it. Unless we actually manage to develop quantum computers, we won't have the computing power to brute force Go in the forseeable future. Programming is another matter and it's certainly possible someone will come up with a clever way of doing it. However, I really doubt it will be in the next five years, if at all. Not least because there are very few people even trying, Go just doesn't have the popularity chess does.


You lose the bet :)

http://www.scientificblogging.com/newswire/dutch_national_supercomputer_huygens_beats_human_g o_professional

Whats interesting is that Huygens is a general-purpose supercomputer rather than being specially built like Deep Blue was. It's not even that big, weighing in at 60 TeraFlops. The world's fastest supercomputer is 1000 TeraFlops.

It still looks like it will be a while before a home-computer can play world-class Go.

CptColumbo
17th August 2008, 06:31 AM
What's the average for computers now? 1200-1600?

huw-l
17th August 2008, 10:53 AM
assuming you mean TeraFlops, no.

The top500 supercomputers in the world run from 1000 to 9 TeraFlops.

Machines bigger than 30 TeraFlops tend to be national or regional supercomputer facilities.

http://www.top500.org/list/2008/06/

Cuddles
19th August 2008, 09:04 AM
You lose the bet :)

Crap. You see, this is why I'm not a betting person.

It would be interesting to know a bit more about this. I notice that they actually played four games, and it was only the fourth, which was the actual exhibition match, that the computer won. The obvious question is how consistently the computer could actually win. Was that a one-off fluke, or could it consistently win at least a fraction of games?

On the plus side, this does support at least part of my point. As you note, this is not a particularly remakable supercomputer, it was advances in programming rather than computing power that have made the difference.

I also note that my post was made on August 4th, while these games were played on the 5th (at least three were, the fourth may have been later). Clearly there's some kind of conspiracy involved here.

TheDaver
19th August 2008, 02:23 PM
The Turk from the Sarah Connor Chronicles (AKA Terminator, The TV Show) was named after the old mechanical Turk, and deliberately so, as mentioned in the show itself.
++postcount

Come back when you have something relevant to add to the topic.

Mark Felt
19th August 2008, 02:26 PM
++postcount

Come back when you have something relevant to add to the topic.
Holy rule10, context.

Foolmewunz
19th August 2008, 06:14 PM
Another point is that making a computer beat a human at chess just isn't that impressive. Chess is a relatively simple game, and once computers were invented there was never really any doubt that they would one day be able to beat us, since even without clever programing it would be possible to just use brute force. Deep Blue was an interesting test to see if we had reached that point yet, with the conclusion that we have just about, but it's still in the realm of supercomputers and is by no means certain. There's really nothing to be gained by showing that computers can still beat people at chess.

On the other hand, a computer that could beat a master at something like Go would be a serious achievement, and is something that no-one is sure would be possible no matter how powerful computers get, since the amount of calculations required to brute force it are so many orders of magnitude higher.

As for the conspiracy, how can anyone possibly claim that a computer could not have made a particular move? A computer can make any move a human can. Neither I nor Kasparov have access to Deep Blue's program, so we can't comment on how likely it was to make a particular move, but there would certainly be nothing ruling out any move completely.

I know this has been discussed, and I'm not surprised that there's a computer out there that can handle Go calculations. I just wanted to comment on the illogic of, on the one hand, accepting that the finite number of moves for chess could be handled by a computer, yet thinking that Go, OR ANY GAME WITH FINITE NUMBER OF MOVES, could not be crunched. Time was, back in the 50s and 60s, when many said that a computer would never be able to handle the variations on chess, either.

Sooner or later, if it's merely a question of numbers and brute computing power, some machine will do it.

Not rubbing your nose in the development of the Go-playing computer. Just that it seems to me that your post was heading towards one conclusion and you got to another.

Cuddles
20th August 2008, 10:19 AM
I know this has been discussed, and I'm not surprised that there's a computer out there that can handle Go calculations. I just wanted to comment on the illogic of, on the one hand, accepting that the finite number of moves for chess could be handled by a computer, yet thinking that Go, OR ANY GAME WITH FINITE NUMBER OF MOVES, could not be crunched. Time was, back in the 50s and 60s, when many said that a computer would never be able to handle the variations on chess, either.

Sooner or later, if it's merely a question of numbers and brute computing power, some machine will do it.

Not rubbing your nose in the development of the Go-playing computer. Just that it seems to me that your post was heading towards one conclusion and you got to another.

You appear to have completely missed my point. Neither I, nor anyone else, has ever claimed that it is theoretically impossible to brute force Go. My whole point was that we will not have the computing power to do so in the forseeble future. The fact that we can use programming tricks to reduce the computing power needed does not alter that point in the slightest. Despite having been wrong about how soon Go playing computers will rival human players, I am still completely confident in saying that we do not currently, and will not in the near future (say, a few decades at least), have the computing power to calculate all possible moves in Go. Hell, we still can't even do that for chess.

As for your claim that anything that involves a finite number of calculations will eventually be solved, that is provably false. There are absolute limits to information transfer and storage that are set by physical laws. I'm fairly sure Go doesn't come close to those limits, but it is entirely possible to construct a similar game with a finite number of moves that can never be solved by brute force, even in theory.

EGarrett
20th August 2008, 10:23 AM
A bit of info about Kasparov's character in big matches:

1. When playing against a bunch of internet voters in "Kasparov vs. The World," when the game got really tough, he accused one of the young advisors of being in cahoots with the Russian Grandmaster School. To my knowledge the girl has since published her own analysis and how hard she worked on the game, refuting that rather batty claim.

2. Kasparov later claimed that Deep Blue had not beaten him because one of his blunders was in a position that was later found out to be drawn. This is of course completely illogical, because it means that if chess is solved to be a draw, then every game ever played is a draw because they actually started from a "drawn position." Victory is determined by the decisions the player makes over the board, not what's discovered later with much deeper analysis.

So we know he does this regularly in questionable circumstances and that he uses illogical arguments.

Random
20th August 2008, 11:07 AM
You lose the bet :)

http://www.scientificblogging.com/newswire/dutch_national_supercomputer_huygens_beats_human_g o_professional

Whats interesting is that Huygens is a general-purpose supercomputer rather than being specially built like Deep Blue was. It's not even that big, weighing in at 60 TeraFlops. The world's fastest supercomputer is 1000 TeraFlops.

It still looks like it will be a while before a home-computer can play world-class Go.

I read the article. The computer had a nine-stone handicap (that's huge), and still managed to lose three blitz games before the final match.

Doesn't bode well for the future, but right now the computer could probably be defeated by a skilled and determined amateur in an even match.

Foolmewunz
21st August 2008, 02:38 AM
You appear to have completely missed my point. Neither I, nor anyone else, has ever claimed that it is theoretically impossible to brute force Go. My whole point was that we will not have the computing power to do so in the forseeble future. The fact that we can use programming tricks to reduce the computing power needed does not alter that point in the slightest. Despite having been wrong about how soon Go playing computers will rival human players, I am still completely confident in saying that we do not currently, and will not in the near future (say, a few decades at least), have the computing power to calculate all possible moves in Go. Hell, we still can't even do that for chess.

As for your claim that anything that involves a finite number of calculations will eventually be solved, that is provably false. There are absolute limits to information transfer and storage that are set by physical laws. I'm fairly sure Go doesn't come close to those limits, but it is entirely possible to construct a similar game with a finite number of moves that can never be solved by brute force, even in theory.


Any known game, then. :spjimlad::spjimlad:

(And no fair counting Calvinball or Mornington Crescent. Infinite whimsical variations cannot be measured when we're not even using the same number system as the players.)

Cuddles
21st August 2008, 09:54 AM
Any known game, then. :spjimlad::spjimlad:

Well, I said it's possible to construct one because I don't know if one actually exists. I wouldn't be all that surprised if someone has invented a game like that at some point though.

(And no fair counting Calvinball or Mornington Crescent. Infinite whimsical variations cannot be measured when we're not even using the same number system as the players.)

Ah, but today is opposite day, which means that we can only count Calvinball and Mornington Crescent.