When a Finesse occurs, it causes temporary information desynchronization.
For example, in the previous scenario, if Bob discarded instead of blind-played, Cathy would go on to think that she had the red 3. But she really doesn't have the red 3, which means that information is not synchronized throughout the team.
For this reason, blind-playing a card into a Finesse is very important - by doing so, it resynchronizes all of the information. So, if a player is Finessed, they should usually blind-play the card immediately, even if they have other important cards to play or some good clue to give.
We define the Finesse Position as the slot that a player's left-most unclued card is in. A player's Finesse Position can move around, and if it does, it is still possible to Finesse them.
In the example below:
Alice clues Cathy red, which touches two red cards on slot 1 and slot 2.
Cathy assumes that the slot 1 card is a red 1.
Next, Bob clues Donald blue, which touches a blue 2.
Now, it is Cathy's turn. Cathy knows that she must have the blue 1 and that Bob is trying to perform a Finesse.
Blind-playing the blue 1 is more important than playing the red 1.
Normally, Cathy's Finesse Position would be her left-most card. However, since Cathy's slot 1 and slot 2 card are already clued, her Finesse Position card has shifted down to her slot 3. Thus, Cathy must blind-play the blue 1 from slot 3.