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Hugh MacGrillen vs Edward W Formanek
London II (1973)
Benko Gambit: Accepted. Fully Accepted Variation (A58)  ·  1/2-1/2
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Kibitzer's Corner
Oct-20-05
Premium Chessgames Member
  Sneaky: Look at the position exactly after 49.Rb7:


click for larger view

Now look at the position in Kasparov vs Karpov, 1984 right after 51...Rb2


click for larger view

Yes, it's the exact same position, with colors reversed. The players were different, the openings were very different, the middlegames were different, but in the end the same position was reached.

What are the odds of this happening by chance? Robert James Fischer says "billions to one" but I think that might be an overstatement. Nobody has a chess database with a billion games, but if somebody ever does, I imagine this sort of thing might be witnessed quite a bit.

Nevertheless, it certainly is a bizarre coincidence if you want to attribute it to pure chance. Frankly I've never heard of this kind of transposition occuring outside of extremely basic endings that include only 3 or 4 pieces. Here there are TEN pieces on the board!

For those unfamiliar, Fischer's long standing allegation is that Kasparov and Karpov staged their world championship matches, simply playing memorized moves. He believes that Soviet chess analysis uncovered a beautiful win for White in this game, so then a game was contrived which employed openings typical of Karpov and Kasparov, the goal being to reach the very same ending. Maybe they thought by flipping the colors nobody would notice? In any case, the stage was then set for Karpov to demonstrate this analysis to the world, as if he was some kind of super chess genius coming up with it on the spot, but in reality it was prearranged down to the last detail.

This could be the "smoking gun" for Fischer's argument that the Kasparov-Karpov match was prearranged, if it is indeed true that the odds of this ending arising more than once is so vastly unlikely. Here's a relevant question: are there any other examples in chess literature where an identical endgame is spotted in two different games, containing 10 or more pieces?

Food for thought.

Oct-21-05  TIMER: <Sneaky> There are four identical such positions, as you could reflect through the centre line too:


click for larger view


click for larger view

Oct-21-05  TIMER: If you use fritz to find a position you set up, it ignores colour and find all games reaching the same position up to symmetry.

If there are no pawns, you can have 8 such identical positions up to symmetry.

Oct-21-05  TIMER: <sneaky> I think the odds would be somewhat less than 1 in a million, but more than 1 in a billion for two games reaching the same (up to symmetry)10 piece endgames. But hard to guess more precisely.
Oct-21-05
Premium Chessgames Member
  Sneaky: For discussion purposes, let's call two games "twins" if they share the same 10-piece endgame.

Is the probability that you describe the odds of two randomly chosen games to be twins?

And what do you suppose the odds are that any one game has a "twin" somewhere in the body of recorded chess games?

I guess the real question is this: out of one million games, how many pairs of twins should we expect to find, on the average? I estimate that we'd find only a handful, and that one of them should crop up in such an important and celebrated game is quite a coincidence indeed. But I could be wrong, maybe it happens all the time and I just never realized it.

Oct-21-05  thomaspaine: Very nice post <Sneaky>.
Oct-21-05  Stevens: <sneaky> this is very interesting, i knew of Fischers allegations but wasn't aware that he referenced specific games.

One note though, it's slightly misleading to label these as 10 piece endgames, as more commonly endgames are referenced by only the number of pieces, not including pawns.

Oct-21-05  AdrianP: <Sneaky> Excellent post, and very thought provoking. But I doubt it's such an enormous statistical anomaly. The odds of two randomly chosen games being "twins" are likely to be huge, but in the position under discussion you've got R+3ps against R+3ps (presumably a very common ending) with a pawn structure which must be very common - i.e. h7, g6, f5; h3 f2; it's also not difficult to imagine how the king gets trapped in the corner. So the coincidence is striking, but the probablilities should take into account "typical features" of the position.

It would also be quite an enterprise, I'd imagine, to concoct a game which stood up to serious analysis to arrive at this specific position.

Was it Fischer himself who spotted the double? If so, quite a testament to his chess knowledge.

Oct-21-05
Premium Chessgames Member
  keypusher: I agree with <AdrianP> (including the part about your post being excellent and thought-provoking, <Sneaky>). I think these correspondences, though not something that happens <all the time>, are not so rare. Here's a concrete example:


click for larger view

According to Dvoretsky's Endgame Manual, p. 181, this exact position occurred in Stean-Hartston, British ch. 1972, Ionov-Karasev, Leningrad 1983 and Matveeva-Rappoport, Baku 1983. I doubt Dvoretsky carried out an exhaustive search, either.

Kasparov points out a bizarre coincidence in OMGP I, pp. 188-189. First, from Alekhine-Yates, Hamburg 1910:


click for larger view

Here Yates played 19...Bxg5?, and lost. The exact same position, except that the rook on QR1 was at QB1, occurred with colors reversed(!) in Dus-Chotmirsky-Rubinstein, Lodz 1907. D-C elected to remain a pawn down with Qb3, and eventually lost.

Also, as long as we're indulging Fischer's fantasies here, do you really think the Soviets would pick a game featuring a well-known American player to copy from? There were scores of obscure competitions in the USSR every year they could have mined for neat endgame combinations.

<Was it Fischer himself who spotted the double? If so, quite a testament to his chess knowledge.>

A testament to the waste of an extraordinary mind, I am afraid.

Oct-21-05  TIMER: <sneaky> Yes, the odds of two randomly chosen games to be twins I would think to be less than 1 in a million, I used my find position function on Fritz 7 which only has about 358000 positions, and keep not getting twins (but only tried five different games), which suggest much less likely than 1 in 358000. If it were 1 in a million, the expectation would be .358*5= 1.79 twins found by that method. So too small a sample, but backs my belief that less than 1 in a million.

If it were 1 in 100 billion, would you expect to find a twin in a million games?

Answer: Yes, 92% chance! The expectation would be multiplied from 0.99999=1- 0.00001=million/100billion for first game not having a pair, ... 0.999995=1-0.000005=500thousand/100billion for 500thousandth game not having a pair,... 0.99999999999 the 999999th game not having a pair, all multiplied together, making << 0.9999995^500000= ~0.08.

If it were 1 in 10 billion, it becomes about (10^11-1)/(10^11) that you have a twin in a random selection of a million games!

So Fischer may be right, it could be one in billions, but then would still could occur numerous times in a random sample of a million!

Oct-21-05  TIMER: Above I was inaccurate in my method. There are millionC2 ~5*10^11 different pairs, so for each one of them not to have a common 10 piece endgame, so you would need odds less than 1 in 1000billion=million^2 to have expectation of less than 0.5, when it becomes improbable.

For 1 in 100billion about 1-(.99999999999)^(1000000C2)= 0.993, much more likely than what I said to find a pair.

Oct-21-05  Stevens: The way to disprove Fischers theory of course is to find a twin featuring one of his own games!
Oct-21-05
Premium Chessgames Member
  Benzol: A strange phenomina these double games

E R Lundin vs Smyslov, 1946

Chigorin vs Rubinstein, 1906

These two games have a thematic position though the colours are reversed.

Oct-21-05
Premium Chessgames Member
  keypusher: Thanks, <Benzol>! An old Reinfeld or Chernev book introduced these two games with something like: Modern masters claim they would come up with the same combinations as the old-time masters if they only got the chance. Here is an example from 'real life.' But I don't have the book anymore, and I had forgotten which games were featured.
Oct-21-05  Chesschatology: Superb posts everyone, especially <sneaky>. Fascinating.
Oct-21-05  hintza: Interesting discussion, I agree.
Oct-22-05  thomaspaine: <Sneaky> One question I have is that is the exact position crucial for the ensuing moves? If, supposing it is as Fischer alleges, then its rather stupid of Russians/Kasparov/Karpov to pick the EXACT position to go to. Certainly it would make things murkier if they changed the position by a pawn up or down, etc. etc. WITHOUT changing the essential elements of the ensueing endgame.
Oct-22-05  ughaibu: This whole theory of Fischer's is utterly daft. There's an entire Soviet conspiracy (why? why did these pre-arranged games start when Fischer retired?) with hundreds of master+ level players available to analyse and create games for use in these title matches yet Fischer claims they use a kown game and that the analysis is Karpov's. Marnoff Mirloney maybe, but I'll be surprised if Sneaky really entertains the possibility of this nonsense having any basis.
Oct-22-05  sharpnova: what exactly do we mean by twins? do just the same pieces need to be on the board or the same exact position?

like.. are all KQRNB vs. KQRRP games twins? or only those that are the exact same position

Sep-21-15
Premium Chessgames Member
  thegoodanarchist: <For those unfamiliar, Fischer's long standing allegation is that Kasparov and Karpov staged their world championship matches, simply playing memorized moves. He believes that Soviet chess analysis uncovered a beautiful win for White in this game, so then a game was contrived which employed openings typical of Karpov and Kasparov, the goal being to reach the very same ending. Maybe they thought by flipping the colors nobody would notice? In any case, the stage was then set for Karpov to demonstrate this analysis to the world, as if he was some kind of super chess genius coming up with it on the spot, but in reality it was prearranged down to the last detail.>

Preposterous.

Everyone has heard of opening preparation. A grandmaster and his team work on opening lines, trying to find improvements. And they do find them, all the time, and not just world champions.

Likewise they study thematic middlegames, and try to find new plans for thematic middlegames that arise from all the openings.

So of course when it comes to endgames, you don't have to be an elite player to study games between strong players, and play over the endgames looking for improvements.

Conspiracy? Memorized moves? Pre-arranged outcomes? Or just hard work by driven, competitive chess superstar?

Of course it was common knowledge that Soviet players would make easy draws against each other in international competition, but that was done to save their best efforts against the Western players, so that Soviets could win the top honors in tournaments.

Once the World Championship was to be decided between 2 Soviets, then what is the point of such conspiracy? It would be pointless.

The allegation by Fischer is that these guys memorized moves and outcomes for money. But once they get to the WCC, the purse is <already> theirs to split.

No, this is just a baseless conspiracy theory created by a poor soul suffering from mental illness.

Sep-21-15  Petrosianic: There was method to the madness. Fischer couldn't bear to think of the world championship going on without him, so he convinced himself that it wasn't (the games weren't real games). He made the same claim about all the Karpov-Korchnoi games too.
Sep-22-15
Premium Chessgames Member
  thegoodanarchist: <Petrosianic: ... Fischer ... made the same claim about all the Karpov-Korchnoi games too.>

Well, I have not seen that claim discussed here on CG.com. Can you provide a link to that discussion, or if the claim is made elsewhere, a link to where I can read about it?

(If you have that readily available.)

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