Just to get the ball rolling, I have found two players with 4: Botvinnik and Topalov:
- For pre-WWII
- The only players to defeat Euwe as champion are: Bogoljubov, Alekhine, Lasker, Liliental, Gauffin. It would be very hard to get 4 pre-war without beating Euwe.
- The only players to beat Capablanca as champion are: Reti, Ilyin-Zhenevsky, Verlinsky, Alekhine.
- Alekhine only has those 2 (his only win against Lasker was in 1934).
- Lasker has 3: he beat Steinitz, and also Alekhine (1934) and Euwe (1936), but never beat Capablanca when Capaplanca was champion. I think he would be the only pre-WWII possibility for 4 or more.
- Botvinnik appears to have 4: Alekhine (AVRO 1938), Smyslov and Tal (WC matches) and a Petrosian game in 1964. (No wins against Euwe until 1948, only win against Spassky in 1966). That might be hard to beat, because of the limited chances to play Smyslov and Tal while they were champions.
- Botvinnik's losses as champion: Bronstein, Smyslov, Kopilov, Geller, Szily, Taimanov, Keres, Reshevsky, Dueckstein, Tal, Unzicker, Uhlmann, Petrosian
- Smylov's only other loss as champion was against Filip;
- Tal's only other loss as champion was in the 1960 Olympiad against Penrose.
- There are a few more for Petrosian 1963-69: Gligoric, Korchnoi, Geller, Botvinnik, Portisch, Boleslavsky, Larsen, Tal, Ivkov and a couple of unknowns
- Spassky's only losses 1969-1972 were against Larsen, Petrosian, Korchnoi and of course Fischer
- Fischer played no games as champion.
- Conclusion: I don't see how anyone can have 4 solely from the Botvinnik to Karpov era (1948-1985). Even with wins against Botvinnik and Karpov, I don't see anyone except Korchnoi and Larsen (both considered below) with wins against more than 1 of the (Smyslov, Tal, Petrosian, Spassky, Fischer).
- Keres: did not beat Euwe or Alekhine when they were champions, nor Smyslov or Tal (see above), nor Karpov; so even if he beat Botvinnik, Petrosian and Spassky that would be 3 at most.
- Reshevsky also did not beat Euwe or Alekhine when they were champions (beat Alekhine in 1936 and first beat Euwe in 1938).
- I can only find 3 for Korchnoi: Petrosian (1963, 1965), Spassky (1970), and of course the Karpov matches; he never beat the others while WC (he beat Botvinnik in 1960 while Tal was WC).
- Larsen has 3: Petrosian, Spassky, Karpov. He never beat Kasparov and never played Kramnik.
- I can only find 2 for Portisch: Petrosian and Karpov. He never beat Kasparov or Botvinnik.
- Since he is the only player I can find with wins over both Petrosian and Spassky, it's hard to think of anyone else who might have 4 in the 60s-2000 era.
- Perhaps there is someone strong enough from early 80s to late 00s to have beaten Karpov, Kasparov, Kramnik and Anand?
- Beliavsky only has 1 (Karpov). He never beat Kasparov, Kramnik or Anand while they were WC.
- Topalov has 4: Kasparov (1994 Olympiad), Kramnik and Anand (WC matches), and he beat Carlsen in 2015.
- Among similar era players to Topalov, I can't find wins for Ivanchuk, Gelfand, Kamsky, Leko, Polgar, Short, Adams, Svidler against Carlsen post-2013, so they have no more than 3. I have gone through all Kasparov's losses pre-2001 and I don't think there could be anyone else who could have beaten all 4 of Kasparov, Kramnik, Anand and Carlsen while they were champions.
Adpete (talk) 01:38, 17 January 2020 (UTC), updated Adpete (talk) 05:36, 7 October 2022 (UTC)