Hello Starship Captains,

Martian Chess rules can be found here. It is a neat strategy game that can be played by two or more players on an appropriate board. In this article, I'd like to talk about the possibility of a draw and how to avoid it.

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Martian Chess' game end condition states:

"The game ends as soon as one quadrant is totally empty."

The question I'd like to ask first is this: will the game always end? If so, then there is no problem, but if not, I'd like to repair the rules.

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Here is an example of a game that does not end (assuming optimal play).

Consider a 2-person endgame with 3 queens. One of the player is 1 point ahead of the other, but has 2 queens, while the other player has the third. Will this game end? If none of the queens can be captured, I believe the game will not end under optimal play. The reason is that the player who is behind, will not want to end the game, because he will lose. The player who is ahead can not end the game, because if they move one of their queens to the other quadrant, then the other player will also move one of his queens to the other quadrant. A queen can not be captured with best play (but this is not a totally trivial statement). So, after every two moves, the situation is basically unchanged and the player ahead still has two queens and the player behind still has one queen.

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I came across this situation in one of my games and both of us realized that the game could go on forever. In other words, the game would never satisfy the game end condition. Who wins?

The player who is behind is dragging the game forever. Should that count to his advantage? The simple answer is 'no'. By dragging the game, no points are being made. So, ultimately, the score is unaffected by this play.
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Note that the rules do not specify who wins in case of such a draw. At first we thought that if we both agree that the game will never end, then we can stop. HOWEVER, why would the losing player agree? You see, the rules do not specify that any player has to agree . . .
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Therefore, I propose to change the following

GAME END CONDITION for Martian Chess:

- The game ends as soon as one of the quadrants is empty OR if after 25 moves (of all players) no piece was captured.

To accommodate for this, we also need to adjust the

WINNING CONDITION for Martian Chess:

- The player with the most points wins. In case of a tie: 1. if an empty quadrant resulted, then the player who moved last wins OR 2. if the game ended after 25 moves and no empty quadrant resulted, the player who captured the last piece wins.

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Note. In effect, if 25 moves have been played and no empty quadrant resulted, then the last capture was the the last "move" that counted.

Note. I realize that the proposal for 25 moves is arbitrary, but a lower number like 10 seems too low. It is also loosely based on an analogy with chess, which has a 50-move rule and starts with 32 pieces. 2-player Martian Chess, there are 18 pieces, hence the number of moves by analogy should be (50/32).18 = 900/32 ~ 28. However, if future analysis shows that winnable endgames require more than 25 moves, I propose to allow these endgames to be played and not be cut off by the rules like in chess. Let anybody with such information present the endgames and how to proceed to win in more than 25 moves!

Note. Perhaps this strange situation will not happen that often in a game with more than 2 players, but we can still conceive of an endgame where everybody has two queens and prevents any of the other players to end the game. Whether this will happen likely or not, the adjusted rules now specify when the game ends.

Note. Even if the scores are equal before the game ends, an optimal strategy could be to drag the game. E.g., in an endgame where both players have two queens. In this case, none of the players will want the other player to end the game, because of the (original) winning condition.

Note. The 50-move rule in chess states that a game can be called a draw by either player as soon as 50 moves have been played without moving a pawn or a capture. It was at one time believed that no longer winnable endgames existed. But ongoing computer search showed much longer winnable endgames. In 2008 the record was 517 moves (assuming optimal play by both sides) to make a piece capture or exchange that achieves a simpler and more obviously winnable sub-endgame, for a particular position involving a queen and knight versus a rook, bishop, and knight. In 2009, this record was improved to 545 moves. (See Wikipedia.)

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Please leave any remarks, thoughts or questions on this incorporation of a 25-move rule for Martian Chess.

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Replies to This Discussion

FWIW I started a discussion about this a while back at BGG:

https://www.boardgamegeek.com/thread/530254/do-2-queens-1-drone-lea...

I play sometimes at SDG and this sort of endgame with few pieces comes up somewhat often indeed. But to my surprise there often seem to be sneaky ways that the person ahead on points manipulates the situation to nonetheless end the game, despite my attempts to keep drawing it out. Or else I am just a lame player (quite possible!) :)

E.g. http://superdupergames.org/?page=archive_play&gid=28819&idx=48

I'm interested whether I (blue) simply bumbled, or whether wil (red) indeed successfully forced termination in games like this.

Either way, I agree that even if termination is force-able with 3 queens, nonetheless with casual players the game will draw out forever. I suppose it's a question of taste whether this is a problem, or whether it's fine for players to simply agree to a tie in that case!

Hi Russ, 

This is really interesting. I replayed the whole game and initially thought that you made a blunder, and I backtracked the game to an earlier point. But I noticed that once you were more than 3 points behind, and the end game with 3 queens started, you were doomed. The reason is as follows.

In order to prevent a similar maneuver, you would have to prevent Wil from occupying either d5 or a5. But you can't, because he can place his queens in any column and on any field on his quadrant. Notice that you can't capture his queen, because you will lose (being behind more than 3 points). So, he will maneuver both his queens to d5 AND a5 (but this is not even necessary), and then put one of his queens in front of the other on your quadrant to force you to take one of his queens (or lose by being captured yourself). After that move, he has only one queen and can end the game and win.

However, as a result of this endgame, I noticed that there is a difference with my scenario. You were MORE than 3 points behind. In that case, the other player can simply attack (threaten to capture) any of your queens. Since you don't want to end the game, you will move out of the way.He is not interested in capturing the queen you have, but will have you capture his! (Sneakiest!)

But if you are 3 points or less behind, then this maneuver would not work. You would be able to win by capturing his queen. Because even if it is a tie, you win by moving last. This does not prove that another maneuver is not possible, though.

I looked at the endgame mentioned on BoardGameGeek. (Thanks for the link!) But I couldn't go over all the variations. It seems, however, that the situation can be extended indefinitely, as long as the player who is behind will always move in such a way as to either cover a4 or d4, or if not, then the other player can not move to both. I've tried a lot of variations, and I couldn't see how the stronger player could force the game to end. As a result, I thought it more interesting to share this challenge with other Starship Captains . . . 

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