Best female chess player

Who is the best female chess player of all time?

I'd say Judit Polgar she used to beat people like Kasparov in those days if currently then Id go with Ju Wenjun just coz of that Tata Steel performance

I don't think comparing female players from different epochs us possible in a meaningful way, just like with male players. Even comparing players who reached their top performance in the same years is often difficult, how do you want compare players who lived and played 100 years apart?

Well you can compare
http://www.chessmetrics.com/cm/CM2/PlayerProfile.asp?Params=199510SSSSS3S102713000000111000000000024610100
http://www.chessmetrics.com/cm/CM2/PlayerProfile.asp?Params=199510SSSSS3S041552000000111000000000009810100
http://www.chessmetrics.com/cm/CM2/PlayerProfile.asp?Params=199510SSSSS3S084775000000111000000000018810100

Judit Polgar of course!

FIDE has declared Judit as the best female player
https://www.fide.com/fide-100-awards-make-history/
No other female has played in the men's world championship or reached the top ten in rating.

she's not born yet. not the others are bad, but they won't be the best soon.

@tpr said in #4:

Well you can compare
You can compare numbers. But are those numbers really comparable? As often discussed, comparing ratings between different player pools is misleading at best. And here we are talking about player pools which are completely disjoint and separated by decades of time. (Maybe not completely disjoint in case of Nona Gaprindashvili vs Judith Polgár but still distinct enough to be effectively incomparable.)

"player pools which are completely disjoint and separated by decades of time"
The statistician Jeff Sonas took on the giant task of calculating elo ratings backwards in time based on all published game results.
That allows to compare Ju Wenjun, Judit Polgar, Nona Gaprindashvili, and Vera Menchik.

As far as I know, funding has not yet been approved for sufficient plutonium for experimental verification of elo-ratings-backwards-in-time conclusions. Maybe a future zombie apocalypse will provide a cheaper alternative opportunity for experiments. Possible problem: Would a Menchik-zombie be a 1929-Menchik or a 1944-Menchik?