# BBO Discussion Forums: Cross Imp Scoring : Opinions wanted - BBO Discussion Forums

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## Cross Imp Scoring : Opinions wanted

### #1jeannief

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Posted 2011-November-22, 17:53

I would be interested to hear opinions on the use of "across the field" cross imp scoring in a pairs competition of
mixed ability. 12 board matches with a cap of 36 Imps available for a win but unlimited Imps to lose. How does this
compare with Butler scoring where Imps are converted to VPs with a maximum available score of 25 and a maximum loss possible of -5.
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### #2mich-b

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Posted 2011-November-23, 03:52

It seems to me that there are 2 separate issues mixed in here:

1. How to calculate a pair's score for each board?
a. IMPs "across the field" which means comparing the result on a board to all other results on this board, as if in teams, IMPing the "total point" result , and then averaging the IMPs.
b. "Butler" IMPs, which means calculating an average "total point" result (with or without removing some extreme scores) , and IMPing the total point difference between a pair's result and that average.

My opinion on this subject is that IMPs across the field are better , reflect better the spirit of the game, resemble more closely teams play (which is good). Actually I believe that "Butler" was only invented in pre-computer era , because it makes calculations somewhat easier. I think it should not be used today , and in fact that is why only "across the field" is used in BBO main club play.

2. A separate (and independent) issue is how to calculate a pair's match score from its per board scores.
You can either just add up the IMPs (with or without any maximum and minimum) or convert them to VPs.
There are 2 issues to consider here:
a. Converting to VPs has the (negative imo) effect of "quantization" , which means that randomly (depending on the VP scale) the 5th IMP may be worthless , but the 6th IMP is worth a VP. This introduces some unnecessary randomness.
b. "Saturation" , or limiting the size of win. This imo is a negative effect in an even field, and only introduces another randomness (If a pair won 50 Imps in a match against another good pair , why should 15 of those IMPs be truncated?). In a Mixed field this is more of an issue , since we don't want the size of the win against weaker pairs to determine the winners. The VP scale is designed to take care of this, and gradually reduce the value of "additional" IMPs. I believe this is better than using IMPs and just truncating them randomly at 36 (or any other number).
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### #3gnasher

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Posted 2011-November-23, 03:53

Cross-IMP is better than Butler, because Butler artificially inflates the IMPs available on swingy deals. For example, if half of the field makes +600 and half scores -100, everyone should win or lose the equivalent of half a game-swing, or 6 IMPs. Cross-IMPing does that, but Butler scoring gives everybody +/- 8 IMPs.

The supposedly good thing about Butler is that it gives people something that looks like a real score to compare against. As it's not, in fact. a real score, that's not much of a benefit.

- You can use VPs with either form of scoring. In a field of variable strength, VPs are a good idea.
- You can cap the winning margin at either form of scoring, but you shouldn't. Victory-pointing is better than capping, because it means that each successive IMP won is similar in value to the previous one - the value of an IMP decreases gradually rather than remaining constant for a long period then suddenly dropping to zero.
... that would still not be conclusive proof, before someone wants to explain that to me as well as if I was a 5 year-old. - gwnn
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### #4dake50

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Posted 2011-November-23, 09:44

Are you suggesting (as ACBL) a
3 board match uses 10 victory points scale,
4 board 14 vp
5 board 16 vp scale?
*** Seems that gets the jist of your question.
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### #5jeannief

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Posted 2011-November-23, 11:28

Many thanks for all the helpful replies. I was most interested to learn the pros and cons of capping either the maximum or minimum score available as opposed to a VP conversion, depending on the nature of the field.
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### #6nigel_k

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Posted 2011-November-23, 14:04

gnasher, on 2011-November-23, 03:53, said:

Cross-IMP is better than Butler, because Butler artificially inflates the IMPs available on swingy deals. For example, if half of the field makes +600 and half scores -100, everyone should win or lose the equivalent of half a game-swing, or 6 IMPs. Cross-IMPing does that, but Butler scoring gives everybody +/- 8 IMPs.

Sorry for my ignorance but nobody uses cross-IMP scoring where I live.

I understand the example, but doesn't Butler just expand the IMP swings on all hands? If half the room gets 100 and the other half gets 200 then everyone gets +/- 2 instead of +/- 1.5. Can the choice of scoring can actually affect the outcome to any siginificant extent?
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Posted 2011-November-23, 16:11

nigel_k, on 2011-November-23, 14:04, said:

Sorry for my ignorance but nobody uses cross-IMP scoring where I live.

I understand the example, but doesn't Butler just expand the IMP swings on all hands? If half the room gets 100 and the other half gets 200 then everyone gets +/- 2 instead of +/- 1.5. Can the choice of scoring can actually affect the outcome to any siginificant extent?

You should try to convince everybody where you live to switch to cross-IMPs.

Butler has one advantage: It is easier to calculate.

It has a lot of drawbacks:

1) It doesn't simulate a team match. This can easily be seen when you calculate the Butler and Cross-IMP scores for a field of two tables. The Cross-IMP score matches the team score, the Butler score doesn't.

2) The sum of the Butler scores does not need to be equal to 0. It can easily be that the EW players on a given board on average get +0.5 IMP while NS on average get -0.5 IMP. This "noise" is pure random. (Imagine that you play matchpoint pairs and at the end of the session the TD takes his dice and starts to announce: "Board 1: a 4. NS get 1% extra, EW 1% less. Board 2: a 2. Too bad for NS: -3%, congrats EW: +3%. Board 3: a 6! NS get a whopping 5%!! Tough luck EW: you lose 5%." This TD is not going to make it to board 28.) The sum of the Cross-IMPs is always 0 (barring TD decisions).

3) In Butler, we need to calculate a datum score. This datum score needs to be rounded to the nearest multiple of 10. This introduces strange errors. As an example, it is perfectly possible that a table that makes 10 tricks in 2 will get the exact same score as the table next to it where only 9 tricks were taken. In Cross-IMPs the 10 trick table will always score better.

4) In a Butler, often the extreme scores are thrown out. The idea is that these scores are strange anyway. This is horrible. There is no a priori reason why the extreme scores should be stranger than the scores in the middle. (Think of a board where NS can take 12 tricks in hearts and EW can take 12 in spades. I would consider all games, small slams and grands normal results, as long as they lead to 12 tricks. The one pair that play 2NT because one of the players forgot a Jacoby 2NT response to 1 produced the result in the middle, but it is not normal.)

5) The calculation method in Butler is fundamentally unsound. In both Butler and Cross-IMPs, an average is calculated. The difference lies in when this is done. In Butler the average is calculated first and then the IMPs are calculated. In Cross-IMPs the IMPs are calculated first and then the average is determined. Every student in science knows that you are supposed to calculate first and then average. (Think of a light bulb that is connected to the power outlet. Because we are dealing with alternating current, the average current is 0 Ampere and the average voltage is 0 Volt. Using the Butler method to calculate the power used by the lamp, by averaging first, we get 0 V x 0 A = 0 W. That doesn't really match with the fact that the lamp does produce light and the fact that we do have to pay a utility bill. However, if we multiply the voltage and current first, we get an alternating power that is always positive or 0. Therefore, the average power consumption is positive.)

Maybe this will give you the arguments to change things.

Rik
I want my opponents to leave my table with a smile on their face and without matchpoints on their score card - in that order.
The most exciting phrase to hear in science, the one that heralds the new discoveries, is not “Eureka!” (I found it!), but “That’s funny…” – Isaac Asimov
The only reason God did not put "Thou shalt mind thine own business" in the Ten Commandments was that He thought that it was too obvious to need stating. - Kenberg
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### #8gnasher

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Posted 2011-November-23, 16:13

nigel_k, on 2011-November-23, 14:04, said:

I understand the example, but doesn't Butler just expand the IMP swings on all hands? If half the room gets 100 and the other half gets 200 then everyone gets +/- 2 instead of +/- 1.5. Can the choice of scoring can actually affect the outcome to any siginificant extent?

Butler exaggerates the IMP swings when the score distribution is bimodal, but not (or less so) when it isn't. Compare these two, in a 100-table event:
99x +600, 1x -100: datum = 593, scores: 99x 0, 1x -12
50x +600, 50x -100: datum = 250, scores: 50x +8, 50x -8

So the cost of going -100 is 16 when the scores are bimodal and 12 when they aren't.

I don't know of any specific example of that effect affecting the result of an event, but I'm sure it has done.

There is another disdvantage of Butler scoring in conjunction with the IMP scale. It's best understood by reading the story at the top of this article:

http://users.skynet....e/bastille.html
... that would still not be conclusive proof, before someone wants to explain that to me as well as if I was a 5 year-old. - gwnn
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### #9Maponos

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Posted 2013-January-16, 15:08

According to law 78D of the WBF Laws of Duplicate Bridge, the conditions of contest (which include the method of scoring) may not conflict with other laws. Those laws specify that a score difference of 700 points is worth 12 Imps. As we have seen, datum (Butler) scoring awards as many as 16 Imps to a score difference of 700 points. This would seem to indicate that datum scoring is illegal in events run under the WBF Laws. Opinions?
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### #10nige1

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Posted 2013-January-16, 22:24

An advantage of imping against a datum is that as soon as the datum on a board is known, each player can calculate his own score. IMO...
• No scores should be dropped,
• A Bastille scale should be used, and
• The datum should be calculated to ensure that the raw imps sum to zero across the field.
However imps are calculated, the totals should be capped, or converted to VPs on a skewed scale.

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### #11pigpenz

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Posted 2013-January-16, 23:12

I always liked total imp scoring where you are compared on imps to each pair, not average
Puts a premium on game and slam bidding.
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### #12gordontd

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Posted 2013-January-17, 03:12

pigpenz, on 2013-January-16, 23:12, said:

I always liked total imp scoring where you are compared on imps to each pair, not average
Puts a premium on game and slam bidding.

The premium is more significant if you add but don't average the cross-imps?
Gordon Rainsford
London UK
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### #13gordontd

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Posted 2013-January-17, 03:23

Maponos, on 2013-January-16, 15:08, said:

According to law 78D of the WBF Laws of Duplicate Bridge, the conditions of contest (which include the method of scoring) may not conflict with other laws. Those laws specify that a score difference of 700 points is worth 12 Imps. As we have seen, datum (Butler) scoring awards as many as 16 Imps to a score difference of 700 points. This would seem to indicate that datum scoring is illegal in events run under the WBF Laws. Opinions?

Law 78B says:

Quote

In international matchpoint scoring, on each board the total point difference
between the two scores compared is converted into IMPs according to the
following scale.

The two scores being compared are the datum and the individual score, and they are converted according to the scale given. There are plenty of objections to Butler that can be made, most of which have been made above, but I don't think your one stands up.

In any case, the law you mentioned specifically allows different scoring methods, which will obviously not be the same as the methods the law has already given. I think the sense in which they should not conflict is that they may not, for example, change the raw scoring table such that hearts score more than spades.
Gordon Rainsford
London UK
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### #14WellSpyder

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Posted 2013-January-17, 05:40

gordontd, on 2013-January-17, 03:12, said:

The premium is more significant if you add but don't average the cross-imps?

Obviously! It will be (n-1) times as large.

Well, OK, I know all the scores will be affected by the same factor and the ranking will be identical, but isn't that a minor consideration??
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### #15rhm

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Posted 2013-January-17, 14:10

You should try to convince everybody where you live to switch to cross-IMPs.

Butler has one advantage: It is easier to calculate.

It has a lot of drawbacks:

1) It doesn't simulate a team match. This can easily be seen when you calculate the Butler and Cross-IMP scores for a field of two tables. The Cross-IMP score matches the team score, the Butler score doesn't.

2) The sum of the Butler scores does not need to be equal to 0. It can easily be that the EW players on a given board on average get +0.5 IMP while NS on average get -0.5 IMP. This "noise" is pure random. (Imagine that you play matchpoint pairs and at the end of the session the TD takes his dice and starts to announce: "Board 1: a 4. NS get 1% extra, EW 1% less. Board 2: a 2. Too bad for NS: -3%, congrats EW: +3%. Board 3: a 6! NS get a whopping 5%!! Tough luck EW: you lose 5%." This TD is not going to make it to board 28.) The sum of the Cross-IMPs is always 0 (barring TD decisions).

3) In Butler, we need to calculate a datum score. This datum score needs to be rounded to the nearest multiple of 10. This introduces strange errors. As an example, it is perfectly possible that a table that makes 10 tricks in 2 will get the exact same score as the table next to it where only 9 tricks were taken. In Cross-IMPs the 10 trick table will always score better.

4) In a Butler, often the extreme scores are thrown out. The idea is that these scores are strange anyway. This is horrible. There is no a priori reason why the extreme scores should be stranger than the scores in the middle. (Think of a board where NS can take 12 tricks in hearts and EW can take 12 in spades. I would consider all games, small slams and grands normal results, as long as they lead to 12 tricks. The one pair that play 2NT because one of the players forgot a Jacoby 2NT response to 1 produced the result in the middle, but it is not normal.)

5) The calculation method in Butler is fundamentally unsound. In both Butler and Cross-IMPs, an average is calculated. The difference lies in when this is done. In Butler the average is calculated first and then the IMPs are calculated. In Cross-IMPs the IMPs are calculated first and then the average is determined. Every student in science knows that you are supposed to calculate first and then average. (Think of a light bulb that is connected to the power outlet. Because we are dealing with alternating current, the average current is 0 Ampere and the average voltage is 0 Volt. Using the Butler method to calculate the power used by the lamp, by averaging first, we get 0 V x 0 A = 0 W. That doesn't really match with the fact that the lamp does produce light and the fact that we do have to pay a utility bill. However, if we multiply the voltage and current first, we get an alternating power that is always positive or 0. Therefore, the average power consumption is positive.)

Maybe this will give you the arguments to change things.

Rik

I am not convinced.
The truth is pairs play is different to team play, since in the first case there are 2 players forming a "team" and in the other case there are 4 (or 6) and there is no rational way 2 Bridge players can act as if they were 4 or 6.
It is as simple as that and no method of scoring can change this.
Butler is not unsound. It is a different way of scoring, which gives more momentum to the big hands and the big results (compared to matchpoints), just what contract Bridge is about.
Your comparison with science students is plain hogwash!
Contract Bridge was original about total point scoring not about IMPs and the first team matches were all played based on this.
It is worth noting that total points is the basis of contract Bridge not IMPs nor matchpoints or anything else. We score our result in total points, which is somewhat arbitrary, and only thereafter we convert them into matchpoints or IMPs.
Imps already reduces the effect of the big results. There is nothing better or worse by taking average of total points instead of taking averages of IMP scores.
There is nothing inherently superior in cross IMPs compared to Butler and if Butler rewards good game and slam bidding slightly more, fine with me.
There are other methods of scoring like Patton etc, all requiring subtle changes in tactic.
So what?
I doubt that anybody changes his tactic whether you tell him the tournament is scored as cross IMPs or Butler.
It is a storm in a teacup.

Rainer Herrmann
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### #16mycroft

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Posted 2013-January-18, 15:24

Butler is absolutely unsound:
1) you compare against a non-bridge score, and then convert using a table that was designed around bridge scores, and their very common breakpoints (Tell me, how many IMPs does a 45 point difference get you?)
2) the nature of datum scoring is such that one side or the other, sort of at random, will have their average be +IMPs, and the other side -IMPs. It maybe be only one or two (but it's been 5 in my memory, long time back), but that still biases the results.
3) there are cases (that have happened) where a score correction in your favour *decreases* your IMP score on the hand. That's almost the definition of an unsound scoring method: doing better hurts your score.

You are absolutely correct that it probably doesn't change the play; but what's a tempest in a teapot is "why would anyone in these days of computers argue for a broken system, just because *they* can check the math?"
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### #17rhm

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Posted 2013-January-18, 17:20

mycroft, on 2013-January-18, 15:24, said:

Butler is absolutely unsound:
1) you compare against a non-bridge score, and then convert using a table that was designed around bridge scores, and their very common breakpoints (Tell me, how many IMPs does a 45 point difference get you?)
2) the nature of datum scoring is such that one side or the other, sort of at random, will have their average be +IMPs, and the other side -IMPs. It maybe be only one or two (but it's been 5 in my memory, long time back), but that still biases the results.
3) there are cases (that have happened) where a score correction in your favour *decreases* your IMP score on the hand. That's almost the definition of an unsound scoring method: doing better hurts your score.

You are absolutely correct that it probably doesn't change the play; but what's a tempest in a teapot is "why would anyone in these days of computers argue for a broken system, just because *they* can check the math?"

Because any method has problems and I favor simple scoring methods, which can be done without a computer even though I happen to be a computer professional.
The IMP conversion and VP conversion in itself can lead to irregularities. Irregularities like revokes by other pairs, who are not in the running, are much more likely to affect your score or even more how others pairs play against each other, where you are not involved at all.
Bridge is a game of skill. Nevertheless luck and coincidence play a big but not overwhelming role, just like in real life.
That seems part of the attraction of this game, because it allows people to play in the same tournament with different skill levels and not always do the best come out on top.
Something, which does not happen in chess for example.
I do not consider the Butler method unsound, just because in very rare cases the result could be slightly different to cross IMPs.
By the way, the result quoted above did not decrease your IMP score and I do not see how this can happen, when your total point score improves. Apparently your IMP score did not improve by the score adjustment while that of others did, because the datum changed slightly too.
A very unlikely but apparent possible outcome and the cause is the IMP conversion table, not the Butler method. I could not care less and do not consider cross IMPs fairer.
Scoring cross IMPs it could happen that you are all the time just below the score difference where the IMP table changes in your favor while another pair just reaches the point where the IMP table changes in its favor. Is this fair? I do not know and I do not care. It does not have a profound influence on the way the game should be played nor is it likely to have a profound effect on the result in general.

Rainer Herrmann
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### #18pigpenz

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Posted 2013-January-18, 18:18

WellSpyder, on 2013-January-17, 05:40, said:

Obviously! It will be (n-1) times as large.

Well, OK, I know all the scores will be affected by the same factor and the ranking will be identical, but isn't that a minor consideration??

True but one hand you can say in a 13 table field you could lose 100+imps on one hand, so not all
hands are created equal,(same as in cross imps) but penalty is more severe
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Posted 2013-January-18, 18:30

If Rainer is a computer professional, he should know enough about mathematics to know that he should average after all non-linear operations have been performed, and never before. After all:

f(Sum(x/n)) <> Sum(f(x))/n

There is a right way and a wrong way to calculate an average (which is exactly what IMP pairs scoring tries to do). If I give you 3 cubes: one with a side of 1 dm, one with 2 dm, and one with 3 dm, can you tell me what the average volume is? Of course, says Rainer. I simply average the length of the cubes and calculate the volume corresponding to this average length. The average cube has a side of 2 dm and, hence the average volume is 8 dm3 or 8 liters.

I would ask Rainer to please fill these three cubes with fuel for me and I will pay him for 3*8 (=24) liters while filling up my gas tank with 36 liters (1+8+27). The next time, I will bring 3 new cubes of 1 dm, 1 dm and 4 dm, respectively and I will be able to fill my gas tank and the one for my wife for the same price. Finally, I will get 3 cubes: 2 with a length of 0 dm, and 1 with a length of 6 dm. The average length is again 2 dm and the average volume, according to Rainer, is again 8 dm3. He will fill all 3 cubes, enough to fill up my wife's car and my own, and the ones for our siblings and our parents and I will pay him for 3*8 = 24 liter.

This is going to be one easy way to improve my fuel economy. Pretty soon I will be trading in my little Japanese one for something bigger. It won't be one of those fancy German cars, though. I don't want to run the risk that it was engineered by Rainer.

Rik
I want my opponents to leave my table with a smile on their face and without matchpoints on their score card - in that order.
The most exciting phrase to hear in science, the one that heralds the new discoveries, is not “Eureka!” (I found it!), but “That’s funny…” – Isaac Asimov
The only reason God did not put "Thou shalt mind thine own business" in the Ten Commandments was that He thought that it was too obvious to need stating. - Kenberg
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### #20mycroft

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Posted 2013-January-18, 19:18

rhm, on 2013-January-18, 17:20, said:

I do not consider the Butler method unsound, just because in very rare cases the result could be slightly different to cross IMPs.
Nor do I.

Quote

Apparently your IMP score did not improve by the score adjustment while that of others did, because the datum changed slightly too.
You are correct. The full quote:

Quote

A fine example of what the Butler system can lead to was provided in a tournament in Scheveningen early in 1994. The main players are none other than Hamman-Wolff and Leufkens-Westra:

In the last round of that tournament, a board had been scored 2 NT+1: +180. The opponents on the board, Mrss. Hamman-Wolff, sought and got a rectification. They expected to gain one IMP and consequently one place, but instead lost one place and 2000 Dutch guilders.

What had happened? Together with a change of score, this rectification induced a change of datum-score, the average with which all scores are compared. This average fell from +240 to +230.

Hamman-Wolff originally got 240-180 = 60 = 2 IMP
After the rectification, this became 230-150 = 80 = 2 IMP

On the other hand, the Dutch pair of Leufkens-Westra (playing North-South) originally scored 400-240 = 160 = 4 IMP. This became 400-230 = 170 = 5 IMP, gaining them one IMP and a lone sixth place (originally they had been classed equal sixths).

Quote

Scoring cross IMPs it could happen that you are all the time just below the score difference where the IMP table changes in your favor while another pair just reaches the point where the IMP table changes in its favor. Is this fair? I do not know and I do not care. It does not have a profound influence on the way the game should be played nor is it likely to have a profound effect on the result in general.
In general, every day nobody dies. It's the specifics that are such a problem :-) Yeah, it was kind of fun to score up the BAM evening by hand and not bothering to look at the official results on the recap. It's not, however, a big enough deal that I want to introduce a system back that has that benefit (but throws out results, generates non-bridge data to compare against, etc.) over one that can't be hand-replicated, but is accurate. And yes, I know IMP pairs is a crapshoot. But again, that's no reason to artificially, for non-bridge reasons, add more luck.
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