[pzhon]

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the Clarkmeister Theorem doesn't require you have none of the suit nor that you fold to a raise

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I didn't say "Clarkmeister theorem" (which is misnamed anyway). I was referring to the discussion in the archives by Clarkmeister, Ulysses/El Diablo, and others. The question is not how to play if you have the nuts. The common problem is how to deal with a good hand like flopped TPTK when the river puts 4 to a flush on the board. When someone talks about whether to Clarkmeister, they almost always mean to bet/fold.

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I believe the basis for the profitability of this move is that:
a) few hands can raise you
b) some hands that are worse will call you, but wouldn't bet if you checked
c) some hands that are better will fold

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Usually, the point is not to get better hands to fold. You are trying to get value from weaker hands that will call if you bet but would check behind. On the other hand, if you check, many better hands will bet and you would call anyway. Against most opponents, you get enough information from a raise that you can safely fold if you don't have a card of that suit.

In position, you need to win most of the time when you are called in order to make a river value bet (ignoring raises). This is not true when you are out of position if checking will allow stronger hands to bet for value. It can be right to make a bet for value even if you are an underdog when you are called because the alternative of checking is so bad. Clarkmeister pointed out that this situation is almost always an example.