H. G. Muller wrote on Tue, Feb 28, 2012 05:14 PM UTC:
Very good question! It had not occurred to me to check that. But the result is surprising: KRKW if won for the Rook! It can take up to 75 moves (to conversion), though, and most wins take more than 50 moves. That makes it one of the most interesting 4-men end-games I have ever seen.
BTW, I released the program with which I calculate the tablebases some time ago as a WinBoard engine, so that people can calculate any 3-, 4- or 5-men ending they want, and then play black against it to see how the computer beats them. It can be downloaded from
http://hgm.nubati.net/fairygen.zip
This contains a README file that explains how you have to install it in the WinBoard GUI. WinBoard supports 22 different piece types, when you switch it to variant fairy, and fairygen knows them all under the same letters as WinBoard uses for them (e.g. W = Wazir). But WA is not one of them. So to calculate the tablebase I just redefined the Elephant (which is used in CWDA by Fairy-Max as WA) as
E: 2,2,* 1,0,*
in fairygen's piecedef.ini file, and used a Wazir for it in WinBoard, with legality testing off.
Below you see how Fairy-Max loses a position I dreamt up against the tablebase. You see from the mate scores (1000.xx = mate or conversion in xx) that the engine defends far from optimal:
[Event 'Edited game']
[Site 'FOM-RHKA8J2A5WY']
[Date '2012.02.28']
[Round '-']
[White 'fairygen']
[Black 'Fairy-Max']
[Result '1-0']
[Variant 'fairy']
[FEN '8/8/8/3k4/4e3/8/8/4KR2 w - - 0 1']
[SetUp '1']
{--------------
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . k . . . .
. . . . e . . .
. . . . . . . .
. . . . . . . .
. . . . K R . .
white to play
--------------}
1. Ke2 {+1000.67/1} Kd4 {-1.78/16 8} 2. Kd2 {+1000.66/1 0.1} Ke5
{-1.72/16 9} 3. Kc3 {+1000.64/1 0.1} Ef4 {-1.77/18 22} 4. Kc4
{+1000.60/1 0.1} Eg4 {-1.86/21 11} 5. Re1+ {+1000.56/1 0.1} Kf5
{-1.85/22 10} 6. Re8 {+1000.55/1 0.2} Ef4 {-1.84/21 9} 7. Kd4
{+1000.54/1 0.2} Ed6 {-1.83/23 14} 8. Re5+ {+1000.50/1 0.2} Kf4
{-1.83/22 14} 9. Re1 {+1000.49/1 0.2} Kf5 {-1.84/22 13} 10. Rh1
{+1000.48/1 0.2} Ed7 {-1.85/21 17} 11. Kd5 {+1000.43/1 0.2} Ee7
{-1.83/20 10} 12. Rf1+ {+1000.40/1 0.1} Kg4 {-1.84/21 11} 13. Ke4
{+1000.39/1 0.2} Kg5 {-1.81/20 9} 14. Ke5 {+1000.32/1 0.1} Ec5 {-1.82/20 8}
15. Rg1+ {+1000.16/1 0.2} Kh5 {-1.86/21 27} 16. Kf5 {+1000.15/1 0.2} Kh4
{-1.84/21 11} 17. Kf4 {+1000.14/1 0.1} Kh3 {-1.85/21 10} 18. Rg5
{+1000.13/1 0.2} Ee7 {-1.84/20 9} 19. Rg3+ {+1000.12/1 0.2} Kh2
{-1.83/20 13} 20. Kf3 {+1000.11/1 0.1} Ef7 {-1.81/21 12} 21. Rg5
{+1000.10/1 0.1} Ef6 {-1.78/20 12} 22. Rg7 {+1000.09/1 0.2} Ed4
{-1.82/20 9} 23. Rd7 {+1000.08/1 0.2} Ec4 {-4.89/21 11} 24. Rh7+
{+1000.07/1 0.1} Kg1 {-4.89/23 12} 25. Rg7+ {+1000.06/1 0.1} Kh2
{-4.88/23 14} 26. Rg4 {+1000.05/1 0.2} Ec3 {-4.94/23 9} 27. Kf2
{+1000.01/1 0.1} Kh3 {-4.96/25 11} 28. Rg3+ {+1000.00/1 0.2} Kh4
{-4.98/27 9} 29. Rxc3
This is where it stops, as fairygen can play only from one tablebase at the time, and does not have KRK loaded here.
Very good question! It had not occurred to me to check that. But the result is surprising: KRKW if won for the Rook! It can take up to 75 moves (to conversion), though, and most wins take more than 50 moves. That makes it one of the most interesting 4-men end-games I have ever seen. BTW, I released the program with which I calculate the tablebases some time ago as a WinBoard engine, so that people can calculate any 3-, 4- or 5-men ending they want, and then play black against it to see how the computer beats them. It can be downloaded from http://hgm.nubati.net/fairygen.zip This contains a README file that explains how you have to install it in the WinBoard GUI. WinBoard supports 22 different piece types, when you switch it to variant fairy, and fairygen knows them all under the same letters as WinBoard uses for them (e.g. W = Wazir). But WA is not one of them. So to calculate the tablebase I just redefined the Elephant (which is used in CWDA by Fairy-Max as WA) as E: 2,2,* 1,0,* in fairygen's piecedef.ini file, and used a Wazir for it in WinBoard, with legality testing off. Below you see how Fairy-Max loses a position I dreamt up against the tablebase. You see from the mate scores (1000.xx = mate or conversion in xx) that the engine defends far from optimal: [Event 'Edited game'] [Site 'FOM-RHKA8J2A5WY'] [Date '2012.02.28'] [Round '-'] [White 'fairygen'] [Black 'Fairy-Max'] [Result '1-0'] [Variant 'fairy'] [FEN '8/8/8/3k4/4e3/8/8/4KR2 w - - 0 1'] [SetUp '1'] {-------------- . . . . . . . . . . . . . . . . . . . . . . . . . . . k . . . . . . . . e . . . . . . . . . . . . . . . . . . . . . . . K R . . white to play --------------} 1. Ke2 {+1000.67/1} Kd4 {-1.78/16 8} 2. Kd2 {+1000.66/1 0.1} Ke5 {-1.72/16 9} 3. Kc3 {+1000.64/1 0.1} Ef4 {-1.77/18 22} 4. Kc4 {+1000.60/1 0.1} Eg4 {-1.86/21 11} 5. Re1+ {+1000.56/1 0.1} Kf5 {-1.85/22 10} 6. Re8 {+1000.55/1 0.2} Ef4 {-1.84/21 9} 7. Kd4 {+1000.54/1 0.2} Ed6 {-1.83/23 14} 8. Re5+ {+1000.50/1 0.2} Kf4 {-1.83/22 14} 9. Re1 {+1000.49/1 0.2} Kf5 {-1.84/22 13} 10. Rh1 {+1000.48/1 0.2} Ed7 {-1.85/21 17} 11. Kd5 {+1000.43/1 0.2} Ee7 {-1.83/20 10} 12. Rf1+ {+1000.40/1 0.1} Kg4 {-1.84/21 11} 13. Ke4 {+1000.39/1 0.2} Kg5 {-1.81/20 9} 14. Ke5 {+1000.32/1 0.1} Ec5 {-1.82/20 8} 15. Rg1+ {+1000.16/1 0.2} Kh5 {-1.86/21 27} 16. Kf5 {+1000.15/1 0.2} Kh4 {-1.84/21 11} 17. Kf4 {+1000.14/1 0.1} Kh3 {-1.85/21 10} 18. Rg5 {+1000.13/1 0.2} Ee7 {-1.84/20 9} 19. Rg3+ {+1000.12/1 0.2} Kh2 {-1.83/20 13} 20. Kf3 {+1000.11/1 0.1} Ef7 {-1.81/21 12} 21. Rg5 {+1000.10/1 0.1} Ef6 {-1.78/20 12} 22. Rg7 {+1000.09/1 0.2} Ed4 {-1.82/20 9} 23. Rd7 {+1000.08/1 0.2} Ec4 {-4.89/21 11} 24. Rh7+ {+1000.07/1 0.1} Kg1 {-4.89/23 12} 25. Rg7+ {+1000.06/1 0.1} Kh2 {-4.88/23 14} 26. Rg4 {+1000.05/1 0.2} Ec3 {-4.94/23 9} 27. Kf2 {+1000.01/1 0.1} Kh3 {-4.96/25 11} 28. Rg3+ {+1000.00/1 0.2} Kh4 {-4.98/27 9} 29. Rxc3 This is where it stops, as fairygen can play only from one tablebase at the time, and does not have KRK loaded here.