It's a question a friend of mine brought up and I found intriguing. Let's say you have the records of a game from a certain move to the end, using standard notation (i.e. Qf6).
Either assuming random play or strong play (which is really hard to define), how many more moves on average would you need to restore the current position?
I don't really know how to approach this question, but it seems to involve retrograde analysis. The factors I could come up with are these.
- Knowing where a piece moved to tells you it's possible locations.
- Knowing where a piece moves tells you about empty squares (on the piece's way). This of course depends on it's original location.
- Checks give you information about both the location of the king and empty squares around it
- Exchanges give you a lot of info, both about the exact position of a piece and about the squares around it.
- Castlings give you info about 5-6 pieces.
Another variant to this question is where the starting square of a piece is also given in the notation, i.e. Nd5-e3 instead of Ne3. This is not the most popular notation but it's still usable. How much would it affect the result?
P.S. Why does CSE have no "soft question" tag?