Thursday, April 18, 2013

Dilemma 14: Dilemma Chess

Dilemma Chess
Dilemma chess is chess plus deterrence, with a dilemma payoff matrix. The board, pieces and moves are the same as in regular chess; but the game is allowed to end with mutual checkmate, or “truce”; a shared outcome which is worth more than draw but less than win. The payoff matrix is:

                                     B
(A,B) outcome        checkmated         not checkmated  
________________|____________________|___________________
                |                    |                  |
  checkmated    |   (truce, truce)   |    (lose, win)   |
A             __|____________________|__________________|
                |                    |                  |
not checkmated  |    (win, lose)     |    (draw, draw)  |
                |____________________|__________________|

Thus a dilemma. If competitive chess is the king of games, then dilemma chess is the queen; for truce opens up a new dimension of play; namely, between competition and cooperation.
The basic innovation in dilemma chess is to allow the “reply” move. The reply move is a final move by the player whose king has been captured. If the other king can be captured in the reply move, then the first capture is “deterred”. You may not capture if your check is deterred. You may move into deterred check, or respond to check with a deterrent. You may not cancel your opponent’s deterrent without also escaping check (no “forced exchanges”).
Mutual deterred check is “tryst”; both sides can capture and retaliate. Truce is mutual assured check (MAC), or inescapable tryst; one move after truce, both sides can still capture and retaliate. In tryst, capture is deterred; the other player could capture next move, but would suffer retaliation.

I first found tryst on this board, from Escher’s Metamorphose print:

          a      b      c      d      e      f      g      h  
       ______ ______ ______ ______ ______ ______ ______ ______
      |      |      |      |      |      |      |      |      |
     8|  BK  |      |      |      |      |      |      |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     7|  BP  |  BP  |      |      |      |      |      |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     6|      |  BB  |      |      |      |      |      |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     5|      |      |      |      |      |      |      |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     4|      |      |      |      |      |      |  BN  |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     3|  WR  |      |      |      |      |      |      |      |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     2|      |      |      |      |      |      |  WP  |  WP  |
      |______|______|______|______|______|______|______|______|
      |      |      |      |      |      |      |      |      |
     1|      |      |      |  WQ  |      |  WR  |  BQ  |  WK  |
      |______|______|______|______|______|______|______|______|

In zero-sum play, the next moves are Rf1xg1, Ng4‑f2; Black wins by a smothered mate which is also a queen fork. (How Escherian!)
Now consider this:
     Qd1‑d8 tryst    Qg1xf1 tryst
     Qd8‑c8 truce

Black took the rook instead of the queen because then White would have won by taking the black queen with his king. White was briefly in checkmate, but was able to complete the truce in time; otherwise Black would have left check and declared victory. I call this endgame Escher’s Tryst, in the memory of a master of paradox and symmetry.

Escher’s Tryst employs a “delayed deterrent”; one side’s king is momentarily trapped, but has a move to deploy a deterrent. This shows how deterrence strengthens the king; for under deterrence, the king cannot be taken. With deterrent and at close range, the king is probably the most powerful piece on the board, being unstoppable, omnidirectional, and invulnerable. It is free to walk straight up to the other side’s pieces and capture them with impunity.
I call this the “brave king” phenomenon. It is a paradoxical kind of safety which should not be overplayed; the other player may lure your king into the midst of his pieces and then nullify your deterrent. Nonetheless, in dilemma chess the king can be far more active than it is in competitive chess. Consider this tryst:
  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |  WR  |      |  BP  |  BK  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |      |  WK  |  BP  |      |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |      |      |      |  WP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|  BP  |      |      |      |  BQ  |  WP  |      |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
    a      b      c      d      e      f      g      h


Ke6xPf6 dt ch    Qe3xPf3 try
Kf6xPg7 try      Qe3‑d3  try
Pg4‑g5  try      Qd3‑f5  tr 


     The first move was into a deterred (or “pinned”) check. White’s king was in check, but the checking piece was pinned; White’s king could not be taken without exposing Black’s king to countercapture.
The last two moves were agreed on; a negotiated truce.


  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|      |      |  BR  |  BR  |      |      |  BK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |  BQ  |  BP  |  BP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|  BP  |  BP  |      |      |  BP  |      |      |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |  WP  |  BB  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|  WP  |      |      |      |  WP  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |  WQ  |      |      |  WN  |  WP  |  WP  |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |  WR  |  WR  |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h       


     Ne2‑f4         Rd8xRd1 ch
     Rc1xRd1        Rc8‑d8    
     Nf4‑h5         Rc8xRc1 m 
     Qb2xPg7 tr        

This game shows a “momentary mate”. Black briefly had White
cornered, forcing him to deploy a last-minute deterrent.

  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|      |      |  BR  |      |      |      |      |  BK  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |  WQ  |      |      |  BP  |  BP  |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |  BN  |      |      |  BR  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |  WR  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|  BP  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |  BQ  |      |      |      |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  WB  |      |      |      |      |  WP  |  WP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |  WR  |      |      |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h


  ...               Qd3xPh3!
  Rb1‑b8     Rg6xPg2ch
  Rb8xRc8try          Nd6xRc8ch
  Rd5‑d8try            Rg2‑g6try
  Kg1‑h2try            Qd3‑d6 tr

Combinations and sacrifices in pursuit of truce. Black’s Rook and Queen retreated before the White King’s advance.






  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|  BR  |  btm |      |      |      |  BR  |      |  BK  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |  BB  |      |      |  BB  |      |  WR  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|  BP  |      |  BQ  |      |  BP  |      |      |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |  BP  |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |  WP  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |  WP  |  WP  |      |  WK  |  WN  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  WP  |      |  WQ  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |      |  WR  |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h


  Qc2-h7 m             Qc6xNf3 try
  Ke3‑d2 ch            Qf3-f2 try
  Kd2-c1 ch            Qf2-e3 try
  Kc1-b2 ch            Rf8-f2 try
  Kb2-b1 ch            Qe3-d3 try
  Kb1-c1 ch            Qd3xPc3 try
  Kc1-b1 ch            Qc3-d2 truce


Persistent trysting persuades a “dodging king”. Note that the White King never took the Black Queen, lest the Black King take the White Queen.


Purely cooperative chess play permits the “fool’s truce”: a quick truce which ignores obvious wins. A fool’s truce is a fool’s mate for two fools.

1. P-K4         P-Q4
2. PxP PxP
3. K-K2        K-Q2
4. K-K3        K-K3
5. Q-R5        Q-N6 ch
6. K-K4        Q-Qb6
7. Q-N6 ch   K-K4 truce

1. P-K3         P-K3
2. Q-R5        Q-R5
3. K-K2        K-K2
4. K-B3        Q-R6 ch
5. K-B4        K-B3
6. Q-R6 ch   K-B4 truce

1. P-K4         P-Q4
2. PxP PxP
3. Q-N4        B-B4
4. K-K2        BxP
5. Q-B8 ch    Q-K5 truce

1. P-QB4      P-QB4
2. Q-R4        Q-R4
3. QxQP ch   QxQP try
4. QxB try     QxB truce

The next few pages are a gallery of dilemma chess positions and play.

  ______ ______ ______ ______ ______ ______ ______ ______
 |                    |      |      |      |      |      |
8|   white to move    |      |      |      |      |      |
 |______ ______ ______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |      |  BB  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |  BP  |      |      |      |  WP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |  BP  |      |      |      |      |  BP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  BP  |      |  WB  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|  BK  |  WK  |      |      |  BR  |      |  BB  |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h
  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| wtm  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |      |      |  BQ  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |  WR  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|  BP  |      |  BN  |      |  WK  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |  BK  |      |  WP  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |  BN  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |  WQ  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h














  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| btm  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |      |      |  WR  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |  BP  |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |  WP  |      |      |  BP  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |      |  WK  |  BK  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |      |  WP  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |  BR  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h


  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| wtm  |  BN  |      |  BR  |      |      |      |  BR  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |  BP  |  BQ  |  BP  |  BP  |  BB  |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |  BP  |      |  BP  |      |      |  BP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|  BP  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|  WK  |  BK  |      |  WP  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |  WP  |      |      |  WP  |  WN  |  WP  |  WB  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  WP  |      |  WP  |      |      |  WP  |      |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |  WN  |  WB  |  WR  |  WQ  |      |      |  WR  |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h

  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| btm  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |  BP  |      |      |  WQ  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |      |  BK  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |  WK  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |  BQ  |      |      |  WP  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h
  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| btm  |  WQ  |      |      |  BK  |  BR  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |  WR  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |      |      |      |      |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|  BP  |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |  WP  |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |  WP  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |      |      |  BB  |  WP  |  WP  |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|  BQ  |      |      |      |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|

  Black to move. If it were white to move, then:
  Kf1‑g1 (brave king);  Qa1‑d1, truce.




  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8| wtm  |      |      |      |      |      |  BK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |  WR  |      |      |      |  BP  |      |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|  BP  |      |      |      |  BP  |  BB  |  BP  |  WB  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |      |  WP  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |      |  WP  |      |      |      |  WP  |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|  BR  |      |  WK  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
Rb7‑b8 try   Bf6‑c3 tr

  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|  BB  |  wtm |      |  BR  |      |      |  BK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |  WR  |  BB  |  BP  |  BP  |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |      |      |      |  BP  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |  BP  |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |  BP  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |  WB  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |  WP  |      |      |      |  WP  |  WP  |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|
Rd7xBd7     Rd8‑d1 mate
Rd7‑d8 truce


  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|  wtm |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |  BP  |      |      |  WQ  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|  BP  |      |      |      |      |      |      |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |      |  BP  |      |      |  BK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |      |  BB  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|  WP  |      |      |      |  BQ  |      |  WK  |  WP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|      |  WP  |      |      |      |  WR  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h



White, in tryst, to move.           

            Kg3-f3 try           Kh5-f4 try  
            Qe7-f6 truce              
                                 
A summit meeting of the powers.





  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|  btm |      |      |      |  BR  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|      |      |      |      |      |  WR  |  BK  |  BP  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|  BP  |      |      |  BP  |      |      |  BP  |  WN  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |  BP  |  BP  |      |      |      |  WP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |      |      |      |      |      |  BQ  |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |  WP  |  WP  |      |      |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  WP  |      |      |      |      |      |  WQ  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|
    a      b      c       d      e      f      g      h



Black, in check, to move.

       ...    ch            Re8‑e1 try  
       Qg2‑a8 try     Qh4‑g3      
       Kg1‑f1         Qg3‑g1 truce 


Both traps snap shut.






  ______ ______ ______ ______ ______ ______ ______ ______
 |      |      |      |      |      |      |      |      |
8|  btm |      |      |      |      |      |  BR  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
7|  BP  |      |      |  BQ  |  BP  |  BP  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
6|      |  BP  |      |  BP  |      |      |  BK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
5|      |      |  BP  |  WP  |  BB  |  WP  |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
4|      |      |  WP  |      |      |      |  WK  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
3|      |      |      |      |      |      |  WP  |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
2|  WP  |  WP  |      |      |  WN  |      |      |      |
 |______|______|______|______|______|______|______|______|
 |      |      |      |      |      |      |      |      |
1|      |      |      |      |      |  WR  |      |  WQ  |
 |______|______|______|______|______|______|______|______|
    a      b      c      d      e      f     g       h


     Black to move. Note that PxK is deterred.


    ...         Kg6xf5 try
    Qh1‑f3 try  Kf5‑f4 try
    Kg4‑h5 ch   Qd7‑f5 try
    Kh5‑g6 try  Rg8‑h8 truce.     


     Two courageous kings!



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