Suggestion for clocked tournaments: movement

[Gerardo]

As mink pointed out somewhere else in these forums, a clocked tourney is actually two disjoint tournaments, as NS pairs only competes with NS pairs, and EW competes only with EW pairs.

This is solved live changing direction of boards if monosession, or changing direction of pairs if multisession.

As the costs for us to move people is zero (unlike live bridge), I suggest the following movement:

 

Pair in table N NS moves to table N EW.

Pair in table N EW moves to table N+1 NS.

[uday]

> Pair in table N NS moves to table N EW.

> Pair in table N EW moves to table N+1 NS.

 

This works? I guess it will, right? I'll try it. If it works, i agree it would be a good thing.

 

( great idaa, if it work, G!)

[mink]

This was not what I suggested. It doesnt work either. My suggestion was the the following:

 

NS Pair at table 1 stays there

EW Pair at table 1 --> table 2 NS

NS Pair at table 2..n-1 --> table 3..n NS

NS Pair at table n --> table n EW

EW Pair at table 2..n --> table 1..n-1 EW

 

n must be at least (#rounds+2) div 2.

It should not exceed #rounds as the scrambling effect is less good. I consider #rounds to be the optimal value. Sections should be formed of this size, and the movement should be run in each section independently of the other sections.

 

Karl

[uday]

I dont see the NS and EW switching, tho, except for

 

EW Pair at table 1 --> table 2 NS

 

and

 

NS Pair at table n --> table n EW

 

So each round only 2 pairs change direction? What am i missing?

[mink]

Uday, you got it right!

 

but if you set n to the lowest possible value, all moving pairs have been n-1 time NS and n times EW.

 

Chosing greater values for n causes different numbers of being NS and EW for each pair.

 

Karl

[uday]

What if there are more rounds than tables?

 

that is, a 8 table movement with 12 rounds (some playbacks)

 

I'm trying to figure out how to compute N

 

what i have at start time is

 

T = number of tables

R = number of rounds

bpr = boards per round

B = number of boards

[mink]

bpr and B dont matter.

 

sections := (tables-1) div rounds + 1

 

n := tables div sections (for some sections)

n := tables div sections + 1 (for other sections)

 

Just an example.

 

You can think of other ways to compute n but should ensure that n >= (#rounds+2) div 2 to avoid replays.

 

Karl

[mink]

btw, your example:

 

with an 8 table / 12 rounds tourney you have no other choice to set n to 8 (only one section). But then, you have no playbacks at all!!!

 

Karl

[hrothgar]

I would like to throw out a simple suggestion:

 

The Bridge Laws Mailing list is probably the best source of information available about movements. The list contains both top directors and some good mathematicians who have spent a large amount of time thinking about these very issues.

 

Potentially, it might be worthwhile to consider migrating this thread over to that environment. We could only benefit from the additional resources. At the same time, it might be useful for the BLML to get better perspective about some of the issues that are unique to online bridge.

[mink]

hrothgar,

 

most movement problems come from the fact that in real life you normally have only a limited number of boards that carry the same distribution - far less than the number of tables in a tourney. Therefore normal movements solve problems that you do not have in online tourneys. For clocked non-swiss movements the one I described is the only one you need.

 

Karl

[hrothgar]

Hi Carl

 

I agree that the formula you suggested will solve the specific problem at hand.

However, I'm not sure whether the global "environment" is necessarily the best.

 

Given a computerized playing environment, there are enormous numbers of different ways that a movement might be run [or, for that matter, that scores could be assigned]

 

As a simple example: Should a barometer be used? Should separate sections be maintained, or is it best to lump everyone into one bid pool? Is it best to match fast pairs. To what extent do we want to trade off between different attributes?

 

This is a complex question, which might deserve more broadbased discussion.

[uday]

Sorry to be so thick, mink!

 

Lets say I have only one section ( I dont want to mix up the movement with how and why i assign tables to sections, since there are external factors in play like bbo limitations and the ACBL )

 

> if you set n to the lowest possible value, all moving pairs have been n-1 time NS and n times EW

 

 

MINIMUM_N = (#rounds+2) / 2)

n = tables // but why would you add 1 to this?

if ( n < MINIMUM_N ) n = MINIMUM_N

 

 

 

I dont know why i'm finding this so confusing B) too early in the AM for me! Anyway, cheaper for me to understand this in the forums now than in the code, later

[uday]

Hrothgar, I sorta agree. But the discussion itself is expensive B)

 

If anyone offers me a better movement that I can understand to replace the simple clocked movement, i'll use it. Isnt mink's answer (once i get it :) ) better than what we have now?

[hrothgar]

I have long subscribed to the belief "Don't make the best the enemy of the good".

I much happier with a good solution running today, rather than a perfect solution in 3.2 years.

In short, don't let anything I say distract you from from Mink's immediate term solution.

 

I'll probably start a generic discussion on the Bridge Laws Mailing List.

If anything useful emerges, I'll let people know.

[Gerardo]

Karl:

You're right, it doesn't work at all B) Sorry!

I was trying to see why do you have a fixed pair, and found it (same reason [to not repeat matches]).

Maybe fixed pair can switch directions in consecutive rounds, maintaining, the same pair movement? Then all pairs have a +1/-1 difference between NS and EW, am I right?

 

THere are other movements possible, like the first N rounds of a round robin, or Howell (these two are too similar, if not equivalent, I think, big tables), or

 

S,p,q odd primes, p!=q

#tables in section S, S>p, S>q

Two lists of S pairs

List 1 jumps p tables, List 2 jumps q tables (mod S)

Odd rounds List 1 sits NS odd tables

Even rounds List 1 sits NS even tables

 

In this one, all pairs visits each table once, changing directions each round, never repeating opps (not in p*q rounds)

 

Tried S not prime but then, you have to discard some rounds which repeats (when lcd(S,R)!=1)

 

Would need sections of different size :-/

[hrothgar]

Here ios the note that I am forwarding off to BLML

 

Hi All

 

I have a question for the peanut gallery: As people are no doubt aware, computerized bridge uses a very different playing environment that normal “face-to-face” games. Has anyone given much thought to how this might affect tournament “movements”?

 

Traditionally, when I think of a “movement” I am conceptualizing an ordered set of pairings that is attempting to fulfill a specific set of goals. For example, I might want to design a movement such that

 

1. A total of 27 boards will be played

2. Each North/South pair will play every East/West pair

3. Each N/S pair will play the same number of boards against every E/W pair

 

Alternatively, I might prefer a movement in which

 

1. A total of 24 boards will be played

2. Each pair will be matched against every other pair

3. Each pair plays the same number of boards against every other pair.

 

Or, the radically different:

 

1. Play will continue for 2.5 hours +/- epsilon

2. All players are grouped in a single pool

3. All players will play three boards against the pair that they are currently matched against

4. Pairs will be matched barometer style at the end of each round. Multiple contests against a single pair are permitted.

 

To look at an extremely simple case, is it better to use a single large pool in which all pairs could potentially be matched or large numbers of small sections, which guarantees that all pairs in a section play are matched against every other pair?

 

I suspect that it is impossible to define a single optimal movement. In particular, some dimensions that can be used for mappings must be traded off against others. Movements that strive to match pairs that play quickly seem antithetical to barometers. However, I would be interested to understand what attributes are valued “most” in a movement. Ideally, we might be able to define a small set of “movements”, each optimized for a given set of preferences.

[mink]

Hi Uday,

 

sorry this answer is delayed a bit, but I had a face-to-face tourney to direct in the meantime B).

 

I suggested to have sections as you once wrote you already implemented such a thing. I understood that each section runs independently of the other sections and has its own clock. This implies that a pair can never move from one section to another. But this implies that a movement has to consider the existence of sections.

 

Of course my movement can be applied to sections of any size, and it can also be applied if all tables of a tourney are the one and only section. But only if

 

(#rounds+2) / 2 <= size(section) <= rounds

 

the movement does care for scrambling without further things to do. If you have larger sections, you have to implement additional mesures in order to maintain scrambling. Thats why I suggested to adjust the size of the sections to the number of rounds.

 

 

"if (  n <  MINIMUM_N )    n =  MINIMUM_N "

 

This does not make sense, as n can never be greater than the number of tables. If you have less tables than "MINIMUM_N", then you cannot avoid replays.

 

 

Gerardo: "Maybe fixed pair can switch directions in consecutive rounds, maintaining, the same pair movement? Then all pairs have a +1/-1 difference between NS and EW, am I right?"

 

Yes, but in my oppionin scramble does not mean that all pairs have to be NS a often as EW. It is sufficient and maybe even more efficient if the NS/EW ratio is different for most of the pairs.

 

Will sleep now and work tomorrow.

 

Karl

[Karma]

Yes, the movement is controlled by a computer, so a fancy scrambling movement is desirable in order to create meaningful overall results. This of course, is not something that can be done with live players except in a small field Howell movement.

 

However, I believe that the efforts here are trying to bite off more than needs to be chewed. I remember reading an article on switching directon for a few pairs for only 2 rounds of the tourney.

The analysis showed that this dramatically improved the overall comparison so that an overall winner could be determined.

The movement is simple enough that with a bit of learning, it could be done with a live field.

 

I will post more details when I find the article.

 

With the aid of the computer, the movement can be a little more advanced. Something like each round, 2 pairs change direction.

Or even (Number players)/(Rounds of play-1) switch each round. Then almost everyone will have one round in the other direction.

 

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.

 

cheers,

[hrothgar]

For what its worth, I received some useful comments when I posted my questions about bridge movements to the Bridge Laws Mailing List.

 

First, the EBU has some useful documentation available about moves that describes different optimal characeristics for a movement. It is interesting to note that many of the design criteria that are most desirable in a computerized movement do not even seem to be considered significant in the EBU booklet. Most notably. Uday metnioned that he very much wanted to design a movement that would be self-healing. Ideally, multiple pairs could be removed from the tournament without the need for manual intervention from the director. Given that this isn't even an option in most face-to-face games, the EBU never really considered this as a potential design goal.

 

With this said and done, most existing movements are deliberately designed to minimize luck. The organizers wish to implement a scheme in which the conditions of contest maximize the chance to identify the best pairs while minimizing the role that luck plays in the event. To this end, most existing movements are designed to feature relatively large numbers of efficiently sized sections. Ideally, the movement will be such that either:

 

(a) every pair in the section plays against every other pair OR

(:) every North South pair plays the same number of boards against every E/W pair.

 

Given this as a basic goal, it should be possible to define a simple algorithm based on the following:

 

The tournament organizer selects how many boards that he wishes to run, along with a rough guess at the total number of pairs that he is willing to support.

 

Based on this, the software automatically defines a combination of section numbers and movements that is consistent with the the input parameters. If necessary, residual pairs are either bumbed from the tournament or paced into a "garbage" section that features a unique movement optimized for the number of residual pairs.

 

Obviously, this scheme runs into clear problems with Uday's basic design goal of a self healing system.

[Cave_Draco]

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

 

Taking that as the aim, why tie pairs to NS/EW?

 

 

Aim 1. No pair plays the same board twice,

 

Aim 2. No pair plays the same opps twice.

 

Aim 3. Minimise the number of boards.

 

 

Aims 1 & 3 are easy; each round every table plays the same, new boards, ;D!

 

Most traditional movements are designed to deal with physical objects; people, boards and tables! This is not a constraint in a computer mediated game.

 

The most efficient way for a computer to deal bridge hands, is just a constrained random distribution, why would a computer need to shuffle?

[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]

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]

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.demon.co.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