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Consider the following chess variant:

  • Black can, once per game, make two moves in a row (the second move may not capture the King)
  • To compensate for this advantage, Black gets a material handicap
  • Otherwise, the standard rules of chess apply

The question is, approximately what material handicap would be needed for the game to become roughly balanced? It is clear that making two consecutive moves, even only once per game, is a tremendous advantage. My guess is that at least a Queen handicap is necessary, since it is trivially easy to capture White's Queen with two consecutive moves once the pieces are out.

Has this chess variant been studied before?

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    +1 Very interesting variant, but I doubt it would be possible to answer this without making speculations. – Wes Apr 2 '14 at 18:02
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    I doubt that will work either, because chess programs need evaluation functions. How will you evaluate a position if you know Black still has the extra move option? – Wes Apr 2 '14 at 18:10
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    Monte Carlo Tree search engines do not use (at least do not necessarily need) an evaluation function. They work by playing out thousands of random, complete games and deciding on a move based on the worst outcome they encounter. The only terminating condition in this case would be either draw or checkmate, which is unchanged for this variant. – user2659 Apr 2 '14 at 20:55
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    I don't know the answer to your question, but there is a simple way to make the game fair: Before the start of the game, have an auction where the players bid how much material they are willing to give up for playing with the black pieces. – Dag Oskar Madsen Apr 3 '14 at 14:31
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    @Wes: You don't need any assumptions about the quality of the sample. The whole point of Monte Carlo methods is that you sample randomly and use the average outcome to guide you, invoking the law of large numbers. If a move leads to random games where you get checkmated 90% of the time, it's probably not a good move. – user2659 Apr 3 '14 at 16:57
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The question can never be answered in a general fashion. Every move has its own perks and advantages. The major variables are these:

Is the same piece allowed to move twice or can black move two pieces once?

Are captures allowed? With just one move of the king's pawn already made, it is possible for any party to capture the opponent's queen within two moves. (Or put them in a position where it cannot escape capture in the next few moves). Here the price for two moves is AT LEAST a queen (since the two moves party would not only have captured the queen, but also invaded inside the enemy ranks).

Starting from midgame, two moves can easily put the opponent in a mate-in-x position where they cannot avoid mate. For example, if one has several mating combinations available, there can be no possible compensation to that!

All in all, I think the option of two moves can/should be made available only in the opening and the price is the queen. It is disastrous and potentially game-losing to allow the opponent double moves in the middlegame or endgame and there can be no compensation to that.

  • You state that there can be no compensating mating, but if you give up all your material then you cannot mate at all... – hkBst Aug 5 '17 at 14:43
0

My feeling is that a queen would be too much.

My reasoning is that without a queen it is very unlikely that the double move will ever lead to a winning attack. So at one point the double move will have to be used to "win" the queen, but if white takes care to always protect the queen this will probably lose some material.

Something materially equivalent like both rooks strikes me as better, because it doesn't impede blacks dynamical chances in the same way. Possibly rook+knight or rook+bishop would be even more balanced.

-3

In most opening gambits, a pawn is worth two tempi(Two moves). So I guess that a pawn would be fine. To be more precise, the f pawn. I think that is the most logical way.

But yet there remains a problem. I can mate you like this:

  [Title "White to move"]
  [fen "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

  1.e4 e5 2.Bc4 Bc5 I use the move now 3.Qf3 h6 4.Qxf7#

I used h6 as a waiting move to show that a double move is made.

In a similar way, a player can trap or take a big piece, such as a queen.

So the rules so far:

  1. White(Or black) lacks his f pawn.
  2. The person with the right to double move cannot mate. If a mate is inevitable, he cannot use the double move.
  3. The person with the right to double move cannot take a piece. If taking a piece is inevitable, he cannot use the double move.

About check now. I do personally think that if you are checked, the double move doesn't count, so:

  1. The person with the right to double move cannot check. If a check is inevitable, he cannot use the double move.

     [Title "White to move"] 
     [fen "rnbq1rk1/pppp1p1p/5BpQ/4p3/4P3/8/PPPP1PPP/RN2KBNR w KQ - 0 1"]
    

But there are also positions like this. So this idea comes up:

  1. Right after the double move, the non-double move player can exchange one of his pieces for a piece of equal value. You can exchange a bishop for a knight. You cannot exchange say, two rooks for a queen and pawn.

So I think that this is the best way to answer your question.

Hope it helps.

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    I don't understand your answer. Up to the first line, you stand great, but then you digress and simply provide different rules for the game. – Pablo S. Ocal Sep 20 '14 at 20:57
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    I use reasoning to support what the first sentence clears out. Please reread it. – MikhailTal Sep 21 '14 at 17:40
  • You prove that in the chosen opening (1.e4 e5 2.Bc4 Bc5??) Bc5 is a losing move. This is a consequence of allowing White the double move (the question is about Black having a double move) and it does not follow that the rules need to be fixed to make Bc5 a good move... – hkBst Aug 5 '17 at 14:50

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