Measuring the Efficiency of Relay Structures

[hrothgar]

Hi All

 

I am playing arround with "objective" metric to judge the efficiency of a relay structure. I argue that the efficency of a relay structure can be judged by multiplying the level at which a particular hand shape is resolved by its frequency.

 

For example, playing Symmetric Relay, a 5431 shape is resolved with a 3D bid.

 

3D is the 17th step in bidding

5431 hands occur ~12.93% percent of the time.

 

17 * .1293 = 2.1981

 

Repeat for all bids and calculate the sum

 

The lower the index, the more efficient the system

 

I'm planning on calculating this index for MOSCITO. I was curious whether anyone might be interested in doing the same for Viking Club, Ice Relay, or another pure relay struture. The same methodolgy could be modified for Ultimate Club, compensating for the initial range show.

[Free]

wow, seems like a lot of work, but a pretty accurate comparisson!

 

if someone would do this, the frequencies are available at http://public.aci.on.ca/~zpetkov/TheDistributions.html but they seem not to be as accurate as Richard's...

[mikestar]

Your index seems to be a fine contribution to the theory of the game.

 

It could also be extended to comparing similar non-relay auctions. For example, how much does the Kaplan Inversion gain over 1NT forcing when the opening is 1♥? Different NT response schemes could be compared. . .

[MarceldB]

Hi all,

Hi all,

 

I'm new to this group and interested in relay systems (specially WOS), reason for following comment on hrotgar's nice posting:

 

When I divide the 560 possible distributions roughly in f.e.:

 

•balanced

(4333, 4432, 5332, 5422, 6322 and 7222)

64,36% with 56 possible distributions

 

•Singleton/Void regular

(4441, 5431, 5521, 5530, 5540, 6421, 6430, 6331, 7321, 7330)

32,86% with160 poss. distributions

 

•extreme 2 suiters

(7/8/9-4 and 6+/5+)

2,32% with 156 poss. distributions

 

•extreme 1 suiters

8/9 including 8-5

0,45% with 108 poss. distributions

 

•very extreme 1 suiters

10/11/12/13 carders

0,0015%, with 80 poss. distributions

 

I think you can not say that the balanced one has to end in the lowest level in a relay sequence to be able too reach a very good index number, because the next one with 32,86% but with 160 poss. distributions needs more bidding space taking into account that you want to end below 4C and to be able to give f.e. an 1-point margin within f.e. an 4p.range.

 

So I suppose if you should compare relay systems by index number only, you will get a indication about the efficiency to *start with* only.

More facts are involved for measuring efficiency as f.e. during the relay sequence (sub or even subsub)-pointranges can be stipulated before ending in the final distribution or pre-info's regarding suit quality; quality of the shape in general; number of control points; mentioning the shortness suit in an very early stage to be able to evaluate the R hand; the relayer normally never has a unbalanced hand opposite a balanced one etc.

Apart of the fact if you can break the relay positively, ask for stopper/control and pick up the relay again and ask for the (final) distribution in case that's the next important matter. Or more or less preemptive like bid which could start on a lower level too for reaching a better index.

 

BUT, nevertheless, this index can be a very helpfull and nice instrument for a first comparison of relay systems.

--------

Dear Hrotgar,

 

Before I will index my own system a

practical question:

When the distribution sequence ends with 3D f.e. for a 5431 min in the range

3H same but now max

(or even max/max-> zoom! if you like), what will be the index number? the average of all possibilities or the most common bid?

 

In your example you mention in Symmetric Relay indeed 3D for the 5431, but how do you count the given number of 17 steps? (12?)

 

Thanks for your answer.

 

Best regards,

 

Marcel

[1eyedjack]

I should be interested in the results of this and shall watch developments. Unfortunately I lack the skills and resources to contribute meaningfully. However there is one point that I think may indicate an alternative strategy.

 

It is my observation that few auctions these days are uncontested, and you generally have little control over the amount of bidding space consumed by opponents when they bid.

 

The measure of the efficiency of your system is largely dependent on the amount of information imparted by the time that the barrage falls.

 

If you (unreasonably, I admit) assume that LHO is going to overcall 2S on every hand that you open, then the more efficient system may be the one that equally divides up the various opening hands among the opening bids below 2S, and this may run conter to the ideal of dividing the hands on the assumption of an uncontested auction based on the number of auctions that can end up in (say) 2S.

[luis]

I think I commented this somewhere else but there're other metrics that should be investigated to determine the strength of a relay system.

 

Hrothgar's metric can be called shape-resolution-level is just one indicators.

Other important indicators are:

- amount of information per bid (ie: how soon relayer has enough info to determine what to do in case of interference, systems where bids are either a or b and then either c or d and then everything is solved are weaker than systems that can quickly show some lengths and points)

- number of things that must be remembered. You can yell if you want but nobody is perfect and forgetting the systems is one of the problems of relay systems so the longer pd has to memorize the riskier the system is.

- average opening level (pass=0,1c=1,1d=2,1h=3) then the average opening level determines the agresiveness of the system.

 

And there're more things but I don't have my "Bidding systems theory" book here :-) Don't ask about the book I never published it.

[MarceldB]

Dear Hrotgar,

 

Before I will index my own system a

practical question:

When the distribution sequence ends with 3D f.e. for a 5431 min in the range

3H same but now max

(or even max/max-> zoom! if you like), what will be the index number? the average of all possibilities or the most common bid?

 

In your example you mention in Symmetric Relay indeed 3D for the 5431, but how do you count the given number of 17 steps? (12?)

 

Thanks for your answer.

Hi Hrotgar,

 

I suppose you have overlooked my above mentioned questions ?

 

Further to this subject.

A final distribution bid with 3S or 3NT will not give a different index number?

Taking into account the follow-up bids: in case 3NT after 3S is to play.

 

regards,

Marcel

[MarceldB]

For many bids I took an average caused by different relay schemes for 1 distribution (depending on the strength/sequence). Furthermore I have a lot of "waiting-bids", that means f.e. that you tell partner I have a 5332 but I'll wait for your instruction (stopper asking before distribution or show the quality first. etc.)

Nevertheless for the figures I took for all the shapes the *complete relay* and knowing then the exact distribution min/max in the range and eventually the quality,

 

resulting for the WOS system REGRESsion (Pass 13+, 1D Fert, all relay style)

 

•balanced (4333, 4432, 5332, 5422, 6322 and 7222)

index 8,6692

 

•Singleton/Void regular (4441, 5431, 5521, 5530, 5540, 6421, 6430, 6331, 7321, 7330)

index 4,4242

 

•extreme 2 suiters (7/8/9-4 and 6+/5+)

index 0,4480

 

•extreme 1 suiters 8-13 carders

index 0,071

 

Totally: 13,6124

 

Regards,

Marcel

[Free]

~snip~

Further to this subject.

A final distribution bid with 3S or 3NT will not give a different index number?

Taking into account the follow-up bids: in case 3NT after 3S is to play.

 

regards,

Marcel

I think you have a point! Since 3NT is to play after 3♠ and 4♦ terminator after both 3♠ and 3NT, I think 3♠ and 3NT are handled the same, BUT they should get weight 15 (not 14) since 3NT doesn't investigate and 4♣ (step 16) is the new relay...

[Danlo]

I argue that the efficency of a relay structure can be judged by multiplying the level at which a particular hand shape is resolved by its frequency.

 

For example, playing Symmetric Relay, a 5431 shape is resolved with a 3D bid.

 

3D is the 17th step in bidding

5431 hands occur ~12.93% percent of the time.

 

17 * .1293 = 2.1981

 

Repeat for all bids and calculate the sum

 

Apart from some reservations I have on this concept (for one: why use hand shape as a criterium, rather then for example game forcing character of the bidding or trump suit establishment? Not that these are no better alternatives. But it seems that a system gets punished for conveying other than shape information and that doesn't seem fair), I have a remark about the calcution.

 

4432 has a frequency of about 21.5%. 5422 has a frequency of about 10.5%. 6322 has a frequency of about 5.6%.

 

Calculate:

4432 with 3C = .215 * 16 = 3.44

5422 with 3D = .105 * 17 = 1.79

6322 with 3H = .056 * 18 = 1.01

 

Total 6.24

 

(are the factors correct? Seems to me 3C should be 12, but that is not really important)

 

Compare this with:

4432 with 2NT = .215*15 = 3.23

5422 with 3C = .105*16 = 1.68

6322 with 4H = .056*23 = 1.29

 

Totalling 6.2

 

So it pays to ignore quite frequent shapes (I think 5.6% is quite frequent) in favor of even more frequent shapes. If we concentrate our bidding on 4333,4432,5332,5422 and 5431 shapes we can gain quite a lot, even though we shift all other shapes to (unreasonably) high bids.

 

I don't think this is the right strategy. Of course, this is not a design tool or design criterium, but an evaluation criterium. And it should be used as that, to measure after the fact. But still, some unwanted quirks in a system may weigh positively in the result and that should be eliminated as much as possible.

 

Is it possible to enhance the metric? I'd like to propose the following: instead of the step number, use the Fibonacci number of the bid. Starting with 1 for pass, 1 for 1C, 2 for 1D, 3 for 1H, 5 for 1S,..., 89 for 2NT, 144 for 3C, et cetera.

 

The measure now becomes:

 

Calculate:

4432 with 3C = .215 * 144 = 31

5422 with 3D = .105 * 233 = 24

6322 with 3H = .056 * 377 = 21

 

Total 76

 

Compare this with:

4432 with 2NT = .215*89 = 19

5422 with 3C = .105*144 = 15

6322 with 4H = .056*4181 = 234

 

Total 268

 

But compare this with:

4432 with 2NT = .215*89 = 19

5422 with 3C = .105*144 = 15

6322 with 3S = .056*610 = 34

 

Total 68

 

So the last variant is the best and bringing the 6322 to a higher level will no longer pay of.

 

At least, this is closer to my intuition of what I would prefer to have in a bidding system. But please let me know if you don't agree.

 

============

Bert Beentjes

Nijkerk (Gld.)

The Netherlands

[MarceldB]

Regarding 3S versus 3NT for the index number

 

3S = step 15 , same as 3NT

resulting (including a correction for 2 bids) for

REGRESsion in a indexnumber now of 14,3291

-------------

Regarding Bert's Fibonacci index number posting: I have made again a calculation

and come to following figures (again 3S or 3NT= 987)

 

•balanced (4333, 4432, 5332, 5422, 6322 and 7222)

step index 9,3046 and acc. Fibon : 579,1341

 

•Singleton/Void regular (4441, 5431, 5521, 5530, 5540, 6421, 6430, 6331, 7321, 7330)

step index 4,5055 and acc. Fibon : 207,9762

 

•extreme 2 suiters (7/8/9-4 and 6+/5+)

step index 0,4480 and acc. Fibon : 192,7725

 

•extreme 1 suiters 8-13 carders

step index 0,071 and acc. Fibon : 7,6903

 

Step index totally 14,3291

Fibon.index 987,5731

 

with my remark that a 1 point margin is known and very often the quality of the exact distribution.

 

Marcel

[helene_t]

I've made some calculations that suggest that it's more crucial to decide whether you want to play a relay system at all, rather than to optimize your bidding system specifically to a relay (or non-relay) structure.

 

The fibonacci-series conveys 0.694 bit per bidding step in a relay system, and 0.960 in a symetric system. The figures for a 0.5-decay-rate-system are 0.667 and 1.000.

 

I also considered the case in which you open in first seat with a forcing 1c, partner must answer acording to some strategy and your RHO is know to overcall 2s. In that case fibonaci conveys 2.47 bit against 1.99 for the 0.5-decay-rate. Choosing all responses from 1d to 2s with the same probability would, of course, be better ( 3.24 bit), but the non-competive efficiencies of such a system are only 0.373 (relay) and 0.422 (symetric). In less extreme competitive situations the difference will, of course, be smaller. One could puzzle with some game theory here: instead of assuming an overcall of 2s, assume the oponents optimize the efficiency of there overcalls against our system. However, taking the semantics and forcing character of the biddings into account would make things complicated.

 

Conclussion: You could use fibonacci or decay-rates or something in between, it doesn't matter much. In a relay system you trade 1 bit conveyed by both partners for 0.7 bit conveyed by the informative partner only. The important question is whether that is a good deal.