Thursday, May 7, 2015

Calculating Forcing Moves: Defensive Idea 5 - Counterattack to DRAW (repetition)

In this series of posts we are looking at “counterattacking to DRAW”, which is using Equal or Greater Threats to force three types of drawn positions:

  • Draw by stalemate;
  • Material draw (equal material, fortresses, etc); and,
  • Draw by repetition.

In the last two posts we looked at positions where there were clear threats on the board, and we created an EGT that allowed us to force drawn positions by stalemate and by reaching a drawn endgame.   In this post we’ll look at a position where the best move is to use a series of EGTs to force the opponent to repeat the position, resulting in a draw.

Black just played 1…Kxf4.  White to move.

2n5/3pB3/p3p3/2Q2n2/3p1kb1/1r6/q4PBK/3r4 w - - 0 1

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

Evaluation:  White is clearly losing. Black is up two rooks, a knight, and three pawns.   White is considering whether he should do the noble thing and resign.  The only thing going for white is his extreme lack of pieces and almost complete immobility…this immediately brings to mind stalemate themes.

Threats:  Black’s threats are many, but the fastest forced checkmate I can find is 2…Rh3+ 3. Bxh3 (only) Qxf2+ 4. Bg2 (only) Qg1#.

Let's look at the five defensive ideas to see what options white has to reply to the threat.

Idea 1 – do something to the attacking pieces (the g4 bishop, both rooks, and the queen).  We cannot capture, pin (absolute, given the mate threat), or deflect any of black’s attacking pieces.

Idea 2 – block the attacking pieces (the g4 bishop, both rooks, or the queen, from getting to h3, f2, or g1).  White has five blocks (2. Qc3, 2. Qc2, 2. Bf3, 2. Bg1, and 2. f3), but in all cases black simply captures with the queen or rook, which reinstates the same threat.  If the bishop leaves g2 (for 2. Bf3 and 2. Bg1), this simply allows a capture-check and a new forced mate (2…Qxf2+ 3. Bg2 Qg1#)

Idea 3 – move the piece being attacked (the white king).  The king has zero legal moves. Creating an escape square for the king by moving the bishop somewhere threatening (like say 2. Bd5) allows the same capture-check and a new forced mate mentioned in Idea 2 (2…Qxf2+ 3. Bg2 Qg1#).  Moving the bishop to f1 blocks the first rank, but still allows the new forced mate.

Idea 4 – reinforce/defend the attacked square or piece (the h3, f2, and g1 squares).  The are two moves that defend h3 (2. Qa3, and also 2. Qc3 that we looked at under Idea 2) but in both cases black simply captures the queen.  There are three moves that defend f2 (2. Bh3, 2. Qc2, and 2. Qxd4) but again black simply captures and checkmate is back on.  There are zero moves that defend g1 a second time.

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.  This is a good place to recall my earlier post on counting checks.  Instead of looking at every piece and then searching for each and every check, we can see that only the queen and dark-squared bishop can check the king, which equals a maximum of 14 checks because the bishop normally has 2 (unless one is off the board), and the queen has 12 when she is on the same color square as the target -- that is three checks in each of the four directions the queen can move.  (She only has ten checks when on the opposite color square, because there are only two on each diagonal instead of three.)  In this position the queen has two checks along the 5th rank (2. Qe5+ and 2. Qxf5+), two checks along the c-file (2. Qc7+ and 2. Qc1+), one check on the a3-f8 diagonal (2. Qd6+) and one check along the a7-g1 diagonal (2. Qxd4+).  The bishop can deliver both of its checks (2. Bg5+ and 2. Bd6+), for a grand total of eight checks.

This process has generated eight specific candidate moves, all of which are checks:

The next step is to calculate all eight of the candidate checks.  As I noted in earlier posts about counterattacks we do not know the outcome of the counterattack when we begin calculating, but in this case the position is so extremely bad for white that we can only accept extreme outcomes – a forced checkmate, or forced draw by stalemate or repetition.  We will not be able to capture enough material to reach an equal (or materially-drawn) position, and we won’t be able to construct a fortress.  Even if we could use checks to allow another defense against the checkmate, we’d still be losing.

How to pick which check to calculate first?  They are all forcing, but some are more forcing than the rest meaning they allow white fewer replies.  Quickly counting replies for each check, I see that two of the checks (2. Bg5+ and 2. Qe5+) only offer black one single reply, so we’ll start with those.  I actually do this “reply count” in my head as I’m counting checks to see which checks offer the fewest replies.  Let’s start with 2. Bg5+:

2…Kxg5 (only) and now white must keep delivering checks, hopefully to rid himself of all mobile pieces (the queen, pawn, and bishop) to force stalemate and we have 3. Qe7+ or 3. f4+.  There could be move order issues here so we’ll try both ways.  Let’s start with the queen check first:

3. Qe7+ Kf4 (if either knight captures the queen, 4. f4+ allows white to immobilize his pawn and self-pin his bishop -- stalemate) 4. Qg5+ Ke5 (4. Qd6+? Nxd6 avoids stalemate; if 4…Kxg5? 5. f4+, stalemate).  Here white has five queen checks and one pawn check.  Black cannot capture the queen if his king is on e5 or g5, since it allows f4+ (and stalemate), so the black king must move away from those squares before he can capture the queen.  White of course does not want to allow the black king to get away from those squares.

That eliminates three of white’s checks (all of the queen checks on the f-file), leaving three checks: 5. f4+, 5. Qg7+, and 5. Qe3+.  Since shedding the pawn is an important goal, and the two queen checks seem to allow the king to leave e5, let’s start with:

5. f4+ Kd6 (only) 6. Qe7+ (only check) Nfxe7, and now there is no stalemate because the pawn can move to f5 without a check.  Let’s try white’s two other checks at move 5:

5. Qg7+ Kd6 (5…Kf4 allows 6. Qg5+ leading to draw by repetition), and here white has five checks but since the black king is now not on e5 black can capture the queen.  This only allows white two checks -- one where black cannot capture the queen (6. Qf8+), and one where the capture would put the black king back on e5 (6. Qe5+).  After 6. Qf8+ Nce7 and now both of white’s checks allow black to capture.  That leaves 6. Qe5+ Ke7 (only) 7. Qc5+ (white’s four other checks allow black to capture) Ncd6, and white has no checks and black has avoided the stalemate.  That only leaves one other candidate check at move five:

5. Qe3+ Kd6 (capturing the queen allows the pawn check, and stalemate), and just like in the last variation, again white has five checks but since the black king is not on e5 black can capture the queen.  This only allows two checks -- one where black cannot capture the queen (6. Qf4+), and one where the capture would put the black king back on e5 (6. Qe5+).  We already know from above that 6. Qe5+ Ke7 allows black to avoid the stalemate, so we only need to calculate:  6. Qf4+ Ke7 (looks best; 6…e5?? 7. Qxe5+!; and 6...Kc5 looks good for black too, but white still has lots of check while after 6…Ke7 white very quickly runs out of safe checks) 7. Qg5+ (only safe check) Kf7!, and now white has no more checks.  White can capture the bishop, and perhaps a rook as well, but this is still completely won for black and white still has too much mobility to try for stalemate.

So all of white’s move 5 ideas failed to force checkmate or force a draw, so let’s back up a move and look at white’s other move 3 option, after 1…Kxf4 2. Bg5+ Kxg5 (only) 3. f4+:

3…Kh4! (threatens …Rh3#) 4. Qe7+ (only check) Nfxe7 5. f5 (only) Rh3#

After our first candidate move (2. Bg5+), white cannot force mate and cannot force a draw but since he has evaded checkmate so far and is in a position to capture some black pieces (in the variation after 5. Qe3+), we’ll make this our KOTH.

Only seven more checks to go!!  Deep breath…and moving on to the next most forcing check:

1…Kxf4 2. Qe5+ Kxe5 (only), and here white has three checks but one of them is the most forcing (allowing only one reply), 3. f4+ Kxf4 (only), and we are one step closer to stalemate.  We only need to get rid of our overly-mobile bishop using checks, of which we have two:

If 5. Bd6+ Ke3 and white will soon run out of checks, and will lose.  That leaves us with one last check in the variation:

If 5. Bg5+ Ke5 (forced, 5…Kxg5? is stalemate) 6. Bf6+ Kd6 (forced, 6…Kxd6? is stalemate, and 6…Ke5 repeats) 7. Be7+ Kc7, white just needs to keep checking and now allow the black king to get to c5 or b6, so 8. Bd8+ Kb8 9. Bc7+ Ka7 (only) 10. Bb6+! Kb8 (not 10. Bb8+? Kb6!, and black can get to a light square and escape the checks) 11. Kb8 Bc7+, and although we can’t force the black king to capture our last mobile piece which would force stalemate, repeating the position is black’s only way to not capture the bishop, which is good enough for the draw!

Normally we would note the drawing option, and then continue calculating the other six checks.  But since a draw is really all we can hope for from the starting position, there is no need to keep calculating!  Here is our final chart:

Conclusion:  So this process has shown us that white has several candidate moves to consider in the initial position, and if we follow the path of the most forcing moves first we are able to find the forced draw!  Black has no say in the matter, and his only choice is whether to allow draw by stalemate or repetition!

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 one of the basic defensive ideas (from Idea 1-4).

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