Best female chess player

"you often get very different results depending on which number you choose"

• I will not discuss CPU or cars, only chess rating.
  The chess rating was invented to compare chess strength of players for the purpose of assigning boards in team competitions or guide pairings in Swiss tournaments or awarding titles etc.
  The core is that the expected outcome of a game between two players is a function of the difference of their ratings.
  Hence when two players have an expected outcome of 50%, then their ratings must be equal.
  If they play and the result differs from 50% then their ratings are adjusted accordingly in that sense.
  All present players are connected to all past players by strings of game results.
  I myself for example have Morphy number 4. https://en.wikipedia.org/wiki/Morphy_number

"Does it mean they would be equal if I were somehow able to let them play against each other? "

• Yes, if you could time travel the young and strong Kasparov 1985 to august 2025 and give him 3 months of time travel jet lag recovery, then he would play on par with Carlsen.

@mkubecek said in #20:

... In August 1985, Garri Kasparov's rating was 2831. In August 2025, Magnus Carlsen's is 2839. Does it mean they would be equal if I were somehow able to let them play against each other? I don't think so.
Perhaps, someday, refinements in reanimation technology will make it possible for a match between 1985-Kasparov and 2025-Carlsen. How will the results be influenced by the amount of extra study time allowed for 1985-Kasparov?
@tpr said in #21:
... All present players are connected to all past players by strings of game results.
And the accuracy verification comes from where?
@tpr said in #22:
... if you could time travel the young and strong Kasparov 1985 to august 2025 and give him 3 months of time travel jet lag recovery, then he would play on par with Carlsen.
Perhaps science as a whole could progress more quickly and cheaply by relying on tpr-assertions.

Carlsen would beat young Kasparov any day because of superior opening prep

@tpr said in #21:

The core is that the expected outcome of a game between two players is a function of the difference of their ratings.
...within the same rating pool. And even that only to some extent and with some additional assumptions. Which, sadly, are not satisfied for FIDE Elo ratings. If I'm going to face a 65 year old Czech guy rated 1800 FIDE, an 18 year old Czech guy rated 1800 FIDE and an 16 year old Indian guy rated 1800 FIDE, It's quite likely it will be three very different experiences and my chances will be also very different.

All present players are connected to all past players by strings of game results.
I myself for example have Morphy number 4. en.wikipedia.org/wiki/Morphy_number
Even within the current FIDE player pool there are "silos" resulting in persistent disbalances between what should be expected based on the ratings and actual player strengths. The farther to the history you go, the worse it will be due to less "connectivity". And comparing ratings between different times is going to work even worse.

"If I'm going to face a 65 year old Czech guy rated 1800 FIDE, an 18 year old Czech guy rated 1800 FIDE and an 16 year old Indian guy rated 1800 FIDE, It's quite likely it will be three very different experiences and my chances will be also very different." * True, but once you play the rating will adjust. You may win from the 65 year old Czech when you gain and he loses rating, you may lose from the 16 year old Indian when he wins and you lose rating. The rating system adjusts itself provided there is enough interaction mainly in international tournaments with mixed ages.

"The farther to the history you go, the worse it will be due to less "connectivity"." * Yes, but there is more connectivity than you would think, e.g. I connect to Morphy in 4 steps, i.e. games.

"And comparing ratings between different times is going to work even worse." * There is some error margin, but to return to the original question it is fair to say based on the data Polgar > Gaprindashvili > Menchik.

@tpr said in #26:

The rating system adjusts itself provided there is enough interaction mainly in international tournaments with mixed ages.
That's exactly the problem. Practical experience shows that even in today's chess, there is not enough interaction to make the ratings universal enough. And it definitely wasn't better in the older days.

If not Judit, who? Here is a woman who proved she could play on a level footing among the world's best men. Among the world champions, her victims include Karpov, Kasparov, Anand, Topalov.
Vera Menchik is debatable - clearly the best female in her time but unfulfilled promise as she was killed by a bomb during WW II while Nona Gaprindashvili mainly played in female events. I would rate Hou Yifan as stronger than either of these two but not at the same level as Judit.

"Practical experience shows that even in today's chess, there is not enough interaction to make the ratings universal enough. "

• There is not enough interaction among the juniors and among the lower ratings.
  At the top it is and was OK.
  So for questions about who of the top players is or was the strongest, it is reliable.

@tpr said in #26:

... once you play the rating will adjust. You may win from the 65 year old Czech when you gain and he loses rating, you may lose from the 16 year old Indian when he wins and you lose rating. The rating system adjusts itself provided there is enough interaction mainly in international tournaments with mixed ages. ...
But how much interaction has there been between 1985 players and 2025 players? Perhaps, there have been secret time-traveling players, but, as I understand it, the historian jury is still out on that idea.
@tpr said in #26:
... there is more connectivity than you would think, e.g. I connect to Morphy in 4 steps, i.e. games. ...
Is there reason to believe that there is enough connectivity to tell us how Morphy would have done in 1924 closed games, hypermodern games, etc.?
"... It is not so long ago that a game in which neither player [advanced his e-pawn two squares] was a rarity. Now such games, at least in the contests of masters, have become the rule.
Many causes have contributed thereto. The other openings are already well known, and to try to introduce winning innovations into them has become a risky business. ..." - Lasker (~1925)
@tpr said in #26:
... There is some error margin, but to return to the original question it is fair to say based on the data Polgar > Gaprindashvili > Menchik.
On the other hand, 1985-Kasparov vs 2025-Carlsen ...