I once read in a book about a "backward" finesse. You, declarer, have AJ9, and dummy has Kxx. Ordinarily, you would finesse twice from dummy toward AJ9. Except that your left hand opponent has indicated by a bid (or double) that he has the queen. If that's the case, you apparently finish "backwards" by leading the J, and covering with the K in dummy if the left hand opponent covers. Then you lead back an x to the A9 on the theory that right hand opponent is more likely to have the T. Why is that?
Another, apparently similar type of finesse is what I call a round trip finesse. You have K854 opposite QT32, and you're apparently finessing for the A, J, and maybe the 0.
So you finesse toward the QT32, then back toward K854.
A third kind of finesse is sometimes called a two way finesse. That is, you have ATxx in hand, dummy has KJxx, and you are finessing for the queen. By counting, or other means, you determine that West/East is short in the suit. Then you win the K/A, to drop a presumed singleton, and then finesse the other way for the queen.
All of these finesses differ from what I call "one way" finesses, low in one hand toward, say AQ, or AQT.
What are the rationale behind the two directional finesses? Is the two way finesse a special case of the "one way" finesse or more like the other two directional finesses. And is the reason for a two directional finesse the fact that opposing honors are more likely to be split than to be concentrated in either opposing hand?