Monday, June 1, 2015

Calculating Forcing Moves: Defensive Idea 5 - Counterattack to DEFEND (Idea 1, capture)

In the last few posts on counterattacking we created Equal or Greater Threats (EGT) that allowed us to force a WIN, and to force DRAWs (by stalemate, repetition, and material).

The next few posts will look at “counterattacking to DEFEND”, which is using EGTs to allow the use of one of the first four defensive ideas:

  • Defensive Idea 1 – do something to the attackers (capture, pin, deflect, restrict);
  • Defensive Idea 2 – block the attackers
  • Defensive Idea 3 – move the piece being attacked
  • Defensive Idea 4 – defend the piece/square being attacked

In this first post we will use an EGT to allow us to use defensive Idea 1, capture the attackers.  How is this different from Idea 1?  The key difference is tempo, as I’ll explain below.

Black just played 1…Nf4.  White to move.

1k1r4/1b2R2p/p1qP4/1p2Q3/1P3np1/P7/2P2PPP/3R2K1 w - - 0 1

Let's evaluate the position, and then find and prioritize all of black's threats.

Evaluation:  White has a two point material advantage (rook and three pawns vs bishop and knight).  White’s pieces are actively placed, his king is less exposed than black’s, and his advanced passed pawn is a major strength.

Threats:  Black’s threat is 2…Qxg2#, as well as …Ng6 forking white’s queen and rook.  The checkmate threat is clearly our priority for calculations.

Let's look at the five defensive ideas to see what options white has to defend against the checkmate.

Idea 1 – do something to the attacking pieces (the c6 queen, f4 knight, and b7 bishop).  We cannot capture or pin (must be absolute) the queen.  We can capture black’s f4 knight, but quickly see that is easily refuted with 2…Qxg2#.
We can also capture black’s b7 bishop.  This is a perfect opportunity to discuss the difference between Idea 1, and Idea 5.  Take a look at the below position, in particular how the new position of the black king (now on a8) changes things.

1k1r4/1b2R2p/p1qP4/1p2Q3/1P3np1/P7/2P2PPP/3R2K1 w - - 0 1

With the black king on its new square, capturing the bishop now does nothing to prevent the checkmate because 2. Rxb7 Qxg2#.  In this modified position neither of the captures we found using Idea 1 would work since black would still be able to checkmate with 2…Qxg2.

But in the original position with the black king on b8, taking the bishop now comes with check (2. Rxb7+) and black has to spend his next move getting out of check instead of delivering checkmate.  A capture-check should always be appreciated for the extra time it gains.  Sticking rigidly with the structure of this blog series I will put this capture-check under Idea 5 because the check is a GREATER threat than the checkmate threat.  However, this capture-check could easily be found by searching the board using either Idea 1 or 5.  Idea 1 has generated zero candidate moves.

Idea 2 – block the attacking pieces (the c6 queen from getting to g2).  White has four blocks (2. Rd5, 2. Qd5, 2. Qe4, and 2. f3).  Both of the queen blocks are very clearly bad for white after the immediate captures.  Only the rook and pawn blocks seem like viable candidates.   Idea 2 has generated two candidate moves.

Idea 3 – move the piece being attacked (the white king).  Since we have time, the king can prepare to move with 2.Kf1, allowing him to escape to e1 if 2…Qxg2+.  Moving the king the other direction (2. Kh1) still allows 2…Qxg2#.  Idea 3 has generated one candidate move.

Idea 4 – reinforce/defend the attacked square or piece (the g2 square).  The are two moves that defend g2 (both 2. Qd5 and 2. Qe4), however, we have already looked at both of these moves under Idea 2 and quickly rejected them.  Idea 4 has generated zero candidate moves.

Idea 5 – counterattack with an Equal or Greater Threat (of checkmate).  Looking at the EGT chart from earlier we can see that against a checkmate threat, you can only counterattack with a check.  White has two checks in this position (2. d7+ and 2. Rxb7+).  Idea 5 has generated two candidate moves.

This process has generated five specific candidate moves:

The next step is to calculate all five candidates starting with the most forcing move, the capture-check 2. Rxb7+:

2…Kxb7 seems the best of black’s four possible replies (two king moves, and two captures), since it keeps the checkmate threat alive, keeps two attackers on white’s passed pawn, gets the king more active, breaks white’s discovered check, and keeps the queen on the c-file attacking the c2 pawn.  Now, since black is still threatening checkmate in g2 white needs to defend, and we see we can now simply capture another attacker (using Idea 1) with 3. Qxf4.  White has traded his rook for two minor pieces and is up three entire pawns.  So far this variation looks very promising for white…but it is not over yet.   3…Qxc2 again threatens mate in 1, but white can regain the pawn and defend his rook (Idea 4) with 4. Qxg4, after which black has no clear refutations.  White is up three pawns, and is winning.  That makes Rxb7+ our King of the Hill (KOTH).

Let’s see if white’s other candidates can force a position that is better than our KOTH, starting with the next most forcing move 2. d7+:

2…Ka8 looks best for black (out of his five possible replies), since it renews the checkmate threat with the fewest complications.  White will be hard pressed to prove that this variation is better for him than the first variation since this leaves black with too much play.  White is again forced to defend against the checkmate, and now only has one check that is clearly bad (3. Qb8+), has the one bad capture (3. Qxf4) from Idea 1 that fails to prevent the checkmate, the same four blocks as above (3. Rd5 and 3. f3 were the only viable options), and he can still move his king (3. Kf1).

Since none of these three options force black to respond, let’s see if we can quickly eliminate any of them as clearly bad.  The rook block seems to be the worst of the three since black can just capture, but let’s see if white gets any compensation:

3. Rd5 and black can just simplify to a won endgame with 3…Qxd5 (the most direct refutation, since black is now threatening checkmate on g2 and d1) 4. Qxd5 (forced) Bxd5 5. Re8 (promotion tricks seem like white’s only hope) Ne6 and black defends his rook and wins.  So we can clearly reject that block.

White’s other two candidates (after 2. d7+ Ka8, and now 3.f3 or 3.Kf1) expose the king to checks which certainly does not help white’s cause, but let’s see if white is still able to force a better position than our KOTH:

3. Kf1 and black can now get very active with two checks 3…Qc4+ and 3…Qxg2+, and the knight fork 3…Ng6.  It is very hard to imagine any of these are any good for white, but let’s just look at 3…Ng6 and see if white has a forced win (better than our KOTH of plus three pawns).

White is yet again on the defensive, and black's threat is to capture his queen (4…Nxe5).  We cannot capture, pin, or deflect the knight (Idea 1), and we can never block knights (Idea 2).  We can move the queen to several safe squares (Idea 3) but they all appear to be easily refuted (after…Qxg2+ followed by …Nxe7), and defending the queen does not make sense (Idea 4).  That only leaves counterattacks (Idea 5).  We can create an equal threat by attacking the queen with either rook (Re6 or Rd6) but black first evades the attacks with …Qxg2+ and then captures our queen.  An interesting counterattack -- and possibly forcing a more winning position than our KOTH -- is to force the promotion of the pawn with 4. Re8:

4…Nxe5 5. Rxd8+ Ka7 (forced, the bishop/queen blocks allow the promotion) 6. Ra8+ Bxa8 7. d8=Q and now white is up one point in material (rook and pawn vs bishop and knight), but alas this is NOT better than our KOTH, and it is black's turn to move and he at least gets his pawn back with 7…Qxg2+.  Even though this forced variation can continue black gets to have all the fine and is likely to win more material.  This is more than sufficient to reject our other candidate move 2. d7+.

That leaves us with three other candidates.  None of them are particularly forcing so it is extremely unlikely that they will be better than our KOTH.  Let's see if we can eliminate any of them as clearly bad.

Our rook block looks losing since after 2. Rd5 Nxd5 white is simply down material, and even though there is some play left he's running out of pieces and will be struggling to even draw.  We can reject this block.

White's other block (2. f3) and the king move (2. Kf1) both expose his king allowing black's pieces even more potential activity.  Let's see if our block somehow gives white a better position than our KOTH, after 2. f3:

White is threatening to capture black's knight.  His discovered check buys him an extra move, but it is not clear that there is a specific threat behind it other than trying to force promotion by following up with Re8.  So white's primary threat is to capture the knight.

We cannot capture, pin or deflect the queen (Idea 1).  We cannot block the queen since it is an 'in-your-face' attack (Idea 2).  We can move the knight (Idea 3) to all eight squares, but the fork (2…Ng6) seems most interesting.  We can defend the knight (Idea 4) two different ways (2…Rf8 and 2…Qc4).  We cannot create an equal threat since white does not have any minor pieces, but we can create a greater threat by attacking his rook and threatening mate (2…Qxc2), or giving check (2…Qb6+).  Of course the most forcing of these five candidates is the check 2…Qb6+:

3. Qc5 is white's most forcing defense (of six possible replies) and limits black's play the most, but I don't see how this is clearly better for white.  We can reject this check for black, and look at his next most forcing move two candidate, the other counterattack 2…Qxc2:

Black is again threatening checkmate, and we can consider this a refutation to white's block (2. f3) but let's play this out a bit further and see if white can pull off something better than our KOTH.  He can capture the knight (Idea 1), but that allows black to take his rook with check.  He can block the queen from getting to g2 (Idea 2) two different ways, but both blocks just lose material.  He can move his king (Idea 3), but one leads to checkmate anyway (3. Kh1 Qxg2#) and the other just loses the rook (3. Kf1 Qxd1+).  He cannot add another defender to g2 (Idea 4) that we haven't already considered under Idea 2.  The only counterattack (Idea 5) possible must begin with a check given the threat of checkmate, and he has two checks (3. d7+ and 3. Rxb7+).  Let's start with the most forcing the capture-check 3. Rxb7+:

Hey wait!  That's the exact same capture-check from the first position, which we know will allow us to next capture the knight.  This must be right!  And it would be except for one key difference.  3…Kxb7 4. Qxf4 Qxd1+! 5. Kf2 (only) and now black is winning.  Of course white does not have to capture the knight, and he can instead give check (4. Qe7+ is the most forcing since it also attacks the rook).   Even though there is more play for white in this line, we can reject it since white can't bring his rook into the attack with check, and he has the same dilemma of how to defend against checkmate (Qxg2#) and the capture-check (Qxd1+) at the same time.  He might be able to get equality but won't be able to force a position better than the KOTH so we can reject 3. Rxb7+.  All of white's other replies at move three were rather passive (the discovered check just buys one move but does not change the position), and are even more unlikely to force a better position than our KOTH.  Since there were no other moves in this variation for white to consider, we can drop this candidate.  Here's what our updated chart looks like:

The last candidate we have to consider is the king move (Idea 3) 2. Kf1:

2…Qxg2+ 3. Ke1 (only) Qg1+ 4. Kd2 (only) Qxf2+ 5. Kc1 (forced, 5. Kc3 Qf3+ looks good for black) Ng6 and black has equalized the material (rook and pawn vs bishop and knight) and it is not clear that white can keep his rook since now his capture-check (Rxb7+) only picks up one minor piece.  Even though there is a bit more play for white in this line, I do not see how from here he can force a position better than our KOTH.  So we can reject this variation as well.

Here is our final chart:

Conclusion:  This process has shown us that white has several candidate moves to consider in the initial position, and by calculating the most forcing moves first we defended against the checkmate and found the forced win!  In a real game we would not need to calculate as much as I did here.  Once we calculated that our most forcing candidate at move one (the capture-check Rxb7+) was winning, we could make the move and enjoy the rest of our win.  But for the sake of this exercise I went ahead and tried to prove that the other candidates were not as good as our KOTH.  

This is the process you should be able to do mentally:  prioritize the threats, use the five defensive ideas to search for specific candidate moves, calculate each one completely, and then pick the best variation based on the final evaluation.

In the next post we will look at positions where we use EGTs to rearrange our pieces to allow another of the basic defensive ideas (from Idea 1-4).

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