phhnguyen wrote: ↑Thu May 16, 2024 2:25 am
My program prints out the index size for rn vs n with full defenders (run the program as: fegtb -n rn-n -subinfo)
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450) krnaabbknaabb 805'180'500'000
Its index space is about 800 G, or 10 times as small as yours. I think it has one of the most compact index space systems.
My size estimates also include all incomplete Palace and Elephant constellations. As I usually generate those at the same time. For the defending Palace these positions are usually on the path to any forced win. For the winning player's defenders this can indeed be contested; even though his defenders could be captured in 2-vs-1 end-games there probably will be winning strategies that avoid this. Nevertheless, to get accurate DTM the successor end-games due to loss of white defenders would have to be calculated as well.
This is why I was calculating with a Palace size of 119 = 70 + 40 + 9 instead of 70 for kaa, and 29 = 21 + 7 + 1 instead of 21 for ee. With two sets of defenders that already explains a factor ~5. I usually ignore collisions between K and E. There are only 16*7 = 112 of those amongst the 119*29 = 3451, and saving 3% of space is usually not worth the hassle of complicating the index calculation.
So when I say KRHAAEEKHAAEE I really mean KRHdKHd, with d = AAEE, AEE, AAE, AA, AE, EE, A, E, or -. Anyway, whether 8000G or 800G, they are too large for comfort, and if an equivalent table could be made with 1.2G positions I think it would be a worthwile development.
As for 3 vs 0: I really don't think these are problematic if you stick to the liberated King (i.e. KxyzKd). Even if you would like to have xyz on both sides of the River, the attacking King could still be represented by its file for xyz being on the 90% of the squares outside their own Palace (without Cannons).
I think it would be a mistake to consider the EGTs as monolithic entities, which have to be done completely or not at all. If 10% of the positions in a certain end-game would be 1000 times more difficult to do than the other 90%, and therefore beyond handling, that should not be a reason for shying away from doing those 90%. An EGT that covers only pieces across the River would have 3*119*29*45*45*45 = 900M positions.