Post by a***@yahoo.co.ukYesterday evening at the monthly cross-IMP pairs evening, the
director, with eight full tables, decided to play a four board round
Mitchell movement, two winners, announcing that playing a Howell or
arrow-switched movement is less fair. I enquired after the play as to
why this is so. He said that if a pair is consistently switching
polarity and they happen to cop the worst hands at the table regularly
as a result, they end up struggling to generate a decent score when
the opponents bid and make the slams, which dumps significant negative
imp scoresd on them which they can do nothing about. I thought about
this, but realise that this can happen with a two winner Mitchell,
which is exactly what had happened that evening. The hands were hugely
biased NS, they declared 18 out of 28 boards against partner and I,
they had 10 games and two slams (one which was only bid once), we had
just four games and no slams. Is it really correct that a two winner
movement is fairer for a cross-IMP scored event?
The fairness of a movement is normally measured in the amount of
competition between pairs. Whenever you play a board, you have direct
opponents (the players sitting across from you), indirect opponents (the
other players who will play the same board in the same direction, thus
hurting your score if you do well), and indirect allies (the other
players who will play the same board in the opposite direction but not
against you, thus helping your score if they do better than your direct
oppoennts do). The amount of competition with a pair is measured in
terms of how much that pair can influence your score as opponents,
minus how much they can influence it as allies. For a movement to be
fair, your total amount of competition with each other pair should be
relatively constant.
As a simple example, when playing a straight Mitchell using matchpoints,
each pair in the opposite direction are direct opponents once and
indirect allies the rest of the time, and it turns out that the amount
of help they can give you in total as indirect allies (changing the
"number of teams you did better than" by 1) is exactly equal to the
amount they can hurt you at the time that they're direct opponents
(changing the "number of teams you did better than" by the number of
teams in the field, minus 1). So a matchpoint Mitchell has zero
competition with the other half of the field, and a constant amount of
competition with your own half (who are always indirect opponents). A
full Howell is likewise considered fair when playing matchpoints,
because the arrow-switches are set up to make the amount of competition
add up to a constant.
However, when you're playing cross-IMPs, there's a problem: using IMP
scoring, some hands have higher scoring potential than others. If a hand
is obviously a partscore hand, especially not vulnerable, the raw scores
being IMPed against each other will be fairly small; no matter how good
a pair you are, you're unlikely to be able to get a large swing. On the
other hand, if you have one of those hands where both sides can make
game and people are strongly considering sacrificing in (or even
making!) slams, you'd expect much higher IMP totals for the hand. So the
amount of competition available on each individual hand is randomized
somewhat, based on the actual cards dealt.
This can screw up both 1-winner and 2-winner movements, although not in
the way your director explained. The basic issue is that if you're
playing against worse opponents on the high-scoring hands, and better
opponents on the low-scoring hands, you're going to have an advantage;
in other words, pairs will get a (fairly random) set of indirect allies
and indirect opponents based on the actual cards dealt. In a 2-winner
movement, this can lead to players having indirect allies and opponents
in the other half of the movement, which isn't supposed to happen; in a
1-winner movement, the extent to which various pairs oppose each other
can vary wildly. (Matchpoint scoring avoids both these problems by
artificially increasing the importance of small scoring variations on
flat hands; an overtrick is typically worth 1 IMP, but it can be worth
anything from 0% to 100% of the matchpoints depending on how flat the
hand is.)
The director's reasoning is wrong, incidentally, because having a bad
hand doesn't actually reduce the amount of IMPs available at cross-IMPs;
if you have a bad hand and the opponents a good one, then you can get a
very bad score by letting the opponents make a slam that shouldn't make,
or a very good score by persuading them out of slam (or pushing them
into a slam that doesn't make when they had a cold game). After all,
IMPing is based on a comparison of two scores, and the scores being
compared with will have been obtained with the same arrangement of
hands on the board. All your indirect allies on the board will have the
same powerful hands as your opponents, and be able to increase the
score by doing better than you. All your indirect opponents will have
hands just as weak as yours, and only be able to hurt your score by
accomplishing something better with them.
(There is a potential argument along the director's lines, though: often
a pair with a very weak hand will have no influence on the bidding or
play, leaving the result of the hand entirely up to how good the
opponents are at finding slams and/or avoiding bad slams. But "not being
able to influence the end score" doesn't actually hurt or help your
score in its own right; for all you know, your opponents will be the
ones who screw up and your indirect allies the ones who bid to the right
level.)
--
ais523