On 09 Oct 2007 11:21:14 +0100 (BST)
David Richerby wrote:

foot wrote:
f8-e6-g5-e4. But is there a shorter route?

Obviously not. e4 and g6 are both white squares so it must take an
even number of moves to get between them. There's clearly no
two-move route so four must be the shortest.

How do you know there's no two-move route?

Because any knight move from g6 either puts the knight on a square
adjacent to e4 (f4 or e5) or on a square a long way from e4.

So, when you say "any knight move", you're pretty much admitting that
you checked to see where every knight move landed. You're essentially
mentally checking to see if there's a two-move route.

From what you describe, it sounds like you thought something like:

"g6t o e7, and it's too far from e7 to make it to e4 in one move.
then, g6 to h4, and it's too far from h4 to make it to e4 in one move.
then, g6 to f8, and it's too far from f8 to make it to e4 in one move.
then, g6 to e5, and it's adjacent to e4, so the knight can't make it
from e5 to e4 in one move. then, g6 to f4, which is adjacent to e4, so
the knight can't make it from f4 to e4 in one move."

Once again, this is exactly the kind of trial and error approach the
book's method is supposed to improve upon.

This really isn't any harder than `How do you know there isn't a
one-move route for a bishop from g2 to d3?'

I think it is harder. Bishops move in straight lines. Seeing that a
given square is on or off the straight line path leading from a bishop
is a lot easier than the process you seem to have used.

By the way, I'm not claiming that the book's method makes recognizing
the minimum number of moves to every single possible destination square
the knight can get to as easily recognizable as a bishop move, but
there are some squares which studying the book will let you recognize
just as easily, and the others you can figure out without the trial and
error of the sort you seem to be using.

You probably tried a number of routes to move your knight from g6 to
e4 and found it couldn't get there in two moves.

No. It's instantly obvious to me that there's no two-move route. And
I'm not a strong player; I'm just familiar with how the pieces move.

Well, "obvious" doesn't mean you didn't try every possible single
move route, and then see if a second move can get you to your
destination square.... which is what you apparently did. It may be
"obvious", but it's not very efficient, and it's easy to make a mistake
when you're trying all these possible moves, or at least wind up
wondering if you really tried them all or might need to go back and
re-try them, just to be sure you got it right... which means more time,
and more opportunity for error.

But I'd bet most people would take some time to figure these out
with any amount of certainty.

Maybe so. But here's how to do it and get it right in seconds almost
every time.

Important knowledge
-------------------
1) Moving between two squares of the same colour must take an even
number of moves.
2) Moving between differently coloured squares must take an odd number
of moves.

Special cases
-------------
3) Moving to a diagonally adjacent square takes two moves, unless the
source or destination is a corner, in which case it takes four.
4) Moving to a horizontally or vertically adjacent square always takes
three moves.
5) Moving to the opposite corner of a 3x3 square always takes four
moves.

Very good. Up to this point, the technique you describe is similar to
what's in the book. However, you still haven't given any rules for
determining if a given square is 3 or 5 moves away (except when the
destination square is a horizontally or vertically adjacent square.

Technique
---------
6) To find the fastest route, move towards the destination in as
straight a line as possible and then use the special cases 3-5 to
determine the answer once you get close enough.

Ok. Well, now you're back to the trial and error method. There is a
better way than this, and the book teaches it.

And if you're comparing how long it would take to get to more than
one or two squares then the time spent on these types of
calculations can really add up...

They really don't. They're so fast that the difference between a
second or two (getting to one square) and two or three seconds
(getting to two squares) is negligible. Why would I ever want to know
how long it takes a knight to get to more than two squares?

Your method will find that moving to a certain square will take a
minimum of 5 moves in a second or two? I don't think so.

And the technique doesn't work when there are other pieces on the
board. Which is to say, all the time.

Actually, it does work even when there are other pieces on the
board, as what the technique tells you is the **minimum** number of
moves that a knight will take to get to any given square.

And so does my technique. Much faster. And actually looking for the
routes will automatically show you which ones are or are not possible.

Try using your method to on a square that's a minimum of 5 moves away,
like g1 to a6 (the example I meant to give in my last message, but said
"h6" for some inexplicable reason). With your method, it sounds like
there will be trial and error involved, and you will be left guessing
as to whether there is actually a shorter route that you might be
missing.

With the method taught in the book there is no guessing or trial and
error. It's just a matter of applying a rule sort of like your
"Moving to the opposite corner of a 3x3 square always takes four
moves," only the rule will apply for squares which are a minimum of 5
moves away.

2, 3, 4, and 5 move paths are much more common, and happen to be the
ones where this method becomes most useful.

If you have difficulty working out that it takes two moves to get a
knight between two squares, I really recommend you spend more time
playing chess and familiarizing yourself with the pieces.

Well, it's not a matter of difficulty. It's a matter of whether you're
figuring out the minimum number of moves it will take a knight to get
to a given square through trial and error and guessing, or whether
you're doing it by applying rules and getting answers you can feel
confident in, and doing it faster than the parts of your method that
involve trial and error.

I'll admit to being utterly flabbergasted as to why somebody would
write an eighty-page book explaining how to do something this simple.

Well, I found the book to be extremely useful, and I bet most other
chess players will too. You seem to already know quite a bit more
about moving knights than the average chess player (certainly much more
than I did before I bought the book), so it sounds like the book may
not be the best investment for you (though even for you, I think
the book could teach you some better methods than the ones you're using,
for certain squares on the board, such as the squares 3 and 5 moves
away).