No-Draw rules and puzzles, round 2

It was June 1, 2018, nine months after the historic inaugural meeting of FIDNDC.

Annie Australia: Ladies and Gentlemen, we meet again. It seems there are some practical problems with the No-Draw Chess rules we came up with at our first meeting. We are here to make some revisions, and to rescue this wonderful concept. First, Bob, could you please read the minutes of that first meeting?

Bob Bosnia: Complete details of that meeting are available here, so a brief summary should suffice. We disallowed draws by agreement, triple occurrence, and the 50-move rule, and we prohibited a player from playing any move that repeated a position which had occurred earlier in the game. We defined a strong stalemate as a position in which the player is stalemated, and would still be stalemated even if repetitions were allowed, and a weak stalemate as a position in which the player is stalemated, but would have a legal move if repetitions were allowed. We declared the game lost by a player who strongly stalemates his opponent, but won by a player who weakly stalemates his opponent. We developed parallel definitions for strong checkmate and weak checkmate, but with the consequences reversed, i.e. a player wins if he strongly checkmates his opponent, but loses if he weakly checkmates his opponent.

Annie: Thank you, Bob. As I said, some problems have been discovered in the last few months. Most of these problems relate to dead positions, such as king versus king. As I’m sure you all recall, these are no longer draws. Instead, the players must play on until one player runs out of legal (i.e. non-repeating) moves. At that time, that player is weakly stalemated and loses.

Charlie Canada: What’s the problem with that? It gets rid of draws, doesn’t it?

Annie: Yes, but it often takes hundreds of moves for a weak stalemate to occur. This has caused games to be adjourned, with both players being paired as wins (since there are no more draws). There have even been attempts at adjudication, but it takes so long for the computers to figure out the theoretical result, even in king versus king, that many tournaments have still not been completed, months later.

Deborah Denmark: I guess that would be a problem, wouldn’t it? Maybe we should simply forbid a player from creating a dead position, just as we already forbid a repetition. If a player has no legal moves, other than one which creates a dead position, he is weakly stalemated and loses.

Ellen Estonia: Just a cotton-pickin’ minute. We’d be disallowing something that doesn’t exist. There is no such thing as a dead position in No-Draw Chess. Even king versus king eventually ends in a weak stalemate.

Fiona Finland: Hmm, true. I guess we should define a classically dead position as a position which would be dead in classical chess, i.e. a position in which no checkmate can ever occur, for either player, even with both players collaborating. The most common examples are, of course, K vs K, and K+N vs K, and K+B vs K. But there are others.

George Germany: So I guess it would be illegal to play a move which results in a classically dead position.

Annie: Correct. If a player has no legal move, other than one which results in a classically dead position, he is weakly stalemated and loses.

Bob: Grumble. This whole idea of disallowing classically dead positions bothers me. During the past few months, I have seen several No-Draw games where a player brilliantly sacrifices his second-to-last piece, creating a dead position, and then forces a weak stalemate just a few moves later. This beautiful concept will be lost to us now.

Charlie: I agree. Rather than disallowing classically dead positions, we should add a 20-move rule: Any player who creates a classically dead position has 20 moves to win the game, presumably by weak stalemate. If he fails to do so, he loses.

Deborah: Brilliant! If a player creates a classically dead position on move N, he must weakly stalemate his opponent (or strongly checkmate him, but that’s probably impossible) no later than move N+20. Otherwise, he loses.

Ellen: Now we’re getting somewhere. But if one player creates a classically dead position, then isn’t the other player doing the same thing, half a move later?

Fiona: Nope. The second player isn’t creating a dead position, he’s just following in the footsteps of the dead position created by the first player. Only the player who originally creates the dead position is under obligation to win within 20 moves.

Annie: It sounds as though we have pretty well perfected our idea. We’ll probably meet again in a few more months. See you then! (Bangs gavel.)


To summarize:

  • A player who strongly checkmates his opponent wins.
  • A player who weakly checkmates his opponent loses.
  • A player who strongly stalemates his opponent loses.
  • A player who weakly stalemates his opponent wins.
  • If a player generates a classically dead position, he must win (probably by weak stalemate) no more than 20 moves later, otherwise he loses.

Please enjoy the next three No-Draw puzzles, which follow the above rules.

Bill Smythe

Puzzle #1. See revised rules for No-Draw Chess in the top post. White to move and win:

Bill Smythe

Puzzle #2. See revised rules for No-Draw Chess in the top post. White to move and win:

Bill Smythe

Puzzle #3. See revised rules for No-Draw Chess in the top post. White to move and win:

Bill Smythe

Any (almost) black capture would result in a dead-position loss. You have the following:

  1. Kg2 Kb7, Kf3 Ka8, Ke4 Kb7, Kd5 Ka8, Kc6 (forcing the apparently losing Kxa7, but since that is the only legal move it is actually Kc6 that is the dead position losing move)
  2. Simple is Kg2 Kb7, Kh1 Ka8 (second time for this position), Kh2 Kb7, Kh1. Then Ka8 is a losing third repetition and Kxa7 is a losing dead position
  3. Simplest is Kg2 Kb7, a1=Q+. Then Kxa8 is a losing dead position while Kb6 and Kc7 are normal losses

After the queen is taken a black capture gets to a dead position. You just have to make sure the position isn’t already dead with a forced capture.
ba=Q+ and ba=R+ force Kxa8 and thus are dead position white losses. ba=B is also a dead position white loss. Thus you have ba=N. If black captures then black plays the dead position losing move. That means you have:
ba=N Ka7
Bc8 Kb8
Nc7 Ka7
Ba6 Kb8
Nb5 Ka8
Kb6 Kb8
Na7 Ka8
Bb7+ Kb8
Nc6#

Avoid Kg4 g1=Q+, Bxg1 as the forced Kxg1 means that white played the dead position move.
Do Bg4 g1=any (forced move), Bxg1+ Kg2 (Kxg1 is an optional and thus losing dead position move), Bf3+ Kf1 or Kh3 (Kxg1 is an optional losing move), Bxh1 and then get either the two K+2BvsK win or black making an optional dead postion losing capture.

You got those much too quickly. You’re getting into my mind.

One technical error:

Actually, according to the rules of No-Draw chess, the second occurrence, not the third, loses.

Bill Smythe

Another try is:
Bg3+ Kg1
Ke3 Kf1
Be2+ Kg1
Bg4 Kf1
Bh3 Kg1
Bf4 Kf1
Bh2 Ke1
Bg4

then
… Kf1
Be2+ Ke1
Bg3#

or
…g1=any
Bxg1 Bmove (other than f3)
Be2 any
Bf2#

or
… g1=any
Bxg1 Kf1
Bh2
which gives
… Ke1
Be2 any
Bg3#
or
… Bg2
Be2+ Ke1
Bg3#
or
… Kg2
Bf3+ (either forcing the dead position KxB or allowing white to play the decisive BxB)

but finally
… Bb7 (or other diagonal move)
Bh3+ Ke1
Bd6 Kd1
Bf5 Kc1
Ba3+ Kd1
and the king can’t be forced onto e1 at a time that white can follow that with Be2.

I don’t know if anybody will be able to find an improvement.