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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. – NM Wesley Falcao Apr 02 '14 at 18:02
  • One could program the variant into a computer and do a Monte Carlo Tree search, which should give a pretty good idea of how the balance is. I must admit, though, that I'm a bit too lazy and inexperienced with chess engines to attempt that :) –  Apr 02 '14 at 18:05
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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? – NM Wesley Falcao Apr 02 '14 at 18:10
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    @Wes some sort of "double move" wrapper can be written around an existing engine to handle this sort of situation. –  Apr 02 '14 at 19:20
  • @RauanSagit but just how exactly will you evaluate the position? The evaluation function is unknown as of now, because there are no "masters" in this variant of the game yet. – NM Wesley Falcao Apr 02 '14 at 19:49
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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. –  Apr 02 '14 at 20:55
  • My point is, how do you know you're working with a good sample? In regular chess, if you take the games of all top chess programs or grandmasters, you know you're working with a good sample. But here, how will you know the quality of the random games you select? – NM Wesley Falcao Apr 02 '14 at 21:28
  • @Wes my thought was that the "double-move wrapper" would feed the same position plus one extra move to a regular engine. The list of plus one extra move would probably have to be exhaustive (i.e. include all possible moves for a given position) in the very first version of the wrapper. –  Apr 03 '14 at 11:03
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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 03 '14 at 14:31
  • @RauanSagit the engine can surely calculate all moves with the wrapper, but how does it evaluate the position? Good for White or good for Black? By how much? We don't have good information about how to assess the position if Black has an extra move at any point. Consider king and pawn endgames - normal evaluations might be a draw, but maybe black's extra move makes it completely winning at some point. It's "unknown" or "unclear" evaluation, which doesn't help the machine. – NM Wesley Falcao Apr 03 '14 at 14:52
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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. –  Apr 03 '14 at 16:57
  • @DagOskarMadsen: Your proposal makes the whole system, i.e. the auction plus the chess game, a fair game in the sense of game theory. The chess game itself, however, will not necessarily be fair, even if both players were satisfied with the outcome of the auction. –  Apr 03 '14 at 17:00
  • @limulus - The way I understand it, the MC method is appropriate where the next step in the tree is random. In chess, the next step is not random, but determined by the value function of the player - are you sure an MC method without an evaluation function will provide a realistic picture? My gut feel is that the results of the MC simulation will be skewed by countless positions that will never occur in a real chess game. – firtydank Apr 04 '14 at 13:22
  • Queen is too much, black should do two moves to take queen in best case, but then, black just became equal in material, on the other hand white is two move ahead, one because is white, second because black used one of his moves to get equal to white, so I think knight + rook is more reasonable. – Saeed Amiri Apr 07 '14 at 19:22
  • I do not fully understand the "Black can, once per game, make two moves in a row" part. Can Black only open the game this way like 1. e4 d5 and then play dxe4 ? Or Black can play twice anytime he wants if he still has this option available ( you said he can do this only once in the game ) ? Can you please clarify? Thank you. Best regards. – AlwaysLearningNewStuff Apr 20 '14 at 13:04
  • Black would easily be able to trade a Knight or Bishop for the White Queen. Thus, White would need about 2 pieces extra. Or maybe just an extra Rook. Basically, it would be N+N+B vs Q, or B+R vs Q. – Tony Ennis Dec 30 '14 at 23:15
  • @DagOskarMadsen This is not obviously fair actually. If one could prove that X amount of material gives you advantage, but any material more gives disadvantage, then the person who bids first has an advantage. – Cruncher Jan 21 '15 at 17:36

3 Answers3

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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.

Youstay Igo
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  • 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 05 '17 at 14:43
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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.

BlindKungFuMaster
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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.

MikhailTal
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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 05 '17 at 14:50