Here are three examples.
(1) On this first card, the bisected stamp does contribute the necessary 5 kopecks to make up the 10 kopeck postcard rate of 1 June 1931. The card was posted at ALEXANDROV VOKSAL 1 8 31 and arrived at BERDYANSK 3 8 31. There is a long family message in German on the back but at the end the sender writes, " Diese Karte bitte züruck" - Please send this card back (and underlined). So the sender knew that the card was philatelically interesting and maybe was responsible for the bisect. However, when this card was illustrated in The Post Rider in November 1998, Andrew Cronin commented that another bisect is known from the same region [ Added: See now below]. If the sender is not the same person, then the bisect may be non-philatelic but recognised by the sender as philatelically important. The fact that the post office clerk has cancelled the bisect carelessly does suggest that the clerk did not think of this card as philatelic. And another things I have just noticed: the pencil used for the "Please send this card back" is not the same pencil as was used to write the long message! The sender added it later ... So is this card worth 10 € or 1000 € ? Comments?