Convexifying the choice set, an ongoing series

by on April 25, 2009 at 9:53 pm in Games | Permalink

There is a new proposal for chess:

  • 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…"

Andy April 25, 2009 at 10:07 pm

What’s wrong with 2/3 and 1/3?

jn April 25, 2009 at 10:40 pm

Just make stalemate a win (loss) not a draw. The game would be radically changed.

Ann April 26, 2009 at 12:46 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.

kenny April 26, 2009 at 1:46 am

this sounds like a problem of points.
http://en.wikipedia.org/wiki/Problem_of_points

Brian April 26, 2009 at 2:32 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.

Grant Gould April 26, 2009 at 6:11 am

Why not just go all the way and use a double-or-resign system like Backgammon?

capitalistimperialistpig April 26, 2009 at 7:58 am

Great. Having screwed up finance and economics beyond rescue, you guys now want to screw up chess too.

anonymous April 27, 2009 at 12:33 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?

Sean April 27, 2009 at 6:50 am

Changing the rules of games is an epic fail in and of itself.

Dell Laptop Battery May 18, 2009 at 9:13 am

I read somewhere that chess becomes simpler to analyze (in expectation) if players toss a coin to decide who moves next.

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