First puzzle

alexdespres,

Good question. 

42.Qxb3 is a little less efficient.  It would just be a diversion from the forced mate.  Black's Queen is unable to defend, so no need to capture.  I ran it in Fritz and Fritz takes two extra moves to mate if 42.Qxb3.

 (42. Qxb3 Kd7 3. Ra6 Kd8 44. Qxe6 c6 45. Ra7 c5 46. Qd7#)

Rats. I happened upon Qxb8+ first and so completely missed Rxa7. Good puzzle. In case anyone is curious what happens in the Qxb8+ lines...

38. Qxb8+ Kxb8 39. Nxc6+ Kc8 (39... Kb7 40. Na5+) (39... Ka8 40. Rxa7#) 40. Rf8+ Kd7 (40... Kb7 41. Na5+) 41. Ne5+ Ke7 (41... Kd6 $5 42. Rf7 Qb5 43. Rd7+ Qxd7 44. Nxd7 Kxd7 45. Rxa7) 42. Rf7+ Kd8 (42... Kd6 43. Rd7#) (42... Ke8 43. Rxa7 ) 43. Rxa7 1-0

If 38.Qxb8, then Rybka engine shootout, black lasts till move 54.

AquaMan> If 38.Qxb8, then Rybka engine shootout, black lasts till move 54.

The win is obvious by move 45. Of course, checkmate takes longer.

Interestingly, on my PC Rybka 2.3.2mp (depth=17) and Fritz (depth=15/32) choose 39...Kb7 after a few moments, which loses immediately to 40.Na5+... they must be hoping it delays mate a move or two longer! That's why I sometimes user a weaker engine like Crafty to find defenses in lost positions--strong engines know they're beat so they begin to act silly and try delay mate rather than put up a defense their opponent might not see through.

likesforests, that is interesting. Thanks for the observation on engines sometimes using survival time in a lost postion as a main decision factor, rather than positional strength or piece strength.  I was using Rybka21c32-bit(demo), 9 ply. 

In the case of 39...Kb7 40.Na5+ forking the Q and K, if I run my rybka 9 ply shootout from there, black lasts till move 59 now.  So your rybka does appear to be optimizing for survival time. 

At least once I swore I saw one of my engines move into mate when it wasn't yet forced.  This too was in a totally lost position. I was probably wrong.  If so I guess that would be the engine equivalent of resigning :).

AquaMan> I wonder if once the game is lost your rybka is using survival time rather than piece strength as a main decision factor?

Yes, that's what most engines do (if survival time is known). Upto ply-12, Rybka selects 39...Kc8 thinking it gives it can survive. But then it sees White can punch its clock in that line too, so it switches to 39...Kb7 where it loses immediately but survives longer. Hence the paradox that in lost positions weaker engines put up a better fight (and thus have better drawing chances against humans) than stronger engines.  ;)