From: kleber@husc11.harvard.edu (Gwydden)
Newsgroups: rec.games.abstract
Subject: Re: defects in abstract games
Date: 2 Jan 93 20:20:17 GMT
Article-I.D.: husc.kleber.726006017

Stephen L. writes:

>                                                      The no repeats rule
> can be used to create the ko situation and eliminate draws, or it can be
> used as a way to define a draw.  When is one preferable over the other?
> Would Chess be 'improved' by eliminating draws?  

Eeek!  By adding a no-repeat rule?  Say you get to a king-vs-king-and-bishop
position, which is currently a draw, since there's no way for either
side to give mate.  Then if you institute the no-repeat rule, you keep
moving these three pieces around until one player cannot move without
ending up in a previously-seen position, of which there are only about
112,000 so it shouldn't take that long to play out or record, only about
31 hours at a second per move if they actually get to all the positions,
at which point you need to appeal to a new rule about what happens if
someone doesn't have a legal move, which used to result in a draw too...
somehow I suspect this isn't what you intended :-).

Personally, I don't really mind the no-repeat kind of rule, and I'm
coming at least in part from the mathematical elegance side of things.
The chess solution, which essentially says an infinite loop is a legal 
end to the game but isn't a win for either player, is too generous--
if I had my druthers, I'd make an infinite-loop at best a double-loss,
and possibly somehow a "dishonorable loss"?.. but that's not really part
of the rules, I guess, and it still leaves unanswered the quesiton of
which player decides to break the cycle.

I still think "mental jujitsu" has a very low flaw-count.  Description:
played with three suits (say no hearts) from a deck of cards.  Each
player gets a single black suit; the diamonds are shuffled (interesting
questions, what if they are in a prearranged order?... my mind boggles
at the thought) and turned over one at a time.  Each player choses a 
remaining black card from his hand and both reveal simultaneously;
whichever played the higher card gets to "keep" the diamond they are
bidding over.  Discarded black cards are left face up (ie your opponent
knows exactly the cards in your hand), and your "score" is the number of 
diamond points you got at the end (numbers are themselves, J=11,...,A=14).
Ties go to no one (or are split, if you like; irrelevant).

Flaws?  Well, the fact that 13 cards per suit is arbitrary, and I'd
prefer it if the cards were numbered 1..13 instead of 2..14, but ace-high
is so natural it's hard to shake.  I actually like the fact that the
diamonsd are shuffled, since it makes any attempt at an ideal strategy
probabilistic; some people's definition of an "abstract game" wouldn't
allow for this-- ah well; they can play the verison where the cards are
prearranged.  (But if rules specify an order, that's a flaw-- I guess you
could shuffle them but spread them all out face up so you know the order
for this game; I like my normal version much better, though.)  For the
verisons where a suit contains 1, 2 or 3 cards, there is a no-loss
strategy, but for the 4-card verison the game is already hard... I
haven't programmed a computer to play it (neural net time, anyone?)
but I like the idea.  Even storing a complete strategy for a 13-card
game (which would have to be probabilistic, to have any chance, since any
known predetermined strategy loses to play-one-more-than-it) would
require a huge amount of storage, though, so programming it is daunting.

Have other people played this?  Opinions, anyone?  Starting up an
email game of it owuld require some trapdoor cyphering, kind of like
a coin-flip-over-email, to get the simultaneous revelation, but it
could be fun...

--Michael Kleber                 I don't have an overactive imagination...
  kleber@husc.harvard.edu        I have an underactive reality...   --EG
Newsgroups: rec.games.abstract