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It seems to me that the article overlooks one glaringly obvious issue: that the two blunders may not be independent events.

In this case, it seems quite likely that the second player's blunder was made much more likely by the fact that the first player had just blundered. To be more specific, white moved the king which appeared (at first glance) to prevent black from using a check threat to attack white's rook. The blunder was in not realizing that the check threat could still be used to attack white's rook, albeit in a more complicated fashion.

Black responded to this with another "blunder" -- failing to attack the rook and moving elsewhere instead. But this blunder was NOT independent of the first -- it is quite likely (I believe) that black saw the move and assumed white had successfully prevented the attack on the rook. He assumed that such a top-level player would never make such a mistake, and that caused him to not look closely enough at it. The first blunder helped cause the second.

(Thanks to stolio for linking to the game analysis I used here.)

One could test this hypothesis of mine using the same data set. Instead of looking just at single errors, look at error pairs (one error occurring in the move following another error). If the probability of a blunder is significantly higher on the move immediately after a blunder than it is at any other time, then my hypothesis (that the events are not independent, but correlated) is supported.




I was expecting the article to focus on this and dis/prove hypothesis of double blunder.

Most top players would comment (as Anand and Carlsen did after the game) that double blunders are relatively common in top level play.

Here is one famous case: http://www.chess.com/article/view/the-amazing-chess-illusion

In my personal experience this has been common too, when I mix playing against 2500 players and 1900 players in blitz (I am 2350fide), it is relatively easy to skip over simple hanging pieces for a move or two.

In a regular tournament game it has happened a few times as well (one player commiting a gross blunder and other not noticing).

The big question whether it is out of ordinary statistically speaking.


This is a valid point. We're going to be publishing some data in a few days that will have everything you need to test this hypothesis.


"He assumed that such a top-level player would never make such a mistake"

But if top-level players make such mistakes in about 1% of their moves, that assumption is utterly wrong (1% per move translates to (ballpark) once in every five games that an similarly ranked opponent essentially gives you victory, if you yourself manage not to blunder), so one could call making the assumption a blunder.


I agree that they are probably not independent, but I have a different idea as to why. From my personal experience of playing many competitive games, when your opponent makes an obvious mistake you might get too excited or carried away about capitalizing on the mistake and make a subpar move. Consider a situation like this:

"Wow he just left his queen right open! I can't believe he did that! I'll take it with my rook."

Rook takes queen, rook is wide open, could have taken queen with some other piece and had it protected.

It's possible this doesn't apply to chess as much but in more fast paced games if you see an opening, you take it, because even if you don't capitalize 100% on it you're better off than not doing anything about the blunder.




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