strongest players to never becomes world champions!

Rubinstein and Nimzovich wanted to play Alekhine, but could not raise the money and Alekhine preferred Bobolyubov and Euwe.
Keres was Estonian and had to atone for playing in German tournaments during the Second World War.

@tpr I agree with Rubinstein first, Bronstein second and Keres third. Nimzovich was not world champion material. Some would add Korchnoi to the list, but in his top time I think Fischer still had a better chance to win against Karpov, but Korchnoi came pretty close.

#12
Korchnoi got his chance, played Karpov several times, and lost.

Nimzovich won Carlsbad 1929 with 15/22 before Capablanca, Spielmann, Rubinstein, Becker, Vidmar, Euwe, Bogolyubov.
He got no chance to play Alekhine as he could not raise the money.
Alekhine did not dare to play Nimzovich, Capablanca, or Rubinstein and played matches against Bogolyubov and Euwe instead.

My list would be Rubinstein, Pillsbury, Keres, Bronstein and the order would vary according to peak performance or sustained performance.

@tpr #13 en.wikipedia.org/wiki/Carlsbad_1929_chess_tournament Just half a point ahead of Capablanca in a single round robin tournament (where luck plays a greater role as one can have more black pieces against stronger players without a rematch to balance)

"Nimzowitsch expected to become challenger of the world champion and expressed his desire on his visiting cards. Unfortunately Alekhine crushed him in the San Remo 1930 chess tournament and Bled 1931 chess tournament."

IMO at this time Capablanca still deserved a rematch against Alekhine. Capablanca 1929 still much better player than Nimzowitsch. Some of the greatests matches in chess that never happened: Fischer x Karpov, Rubinstein x Capablanca and Keres x Botvinnik.

Cool

#14
Yes: highest ratings:
Pillsbury 2816
Korchnoi 2814
Bronstein 2792
Rubinstein 2789
Keres 2786
Nimzovich 2780

http://www.chessmetrics.com/cm/CM2/PlayerProfile.asp?Params=199510SSSSS3S093234000000111000000000020510100

#15
Yes, but Nimzovich also won some games against Alekhine
www.chessgames.com/perl/chessgame?gid=1007819

You have a point about Capablanca in the Carlsbad 1929 tournament.
For example he lost a piece by a blunder in the opening
www.chessgames.com/perl/chessgame?gid=1066901
Capablanca was already suffering from high blood pressure resulting from marital troubles.
Capablanca also agreed to some early draws.

# 17 http://www.chessmetrics.com/cm/CM2/SingleMonth.asp?Params=199510SSSSS3S093234192909111000000000020510100

#1 Alexander Alekhine 2796 36y11m (#6 all-time among players aged 36y11m)
#2 José Capablanca 2795 40y10m (#5 all-time among players aged 40y10m)
#3 Aron Nimzowitsch 2780 42y10m (#6 all-time among players aged 42y10m)

In september 2019 Capablanca still had a higher rating than Nimzowistch. So ratingwise Capablanca was a possible stronger contender for the title.

Don't read me wrong. Nimzowistch was a superb player, but I don't know if any time in his chess career he reached number 1 spot ratingwise.

See this reply, please: www.chessgames.com/perl/chessgame?gid=1007819&kpage=1#reply11

"Given that Alekhine's record against Nimzowitsch was only 5-3-9 at the time of Aron's incredible +10 =10 -1 result at Carlsbad 1929, I'd say he was justifiably "concerned". However, it appears that this was to be Nimzowitsch's zenith. He played only 82 games afterward, including losing his next four games against Alekhine."

#19
No, Nimzovich never was #1, he was #2 in the world from February to July 1913 see link #17

After Carlsbad 1929 Alekhine imposed bans on Nimzovich as well as on Capablanca: tournament organisers had to chose either World Champion Alekhine or Capablanca/Nimzovich.
Nimzovich was frustrated that he got no match against Alekhine and his health declined. He died in 1935.