On Mar 13, 5:18=A0pm, David Richerby <dav...@[EMAIL PROTECTED]
>
wrote:
> David Kane <davidek...@[EMAIL PROTECTED]
> wrote:
> > Imagine that I have an agreement with Mr. Richerby (both of us being
> > dishonorable people) so that whenever we reach a drawn position, we
> > agree to flip a coin and the loser throws the game.
>
> > We reach such a position, implement our plan, and I lose the toss.
> > Both of us are near the top of the tournament, so it is going to
> > cost me prize money today when I lose on purpose. =A0Sure, he will
> > gain a lot more than I lose, but that does me no good today. I don't
> > know the next time I will play him. =A0It could be years from now.
=A0I
> > don't know that the next time I play him whether there will be any
> > money on the line. I don't know that the next time I play him that I
> > will win the toss.
>
> You don't care when we next meet or what happens when we do. =A0It
> doesn't matter who you cheat with on any one occasion: all that
> matters is that, half the times you cheat, you win and half the times,
> you lose.
Sure you do. If I know that you are going to retire after my game is
over,
it would make no sense to abide by the coin toss. It only makes sense
to lose on purpose if you know that someone is going to do it for you.
Do I *really* know that I will win half the time if I cheat? Not in
the real world, I
wouldn't.
[By the way, I believe a not uninteresting variant of chess (even with
the current scoring) *would* be to resolve all ties by means of a
coin toss, hopefully delayed (say at the end of the tournament).
That would at least eliminate one of the motivations behind the
GM draw (certainty).]
>
> > I don't know that the next time I play him and win the toss with
> > money on the line, that he will keep his side of the deal and throw
> > the game to me.
>
> It's to everybody's advantage, in the long term, to cheat.
Hardly. Each time you cheat you are risking being caught and facing a
penalty.
People don't live in the "long term". They have a finite lifespan.
Suppose
that whatever value I get for a draw nets me $1 million. Am I going
to
throw that away (so that you can win $10 million) for some long term
advantage? Of course not. There might be nothing at all at stake in
our
next 10 games.
What is oddest about your line of reasoning is that you bring it out
to condemn alternate scoring systems but don't seem to grasp
that a similar cheating system is already present in chess. Why?
Because
wins don't have equal monetary value for both sides.
For example, you and are playing each other
in the last round of a round robin tournament. We are equally rated,
so you expect
1/2 a point. But you are near the top of the tournament. With a full
point, you will
either win or share first prize. On the other hand, I'm at the bottom
of the standings,
out of the money, so win, lose or draw makes no difference to me.
Rationally,
we should just negotiate a price for me to lose the game on purpose.
And while this may happen from time to time, it is not perceived as a
problem AT ALL (except for the draw version, already discussed)
>
> > What would more likely happen is a collusion of a different sort. I
> > will play aggressively with White to get an advantage. Suppose that
> > he sees a way to simplify into a drawish position where I have a
> > slight advantage but he can probably hold the draw. =A0That "draw at
> > best" line doesn't look so good if draws don't count as much. So he
> > uses his chess skill to come up with a different plan, based on
> > counterplay elsewhere on the board, etc.
>
> You seem to believe that some position, White has `an advantage' but
> Black can simplify to a position where White has only a `slight
> advantage' and can also produce `counterplay'.
You misunderstand. Black can chose a likely drawable line vs. one
that
is more uncertain but might have winning chances.
For example, Black can chose between two options: a simplifiying line
with
W=3D0, D=3D.9 L=3D.1 or a complicated line with W=3D.3 D=3D.3 L=3D.4
With the current scoring, those have the same expectations, but with
more sensible scoring (D=3D.1-.25) the more interesting, uncertain line
is the better
choice. So we get better chess.
=A0One assumes that the
> counterplay has winning chances or Black wouldn't contemplate it over
> the guaranteed slight disadvantage. =A0This is impossible. =A0If Black
can=
> produce counterplay with winning chances from a position, the
> evaluation of that position is `Black has winning chances' or better;
> not `White has an advantage.'
>
> If a draw is worth 0<p<1 points, it is better to accept a near-certain p
> points than trying to get a whole point with probability less than p.
> If a draw is worth 0<=3Dp<1/2 points, it is better to accept a
fifty-fifty=
> chance of a whole point than a certain p points for a draw.
Exactly. And the fact that we have GM draws (essentially non-
contests)
is strong empirical evidence that p=3D1/2 is too high. The
perceived return on trying to win is low, or negative.
That is the factor that sets chess apart from many other
games and sports, whether they have a theoretical tie possibility or
not.
In those activities it generally makes sense to set out to win. Sure
some contests may END in ties, but that is an accident (both teams
happened
to each score 1 goal), not part of a self-fulfilling plan (a draw is
good for me,
so I'll play drawish moves)
>
> > Of course, the main advantage to reducing the value of draws is that
> > the game will become more interesting to play and watch!
>
> Draws are only prevalent at the highest levels of chess. =A0We assume
> that the world's top players already find chess interesting to play.
Depends on what you mean by "prevalent". They are probably more
prevalent than they should be for optimum enjoyment and fan interest
at every level of chess above ELO 1000.
Do you have some evidence that the current chess scoring system
creates maximum interest?
>
> As for `more interesting to watch', well. =A0It's possible that the
> extra burden of playing games out to the bitter end and not being able
> to take a half-point rest in the middle of a tournament will result in
> lower-quality play. =A0I can't tell whether it would or not but there's
> no data on either side and all I'm saying here is that you can't be
> certain that decreasing the score for draws will result in more
> interesting chess.
>
> Seemingly more significant is that you're removing the value of the
> draw as a safety net. =A0With a half point for a draw, a player can
> sacrifice a pawn, say, for the attack, with the reasoning, `If this
> works, I win; if it doesn't, I'll probably be able to hold the draw.'
> Reducing the value of that safety net seems likely to lead to more
> conservative, drawish play.
???? Why would they play drawishly if they know that draws
aren't going to score well? Both players have to collaborate to play
somewhat riskily - otherwise both will end up with the now
lower value draw.
>
> Dave.
>
> --
> David Richerby =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0
Pickled=
Adult T-Shirt (TM): it's likewww.chiark.greenend.org.uk/~davidr/=A0 =A0
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