Problem #13970

[roq]

Problem #13970 is another interesting example I came across today that doesn’t quite fit the normal mold. I think as it stands it hasn’t yet been solved (its on 30 seconds blitz and 300 seconds standard). The solution move 1. Nd7 leads to a quick gain of  material, but the problem then requires the execution of a very complex mate in seven that only a computer would find. (Maybe a problem with a mate should end when the winning side is up a certain amount of material and if the mate is over some certain number of moves further down the line from the win of material?)

I didn’t find 1. Nd7 but instead played: 1. Na6 intending: 1...bxa6 2.Qxc6+ Kb8 [2...Rc7 3.Qa8#] 3.Rd3 Rb7 4.Qxe8+ winning easily.  Actually this leads to a forced mate in ten!? But it would be hard for a human to see the exact mating sequence from the starting position (although the material gain is so great and the white pieces so well coordinated that a quick mate is clearly inevitable so one wouldn’t need to calculate it).

A further complication though is that due to the fact that black has essentially no counterplay in this position there are many other winning lines that win in various esoteric ways, but are not nearly as good as 1. Nd7 and 1. Na6. So (if you were to give credit for alternatives) in this problem it would be very hard for you to allocate credit in a consistent way. Also of course this is a really fascinating position and the moves Nd7 and Na6 are not standard shots that can be guessed without calculating variations, so it would be a pity if the pruning algorithm were to consistently remove this type of problem.

[richard]

Thanks roq,

I think this is a classic example of where "shortest mate is always best" can lead unsatisfactory outcomes.  This is a slightly different case than the problem brought about by alternative material takes, as here the material take is part of the suggested line.  This kind of problem is probably fairly easily dealt with by rejecting problems that don't reach mate soon enough after a large material advantage (or at least stop the problem after the material advantage has been obtained, in a similar way to non-mating tactics do, although the resulting tactic would then have to go through the disambiguation process again due to possible other winning lines that come into play once you have decided that mate is no longer required).

As I get closer to exhausting obvious problem generator based improvements I'm also planning to look through the problems that don't have successful solutions manually.

Regards,
Richard.