Mr. Issac Kashdan
.br
Chess Editor
.br
c/o Los Angles Times
.br
Los Angeles, Calif.
.sp 3
Dear Mr. Kashdan:

We talked at the ACM computer conference
in San Diego in October.
At that time
you suggested that some computer
chess effort should be
directed toward solving certain
end games.
I believe you suggested that the Q-and-P vs Q
would be a good example.

Right now I am
working on David Levy's R-and-P vs R game.
At this time it is hard to tell if its
possible to get a complete solution,
but I do have partial results I'd like to
relate to you.

Ive completely solved all of the
sub-problems in the R&P vs R game.
This includes the elementary Q and R games
and the Q vs R game.

My only reference to end games is
Fine's "Basic Chess Endings".
(An August 1971 reprint to be exact.)
In there,
I've compared Fine's analysis to the
computer solutions of Figs 1, 2 and 597.
Before I start, I should note that
the computer solutions are based on the minimal
number of moves to mate.
In the Q vs R game, Fine seems to be
minimizing the number of moves to capture
the R.
This is not too important since usually
these goals coincide.

In Fine Fig 1,
the analysis is exactly correct.
Even more,
the position he refers to that
takes 10 moves to win
(WK at QR1; WK at QN2; BK at K3)
is unique.
It is the only position that requires 10
moves to win.

In Fig 2,
there are a few mistakes.
Fine claims that the given position
requires 16 moves with best play.
It only takes 15 since the second
move for white loses a tempo.
The move K-B2 should be R-K1 or K-N3.
For the same reason,
the maximum moves to win
with R+K vs K is 16 and not 17.
The position for this maximum
is not unique.
(There are 139 of them.)
.bp
.m0 0
.m1 0
.m2 0
.m3 0
.nf
(Position from Fine's "Basic
 Chess Endings" Fig. 597)

 1. k-n2	r-b5(a)
 2. k-b3	r-k5
 3. k-q3	r-q5+
 4. k-k3	r-q4
 5. q-r2+(b)	k-b4(c)
 6. q-b4+(d)	k-k3
 7. k-k4	r-q3(e)
 8. q-b5+(f)	k-k2
 9. k-k5	r-q2(g)
10. q-b6+	k-k1
11. q-r8+	k-b2
12. q-r7+	k-k1
13. q-n8+	k-k2
14. q-b8

(continuation d)
14.		r-q7
15. q-b5+	k-q2
16. q-n5+	k-b1
17. k-k6	r-qb7
18. k-q6	r-kr7
19. q-k8+(h)	k-n2
20. q-k4+	k-n3
21. q-kb4	r-r4
22. q-k3+	k-r4
23. k-b6	k-n5
24. q-q4+(i)	k-r4(j)

(continuation e)
14.		r-q8
15. q-b5+(k)	k-q2(l)
16. q-n5+(m)	k-q1
17. q-r5+(n)	k-b1
18. q-b3+	k-q2
19. q-n4	k-b2
20. q-b4+	k-q1
21. k-k6	r-k8+
22. k-q6	r-q8+
23. k-b6	r-q7
24. q-b5

(a) loses 2 moves; right is k-q5
(b) loses 2 moves; right is q-r8+
(c) loses 3 moves; right is k-b3
(d) loses 3 moves; right is q-r5+
(e) loses 2 moves; right is r-qb4
(f) loses 1 moves; right is q-b8
(g) loses 2 moves; right is r-q2
(h) loses 4 moves; right is q-r6+ or q-b6+
(i) loses 2 moves; right is q-b4+ or q-k4+
(j) loses 2 moves; right is k-r6
(k) loses 2 moves; right is q-k6+
(l) loses 5 moves; right is k-q1
(m) loses 5 moves; right is q-kb2
(n) loses 1 moves; right is q-n8+
.bp
1. q-n7+			    21. ... k-r2      31. ... k-b1
1. q-qr1	  9. ... k-b6			      31. ... k-q2
1. q-n8+			    22. k-b4
1. q-r7+	  10. k-b4			      32. q-r7
1. q-r2+	  10. k-b5	    22. ... r-r2      32. k-b7
		  10. k-n4	    22. ... r-r7      32. k-b6
1. ... k-b3
		  10. ... r-qr3	    23. q-q8+	      32. ... k-k1
2. q-b8
2. q-b6+	  11. q-k7	    23. ... k-n2      33. k-b7
2. q-r6+					      33. k-b5
2. q-b7		  11. ... k-b5	    24. k-n5	      33. k-b6
2. q-k7						      33. q-kn7
2. q-n7+	  12. k-q4	    24. ... r-r8
2. q-n6+	  12. q-qb7+			      33. ... k-b1
2. q-n4				    25. q-q5+
2. k-n8		  12. ... r-r8			      34. k-q6
				    25. ... k-b1
2. ... r-qn4	  13. q-k4+	    25. ... k-b2      34. ... k-k1
2. ... r-r4+	  13. q-k3+
2. ... r-k4			    26. k-n6	      35. q-n8++
2. ... r-b5	  13. ... k-n4			      35. q-k7++
2. ... k-n3	  13. ... k-n6	    26. ... r-r6
				    26. ... r-n8+
3. q-k8+	  14. q-q3	    26. ... r-qb8
		  14. q-b2	    26. ... r-k8
3. ... k-b4
		  14. ... k-b5	    27. q-qb5+
4. k-r7
		  15. q-q2+	    27. ... k-q2
4. ... r-r4+
4. ... r-n6	  15. ... k-b4	    28. qxr

5. k-n7		  16. k-k3	    28. ... k-k3

5. ... k-q5	  16. ... k-k3	    29. q-b5
				    29. q-r5
6. q-r8+	  17. q-k2	    29. q-kb3
				    29. k-b5
6. ... k-k5	  17. ... r-r1	    29. k-b6
6. ... r-k4
		  18. k-q4+	    29. ... k-b3
7. k-b6
7. q-r4+	  18. ... k-q2	    30. q-kr5
7. q-r1+			    30. k-b7
		  19. q-n5+	    30. k-b6
7. ... r-r3+
7. ... r-k4	  19. ... k-b2	    30. ... k-k2
7. ... r-b4			    30. ... k-n2
		  20. q-b5+	    30. ... k-k3
8. k-n5
		  20. ... k-n2	    31. q-n6
8. ... r-q3			    31. q-b5
8. ... r-k3	  21. q-q5+	    31. k-b7
				    31. k-b6
9. q-r4+	  21. ... k-n1
