02 Feb '17 21:503 edits

At a major open tournament in Gibraltar, Hou Yifan, the women's world champion,

intentionally lost her last round game, resigning after only five moves.

Evidently, she did it in order to protest perceived sexist bias in her pairings.

Hou Yifan later apologized.

Here seems to be the basis of Hou Yifan's complaint about sexist bias:

Women were only a small minority of the field in this open tournament.

But Hou Yifan was paired with seven women in the first nine rounds.

This seems extremely improbable if the pairings were done by a gender-blind computer.

So Hou Yifan suspects that the tournament officials intervened to keep

pairing her with as many female opponents as possible. Is that sexist?

Here's a statistical analysis by someone at the ChessBase website:

"I can give you a statistical analysis. Among the 83 players who had a

score similar to Hou Yifan (ie. pool of potential opponents), 17 (20.4% )

were female. However, this doesn't mean she has a 20.4% of being

paired against a woman in any given round. That's only true initially.

Once she's paired against a few women, these women are removed

from the pool of potential opponents, and the proportion of women

among potential opponents becomes even smaller. For example, after

she was paired against women 6 times, the probability for it to happen

a seventh time was only 14.3%.

With all that in mind - if the pairings are fair - the probability to be

paired against a woman seven or more times out of ten is: <drumroll>

(17/83 x 16/82 x 15/81 x 14/80 x 13/79 x 12/78 x 11/77)*10!/(7!*3!)

Which is 0.056% (1-in-1,779)

Now, we go to Bayesian probabilities and ask ourselves, what is more

likely: that this sequence of pairings was created as a part of honest

pairings (which, as we know is 1-in-1779) or that the organizers

deliberately skewed the pairings? Each can answer to himself. "

Until this incident, Hou Yfian had avoided nearly all controversy, apart

from her decision to boycott FIDE's upcoming 2017 world championship

'knock-out' tournament in Iran to protest sexist bias in the format.

Hou Yifan pointed out that FIDE has long ago rejected holding 'knock-out'

tournaments to determine the open (men's) world champion, and she

believes that the women's world championship deserves the same format.

By the way, I feel certain that Hou Yifan made her decision to protest on her own,

not in obedience to any instructions from China's chess authorities. Contrary to a

Western stereotype, the top Chinese players today are free to run their own careers.

At the same tournament, Ju Wenjun (the world's second highest rated woman) defeated

Hou Yifan in their game and was among the top players going into the last round.

Hou Yifan might have known that her form of protest (throwing a game)

would result in many people accusing her of poor sportsmanship.

Did Hou Yifan do the right thing in protesting perceived sexism?

intentionally lost her last round game, resigning after only five moves.

Evidently, she did it in order to protest perceived sexist bias in her pairings.

Hou Yifan later apologized.

Here seems to be the basis of Hou Yifan's complaint about sexist bias:

Women were only a small minority of the field in this open tournament.

But Hou Yifan was paired with seven women in the first nine rounds.

This seems extremely improbable if the pairings were done by a gender-blind computer.

So Hou Yifan suspects that the tournament officials intervened to keep

pairing her with as many female opponents as possible. Is that sexist?

Here's a statistical analysis by someone at the ChessBase website:

"I can give you a statistical analysis. Among the 83 players who had a

score similar to Hou Yifan (ie. pool of potential opponents), 17 (20.4% )

were female. However, this doesn't mean she has a 20.4% of being

paired against a woman in any given round. That's only true initially.

Once she's paired against a few women, these women are removed

from the pool of potential opponents, and the proportion of women

among potential opponents becomes even smaller. For example, after

she was paired against women 6 times, the probability for it to happen

a seventh time was only 14.3%.

With all that in mind - if the pairings are fair - the probability to be

paired against a woman seven or more times out of ten is: <drumroll>

(17/83 x 16/82 x 15/81 x 14/80 x 13/79 x 12/78 x 11/77)*10!/(7!*3!)

Which is 0.056% (1-in-1,779)

Now, we go to Bayesian probabilities and ask ourselves, what is more

likely: that this sequence of pairings was created as a part of honest

pairings (which, as we know is 1-in-1779) or that the organizers

deliberately skewed the pairings? Each can answer to himself. "

Until this incident, Hou Yfian had avoided nearly all controversy, apart

from her decision to boycott FIDE's upcoming 2017 world championship

'knock-out' tournament in Iran to protest sexist bias in the format.

Hou Yifan pointed out that FIDE has long ago rejected holding 'knock-out'

tournaments to determine the open (men's) world champion, and she

believes that the women's world championship deserves the same format.

By the way, I feel certain that Hou Yifan made her decision to protest on her own,

not in obedience to any instructions from China's chess authorities. Contrary to a

Western stereotype, the top Chinese players today are free to run their own careers.

At the same tournament, Ju Wenjun (the world's second highest rated woman) defeated

Hou Yifan in their game and was among the top players going into the last round.

Hou Yifan might have known that her form of protest (throwing a game)

would result in many people accusing her of poor sportsmanship.

Did Hou Yifan do the right thing in protesting perceived sexism?