DTM50 : A new (and ultimate ?) metric for EGTs
Posted: Fri Sep 14, 2012 7:47 am
I’m currently looking at DTM50 (distance to mate metric, playing with 50-move rule). I’ve built a generator capable of building raw (uncompressed) DTM50 tables for all 3-men, pawnless 4-men , pawnful 4-men (soon), and 5-men later (I need to upgrade my hardware to handle them, I’m waiting for Haswell for that, but the generator is almost ready). 6-men will require a different coding architecture (my generator works with built-in RAM EGTBs and is limited to 5-men for this reason) but I’ll be able to furnish the general algorithm if needed.
Preliminary results are extremely interesting.
Looking at the first tables built, I can say with good confidence that :
- Optimal DTM50 lines are often the same as DTM (when the 50-move rule plays no role), or the same as DTZ50 (when the 50-move limit forces the winning side to play or force a zeroing move as fast as possible) ;
- But DTM50 lines can also be in-between, and only DTM50 tables are capable of showing these “in-between” lines, displaying optimal play taking care of both mate speedup and 50-move rule restrictions – a play that could be considered as “perfect play, ultimate knowledge” for those playing with the 50 move rule. This is the real added value of DTM50 tables. It can be expected that DTM50 tables will raise a lot of new interesting knowledge about some endings such as kqpkq, knnkp, and many 6-men of course
- DTM50 will take very reasonable space storage, this is very good news and this was unexpected. More precisely, DTM50 will probably be a not-so-big add-on to a set already composed of DTM + DTZ50 EGTs. I’ll try to post later technical explanations showing that the supplementary information carried by DTM50 over DTM+DTZ50 seems to follow a few basic patterns and will therefore be very highly compressible with a well designed compression scheme.
DTM50 is a “movecount (MC) dependant metric”, meaning that it can take several different values for the same position, depending on the current move counter. DTM50 grows with MC (a higher move count is always favourable for the defender), and when MC gets higher than 100 - DTZ50 (in plies), the position is drawn as the defender becomes able to force a 50-move rule draw.
I can give a taste with the following position. It is the only kpk position with DTM50 taking 4 different values depending on the current value of MC :
Kd2, Pc2 / Ka3 (white to move)
For MC < 92, DTM50 = 17
For MC = 92 or 93, DTM50 = 18
For MC = 94 or 95, DTM50 = 21
For MC = 96 to 99, DTM50 = 22
We can see why by following the unconstrained DTM line and spotting the moments when the 50-move limit forces white to follow a different and slower winning path :
1. Kc3 (1) Ka4
2. Kc4 Ka5
3. Kc5 (2) Ka6
4. Kc6 (3) Ka7
5. c4 (4)
(1) This move will force a sequence of 4 reversible moves (Kc3, bk plays, wk plays, bk plays) and will therefore walk into a 50-move rule draw if the initial MC is > 95. In that case, White must play 1. c3 immediately, delaying mate by 5 moves
(2) If the initial position was with MC=94 or 95, MC is now 98 or 99 and White must play 3. c3 instead, which delays mate by 4 moves
(3) If the initial position was with MC=92 or 93, White must play 4. c4 instead. This delays mate by one move
(4) Now and not before pushing the pawn becomes DTM optimal.
Understanding DTM50 is relatively straightforward in this example, but it is far from being always the case. I’ve also built the kqkr DTM50 table and after having a first look I can say that this table contains “in-between” lines that are pretty mysterious, influenced by both distance to mate and distance to capture of the rook.
I’ll keep posting as I get new results. I’ll also try to post some explanatory text (technical and non-technical) about DTM50 because this metric is a little harder to understand than the more popular DTM.
k
Preliminary results are extremely interesting.
Looking at the first tables built, I can say with good confidence that :
- Optimal DTM50 lines are often the same as DTM (when the 50-move rule plays no role), or the same as DTZ50 (when the 50-move limit forces the winning side to play or force a zeroing move as fast as possible) ;
- But DTM50 lines can also be in-between, and only DTM50 tables are capable of showing these “in-between” lines, displaying optimal play taking care of both mate speedup and 50-move rule restrictions – a play that could be considered as “perfect play, ultimate knowledge” for those playing with the 50 move rule. This is the real added value of DTM50 tables. It can be expected that DTM50 tables will raise a lot of new interesting knowledge about some endings such as kqpkq, knnkp, and many 6-men of course
- DTM50 will take very reasonable space storage, this is very good news and this was unexpected. More precisely, DTM50 will probably be a not-so-big add-on to a set already composed of DTM + DTZ50 EGTs. I’ll try to post later technical explanations showing that the supplementary information carried by DTM50 over DTM+DTZ50 seems to follow a few basic patterns and will therefore be very highly compressible with a well designed compression scheme.
DTM50 is a “movecount (MC) dependant metric”, meaning that it can take several different values for the same position, depending on the current move counter. DTM50 grows with MC (a higher move count is always favourable for the defender), and when MC gets higher than 100 - DTZ50 (in plies), the position is drawn as the defender becomes able to force a 50-move rule draw.
I can give a taste with the following position. It is the only kpk position with DTM50 taking 4 different values depending on the current value of MC :
Kd2, Pc2 / Ka3 (white to move)
For MC < 92, DTM50 = 17
For MC = 92 or 93, DTM50 = 18
For MC = 94 or 95, DTM50 = 21
For MC = 96 to 99, DTM50 = 22
We can see why by following the unconstrained DTM line and spotting the moments when the 50-move limit forces white to follow a different and slower winning path :
1. Kc3 (1) Ka4
2. Kc4 Ka5
3. Kc5 (2) Ka6
4. Kc6 (3) Ka7
5. c4 (4)
(1) This move will force a sequence of 4 reversible moves (Kc3, bk plays, wk plays, bk plays) and will therefore walk into a 50-move rule draw if the initial MC is > 95. In that case, White must play 1. c3 immediately, delaying mate by 5 moves
(2) If the initial position was with MC=94 or 95, MC is now 98 or 99 and White must play 3. c3 instead, which delays mate by 4 moves
(3) If the initial position was with MC=92 or 93, White must play 4. c4 instead. This delays mate by one move
(4) Now and not before pushing the pawn becomes DTM optimal.
Understanding DTM50 is relatively straightforward in this example, but it is far from being always the case. I’ve also built the kqkr DTM50 table and after having a first look I can say that this table contains “in-between” lines that are pretty mysterious, influenced by both distance to mate and distance to capture of the rook.
I’ll keep posting as I get new results. I’ll also try to post some explanatory text (technical and non-technical) about DTM50 because this metric is a little harder to understand than the more popular DTM.
k