Author: Anthony Bailey
Date: 12:20:30 10/21/99
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On October 20, 1999 at 13:12:42, guy haworth wrote: >No significant progress to report yet - but what do you think of the Earl >Schulz posts? I already happened to send e-mail to Guy about this, but in case anyone else is interested I'll follow it up here too. Earl made three assumptions in creating his specialised KQPKQP database, over and above the obvious restrictions of the Black d-pawn to d5 through d2 and the White g-pawn to g5 through g7. One seems fine, and presents the only feasible option at present. The second may happen to be OK for this ending but it fairly easy to do without. The third makes his results pretty much useless, although it was still a worthwhile experiment. Details... Let's call a positive result one where we find that Black holds the draw after Qf5 and a negative one one where we find a win for White. (I guess this shows a preference for which result I hope we end up with... it's hard to get out of feeling like I'm playing Black in this position!) We can certainly make the odd wrong position evaluation as a result of any of the plausible assumptions. Although they compromise the tablebase results for these positions, if they are very unusual then I do not expect they will not ripple back to affect anything a few ply back. A combination of wrong evaluations that would ripple back to compromise the evaluation following Qf5 I will term "crucial." In the case where every branch of a drawing move strategy consists of forced moves, every wrong evaluation would be crucial. In practice, where there are many forced moves but also choices that both hold the draw every now and then, one needs to find wrong evaluations following all such choices in order for these wrong evaluations to be crucial. My current understanding of the status of the assumptions is as follows... 1. "No underpromotions" constraint: False negatives: inordinately unlikely. Only possibility seems to be a White underpromotion to knight with check; crucial knight underpromotions are very unlikely, and Black would also have to have King somewhere ridiculous. False positives: extremely unlikely. I can construct KQQKQP positions where only a Black underpromotion to knight with check saves the position, but it's quite a tough puzzle. These aren't likely to be crucial. How to remove constraint: Would have to calculate KQxKQy for all non-pawns x and y. This isn't currently feasible. It will be eventually; at that point the method we propose for retreating pawns one square at a time will become entirely valid and probably for a while will be the only way to feasibly generate six-piece tables including pawns. 2. "Black King in a1-d3" constraint: False negatives: possible, but hard to estimate likelihood. These would occur if there are drawn positions where the Black king leaves this sacred rectangle. They seem most likely where Black e.g. has equalised by catching up in the pawn race but then White has a check to force him out of the rectangle. I do not feel able to judge how important these would be. False positives: impossible. Every draw where we stay in the rectangle is a valid draw when the king is unrestricted. How to remove constraint: Just allow the king to wander anywhere. This just increases the RAM and run-time requirements for one iteration through the algorithm by a linear factor (64/12 = about 5.) Should be very easy to implement. 3. "First to promote wins" constraint: False negatives: common The assumption denies Black even the possibility of attacking the promotion square with his queen to prevent the promotion. It has already been shown to miss crucial ideas only a little way into Qf5. There is no doubt that this one invalidates the usefulness of the Schulz tablebase. False positives: possible Would be just as common if we ever got to promote first! How to remove constraint: Look-up promotion evaluations in a KQQKQP tablebase. Generating these tablebases is not trivial, and nor is writing the new look-up code; however, this approach (the one John is currently pursuing) is necessary since the assumption is unacceptable. Summary: Constraint 1: We have to use it, but almost certainly not damaging. Constraint 2: Relatively simple to avoid using, and its effects are unknown. Constraint 3: Some work to avoid using, but vital to do so. - Anthony.
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