[hrothgar]

Cave_Draco wrote

"Isn't the aim of an ideal movement just to scramble the pairs?"

And I reply

Suppose the you have 500 pairs participating in a tournament.

Each pair's strength is represented by a point on the interval [0,1]
0 represents a very weak pair, 1 respresents a very strong pair.
[Presumably, the distribution of the strength of pairs is distributed normally]

The tournament can be treated as a statistical sampling process that seeks to rank the pairs as accurately as possible.

The problem for tournament organizers is the following: Suppose I had all 500 pairs in the tournament play in one large pool. In this case, the ranking system for the pairs is likely to be dominated by the luck of the draw. Your place in the tournament might very easily be dominated by the strength of the pairs that you happened to play against rather than your own strength.

Tournment organizers are faced with an unfortunate balancing act:

Running large numbers of small sections prevents organizers from making accruate cross comparisons between sections. Running small numbers of large sections allows cross comparisions, however, decreases the accuracy of the rankings.

[Cave_Draco]

"The tournament can be treated as a statistical sampling process that seeks to rank the pairs as accurately as possible."

Change possible to feasible & I agree, ;D.

It is not feasible for 500 pairs to play the same hands in a "live" tournament! Closest approach is probably simultaneous tournaments, which take significant organisation.
IMO, most of the luck-of-the-draw comes from who you play what hands against. The statistical approach doesn't allow for the distribution of hands.

For example, if the whole room is in 3NT tick, it doesn't matter who you get that hand against... world champions or bunny rabbits.
Whereas, a marginal slam?


I was just suggesting that modelling computer mediated tournaments on "live" tournaments was to accept unneeded constraints.... Why can't all of the tables in round one play the same board? Ditto round 2...
In "live" tournaments it would be unwieldy, but in a computer run tournament?

[Karma]

Quote

I was just suggesting that modelling computer mediated tournaments on "live" tournaments was to accept unneeded constraints.... Why can't all of the tables in round one play the same board? Ditto round 2...
In "live" tournaments it would be unwieldy, but in a computer run tournament?

In fact, that is the way it is done here.

cheers,

[Karma]

Quote

Eg, 50 players, 16 boards in 8 rounds. N=50, R=8.
(50_/(8-1)=7 players each round. First round, no switching, in the next 7 rounds, 49 players will switch direction for 1 round. Simple and very effective.

Further information is available at http://www.blakjak.d...uk/lws_men1.htm

The ideal ratio is for 1/8th of the boards to be switched.
So, I modify my example a little bit (and it is very hard for 7 players to switch, that is 1.75 tables).

With 50 Pairs, 25 tables, 16 boards, 8 rounds, 2 board/rnd.
In round 1, 3 tables switch (say tables 1, 2 and 3). In round 2, 3 different tables switch (such as 4, 5 and 6).
And so on until the last round when tables 22, 23, 24 and 25 switch. In total there were 25 tables x 16 boards = 400 boads played. Of these, 25 tables x 2 boards/round = 50 boards were played with the switch.
That works out to 50/400, or exactly 1/8th the boards.

cheers,

[McBruce]

Arrow switching is NOT needed online. Arrow switching works in a normal club game where most of the NS pairs are good and most of the EW pairs are not. In a eight table, seven round game with a perfect pair sitting NS, and the other seven NS pairs and all the EW pairs average, the EW pairs will get 50%, the good pair will get 100%, and the other NS pairs will get 42.86%. Use the arrow switch movement and the good pair will get 100%, followed by two EW pairs at 50%, then a bunch of pairs at 46.43% and one unfortunate NS pair at 42.86%. Arrow switching improves matters, but there are no perfect pairs. The best pair in any game is not 100% rated but only 60% rated. The remaining difference in initial seat positions is minimal. From doing an analysis of an alleged poor seeding at a recent local game of twenty tables, I came up with this conclusion: A pair's score depends on three factors:

1) STRENGTH: how strong they are compared to the field
2) FORM: how much better or worse than your strength you actually play
3) CHANCE: the effect of movement inequities on your score

In a somewhat poorly seeded local game, I came up with these figures for the relative importance of #1, 2 and 3:

Strength 58.2% Form 38.6% Chance: 3.2%

So when we speak of movement inequities we are talking about virtually nothing: in the poorly seeded game I studied, the biggest "movement tax" paid to the gods of chance was less than one board.

It would be virtually indistinguishable to use a straight Mitchell movement and arrow-switch 50% of the tables, instead of arguing what the most perfect movement is and using that. Sure, it 'feels' better to have people play some NS and some EW hands, so flip coins for the arrow switched tables. But there's no significant advantage in finding a better movement than a straight Mitchell with random, cosmetic arrow-switches. The variance in a pair's form is, on average, TWELVE times as high as any variance resulting from the worst movements there are.

HOW WELL you play matters twelve times as much as WHO you play and WHICH DIRECTION others play.

So all this talk about movements is much ado about virtually nothing. Uday, I would suggest you put in a random number generator (doesn't even have to be an MIT-quality scientific one!) to decide which pairs to flip, keep the Mitchell movements with the random arrow switches, and turn your attention to the Swiss pairing option.

--McBruce