Probabilities: a 0.27% chance happened

A great deal will be written in the coming days and weeks about the Candidates Tournament which ended yesterday. I fully agree with many of the comments made yesterday, that it was truly one of the most memorable events in modern chess history.

For sheer drama, it couldn't have been surpassed.

And if you had said at the start of the final round, on 1st April, what the results of the two leading games would be that evening, it would be regarded as a poor April Fool’s prank.

Chessbase gave various statistical analyses during the tournament, particularly the last few days. Before Carlsen's loss to Ivanchuk, he was 87% to win; after that loss, Kramnik was 65% to win, before Magnus equalised by beating Radjabov in round 13. So before the last round, the odds were:

I didn't check these figures, knowing (giving their source) they would be right, but did sense check Kramnik's chance of winning: 24.1% of him winning multiplied by Carlsen's chances of drawing or losing, plus 63.8% chance of him winning, times Carlsen's remote (2.2%) chance of losing.

I also noted the disparity of Carlsen's winning chances compared with Vladimir's, which must be a combination of Carlsen being white, and also the specific pairings: and similarly for their chances of loss.

Lightning struck both chessboards yesterday: both lose, a 0.27% chance. A bookmaker would have given 372:1 odds on this, but it happened.

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