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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