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.
How do you decide which way to finesse for an ace?
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?