WDL and DTZ, WDL50 and DTZ50
Posted: Wed Sep 03, 2008 8:49 am
I am not sure what the concern is here.
By the way, to avoid possible misunderstanding, the established notation is 'DTZ50', not 'DTZ(50)'. 'WDL(50)' is used for 'WDL or WDL50'.
Provided you have a good indexing-system for the positions (and I see that as the key issue), WDL EGTs can be generated regardless of the k-move rule.
This is what Jonathan Schaeffer did for Checkers, which is now enabling his proof that Checkers is a theoretical draw.
JS went to 10-man EGTs. Of course, advancing every checker in Checkers is irreversable, like pushing a Pawn in Chess. Not so with the Kings though.
The WDL EGTs are also useful in generating other EGTS such as DTC, DTM and DTZ in that they have already identified the draws (and losses).
Two points maybe worth noting. The generation of an EGT starts off by identifying all stm-mated positions _plus_ all stm-forced-to-move-to-loss-in-next-phase. All these are depth zero, counting in winner's moves. There is another table, which is not WDL50 but helps generate WDL50, which is the 'WDL50trunc' EGT created after 100 cycles after identifying stm-mated/(forced to move to loss in next phase). These positions will have DTZ =< 50 and no others will. It is useful to 'lop the head off' WDL.
Just as WDL EGTs help generate the DTZ EGTs, they (or WDLktrunc) help generate the WDLk (e.g. WDL50) EGTs. They have already identified _some_ draws.
But the WDL50 EGT for an endgame can only be generated once the WDL50 EGTs for its sub-endgames are known. Example KBBKNN needs KBBKN et al.
As kronsteen says, you might use the KPPPKPP DTZ EGT to navigate to 6-man and/or conversion, and then rely on 7-man WDL EGTs thereafter.
The integrity of WDL50 is an issue. It looks very much like WDL49 and WDL51 but one could check that the 'boundary converts' are to a WDL50 EGT.
I think MB or someone once said that the issues tend to be at the 'edges' of the EGT, not in the routine within-endgame retro'ing.
An example of this was the FEG-error, spotted by MB and now cured, in missing some shallow wins in a subgame (KNNK I think).
g
By the way, to avoid possible misunderstanding, the established notation is 'DTZ50', not 'DTZ(50)'. 'WDL(50)' is used for 'WDL or WDL50'.
Provided you have a good indexing-system for the positions (and I see that as the key issue), WDL EGTs can be generated regardless of the k-move rule.
This is what Jonathan Schaeffer did for Checkers, which is now enabling his proof that Checkers is a theoretical draw.
JS went to 10-man EGTs. Of course, advancing every checker in Checkers is irreversable, like pushing a Pawn in Chess. Not so with the Kings though.
The WDL EGTs are also useful in generating other EGTS such as DTC, DTM and DTZ in that they have already identified the draws (and losses).
Two points maybe worth noting. The generation of an EGT starts off by identifying all stm-mated positions _plus_ all stm-forced-to-move-to-loss-in-next-phase. All these are depth zero, counting in winner's moves. There is another table, which is not WDL50 but helps generate WDL50, which is the 'WDL50trunc' EGT created after 100 cycles after identifying stm-mated/(forced to move to loss in next phase). These positions will have DTZ =< 50 and no others will. It is useful to 'lop the head off' WDL.
Just as WDL EGTs help generate the DTZ EGTs, they (or WDLktrunc) help generate the WDLk (e.g. WDL50) EGTs. They have already identified _some_ draws.
But the WDL50 EGT for an endgame can only be generated once the WDL50 EGTs for its sub-endgames are known. Example KBBKNN needs KBBKN et al.
As kronsteen says, you might use the KPPPKPP DTZ EGT to navigate to 6-man and/or conversion, and then rely on 7-man WDL EGTs thereafter.
The integrity of WDL50 is an issue. It looks very much like WDL49 and WDL51 but one could check that the 'boundary converts' are to a WDL50 EGT.
I think MB or someone once said that the issues tend to be at the 'edges' of the EGT, not in the routine within-endgame retro'ing.
An example of this was the FEG-error, spotted by MB and now cured, in missing some shallow wins in a subgame (KNNK I think).
g