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Convexifying the choice set, an ongoing series
There is a new proposal for chess:
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Slight Win: A player wins slightly if any of the following conditions hold:
d. The opponent offers to concede a slight win and he or she agrees,
e. He or she stalemates his or her opponent.
f. Without making a move, a player calls the arbiter and proves that as a result of her opponent's last move, the same position has occurred thrice.
The player that wins slightly gets 4/6 points, and the player that loses slightly get 2/6 points.
Why not go further and allow the players to bargain for a split sum of any magnitude? "I offer you .5713 to stop playing now..."
Posted by Tyler Cowen on April 25, 2009 at 09:53 PM in Games | Permalink
Comments
What's wrong with 2/3 and 1/3?
Posted by: Andy at Apr 25, 2009 10:07:27 PM
I think that allowing the players to bargain would lead to a test of bargaining skills, rather than chess skills.
Posted by: Will at Apr 25, 2009 10:28:51 PM
Just make stalemate a win (loss) not a draw. The game would be radically changed.
Posted by: jn at Apr 25, 2009 10:40:17 PM
I read somewhere that chess becomes simpler to analyze (in expectation) if players toss a coin to decide who moves next.
Posted by: Unit at Apr 26, 2009 12:39:17 AM
Really? My brother and I made this up and he was able to beat me more frequently than usual. I've never heard of it before.
Posted by: Ann at Apr 26, 2009 12:46:24 AM
"Why not go further and allow the players to bargain for a split sum of any magnitude? "I offer you .5713 to stop playing now...""
Because bargains lead to peaceful solutions and peaceful solutions aren't fun to watch.
Posted by: Tony at Apr 26, 2009 1:21:07 AM
this sounds like a problem of points.
http://en.wikipedia.org/wiki/Problem_of_points
Posted by: kenny at Apr 26, 2009 1:46:00 AM
Why must it be zero-sum?
If you want to discourage draws, make them 1/3 - 1/3. Or make a slight outcome 1/2 - 1/3.
Posted by: Douglas Knight at Apr 26, 2009 2:26:27 AM
It's an interesting idea. I think it actually hurts on the spectator/sponsorship side, though, as games that would previously be agreed draws turn into an extra 2 hours of endgame jockeying for an extra 1/6 of a point (Re: Andy, it's easiest to keep everything in the least common denominator if we're allowing 1/3 and 1/2 points.) Also, while grandmasters will be more likely to make "mistakes", a mistake that turns a draw into a slight loss is going to be very hard for the amateur spectator to see.
The fundamental effect that changes the game is noted in the article, that now K+P vs. K is at worst a slight win for the K+P, making endgames a lot more perilous for the defending side. I'm not sure whether I like the idea of 3 position repetition becoming a slight loss for the side that forces the repetition.
Posted by: Brian at Apr 26, 2009 2:32:18 AM
Hmm.. Why not more bughouse? That would take care of the existing opening theory... It detracts from deep analysis and computers would be 100x better than humans, but it would be interesting to see how the best players play a hyper-tactical game. They are also more fun to watch.
Posted by: agent00yak at Apr 26, 2009 2:37:20 AM
Why not just go all the way and use a double-or-resign system like Backgammon?
Posted by: Grant Gould at Apr 26, 2009 6:11:40 AM
"Why must it be zero-sum?
If you want to discourage draws, make them 1/3 - 1/3. Or make a slight outcome 1/2 - 1/3."
In other words, use a 3-1-0 scoring system, where wins are worth three points, draws one, and loses zero. This has been done at major tournaments before, for example, Bilbao 2008. As far as I can tell, it does not significantly reduce the number of draws.
Posted by: . at Apr 26, 2009 6:18:05 AM
Great. Having screwed up finance and economics beyond rescue, you guys now want to screw up chess too.
Posted by: capitalistimperialistpig at Apr 26, 2009 7:58:46 AM
Merely changing the scoring system will not turn a drawn position into something else, and will thus not significantly reduce the number of draws.
However, what this is proposing instead is a small change in the rules of chess, such that a drawn position is no longer a drawn position.
In the former case, there is little point and much tedium in slogging through a drawn game hoping that one side will blunder; in the latter, it may often make sense to play out the game or for one player to "slight-resign".
Posted by: anonymous at Apr 27, 2009 12:22:05 AM
Maybe chess needs to borrow the possibility of bluffing from poker.
How about this: when a pawn reaches the last rank, the player cannot choose the piece it is promoted to; rather, this should be pre-selected at random before the game and known only to the player himself, not his opponent. The pawn might become a queen, a rook, a bishop, a knight, or it might simply vanish.
Or perhaps one randomly pre-selected non-king piece for each player is designated as a "land mine"... any piece attempting to capture it will instead itself be removed from the board. The identity of the player's land-mine piece will be known only to him or her, not the opponent. Yeah, I left my queen open to capture, so? Do you feel lucky, punk?
Posted by: anonymous at Apr 27, 2009 12:33:27 AM
Why not an infinitesimal "draw-plus" that counts as "more than a draw" for the plus winner if points are equal in the end of the tournament, but never counts as more than 1/2 points.
In the 2/3 scenario, two wins and a loss count the same as 3 slight wins, which would encourage almost-matched players to play for slight wins only, and never take risks to get a full win.
Posted by: Zamfir at Apr 27, 2009 6:24:27 AM
Changing the rules of games is an epic fail in and of itself.
Posted by: Sean at Apr 27, 2009 6:50:41 AM
Most of the games where a player "stalemates" his opponent, I can only presume, are ones that the player is already losing. The half-point, in this case, is already quite a reward for having escaped from the jaws of defeat.
Posted by: trostsky at Apr 27, 2009 4:49:36 PM
I read somewhere that chess becomes simpler to analyze (in expectation) if players toss a coin to decide who moves next.
Posted by: Dell Laptop Battery at May 18, 2009 9:13:19 AM
