How common is cheating OTB at top levels?

With the curent drama with Hans, and yesterdays announcement "Norwegian Chess Federation President Resigns After Admitting To Cheating" I wonder how common cheating is at the top levels? 

With modern engines this is a reletively recent possibility - can't imagine that in Alekhine's era even the most obsessed power hungry chess player contemplated having an opening book hidden about their person to cheat with.

I don't think it was very common on Alekhine's era, I can't picture him smuggling a chess book or something.

And I think there are more cheaters out there, and when technology advances, they'll be discovered.

There is no evidence Niemann cheat over the board against Carlsen.  There is only the report from chess.com that claims Niemann likely cheated in some online games (based on statistical analysis).

For over the board games, players are often searched, watched during the game and monitoring equipment in place.  It is more difficult to cheat over the board compared to online.

https://en.wikipedia.org/wiki/Cheating_in_chess

Exactly. No evidence, just Carlson making a dramatic gesture of withdrawing from the competition because he feared Niemann might cheat. It just shows how easy it is to ruin someone’s reputation in chess.

I am sure that it has always happened. Not with engines of course but just a whispered move suggestion  between team mates in a crowd tournament hall and in a language that the opponent would not understand.

@3
It is essential to delay the broadcast of the games e.g. by 15 minutes and to also check the spectators for electronic devices. Also the spectators should be able to see the players, but the players should not be able to see the spectators.

@5
Yes, Fischer complained about the 1962 Curaçao Candidates' Tournament:
"If I was playing a Russian opponent, the other Russians watched my games, and commented on my moves in my hearing."
https://vindication-of-bobby-fischer.co/history-rodriguez/si/index.html 

It is also known that in round robins like 1953 Soviet players were pressed to lose games on purpose against each other.

@8
In Moscow 1936:

Stalin: “How do you like my tournament?”
Capablanca: “It’s terrible; your players are cheating.”
Stalin: “What do you mean?”
Capablanca: “When they play against each other, the Soviets make quick draws and they get to rest. When they play against me, they fight on and on just to make me tired.”
Capablanca: “Your Soviet players are cheating, losing the games on purpose to my rival, Botvinnik, in order to increase his points on the score.”
https://www.chesshistory.com/winter/extra/capablancaolga.html 

Fischer did understand Russian quite well, which is something that many of the Russians did not realise 

When you cheat, you only cheat yourself, same applies in golf!

If you're going to make the claim that cheating over the bord is extremely common you need to cite some examples and numbers.  What percentage of GM games played over the board involve cheating?

Chess.com estimates that fewer then 0.02% of players cheat online.  I haven't found an estimate for OTB, however, this will be even lower because the likelihood of getting caught is even higher.

Its going to be.

Why not? They(pop culture) has always said what ever makes you happy,

We are in a time of increased corruption...and people using PR to confuse/delay

Enjoy your increased agnostics/hedonism.

They also catch only 25% of those who cheat against me, so their estimate must be rejected. Nonetheless, OTB cheating is rare.

Topalov was a known cheater.

He reportedly cheated at the San Luis Candidates tournament (held in Argentina in 2005) which was to pick a challenger for Kramnik in the 2006 World Championship match, held in Russia, during which Topalov was accused of cheating again (despite claiming that Kramnik was cheating due to his frequent restroom visits - which was total defamation of character by the Topalov team since Kramnik had a genuine medical condition). Even still, Topalov was "unlucky" to lose in rapid tiebreaks (i.e. easier to cheat in classical?)

There is a reason Topalov was showing a "different level" in the period of 2004-2006, and why he is not regarded by serious chess fans (or professionals) as a legitimate champion / challenger.

2005 CANDIDATES TOURNAMENT:

(6 wins, 0 losses, 8 draws)

https://www.chessgames.com/perl/chess.pl?tid=47798

2006 WORLD CHAMPIONSHIP MATCH:

https://www.chessgames.com/perl/chess.pl?tid=52037

(3 wins, 3 losses, 5 draws... 1 win, 2 losses in rapid tiebreaks)