Here are some bridge problems faced byBalicki and Zmudzinski in the 2014 EBTC.

vs. FRANCE, board 27. Balicki is East.

1♣ = 12-15 bal or 16(15)+ natural or 19+ any hand

Balicki knows his partner has a strong balanced hand, so he wants to compete to 3♣. However, he does not want his partner to bid any more. Balicki would like to be able to make a "weak" 3♣ call.

Here is the video of his action on this hand:

Notice howBalickiplaces his bid almost completely covering the previous pass.

vs. DENMARK, board 26. Balicki is North.

1♣ = Strong, artificial

1♥ = 2 suit same shape (or any 3-suiter) 8-15

1♠ = Pass or correct

Double would show diamonds and spades, good hand.

Balickihas the strongest hand he could have for this sequence. He is 5-5, and he has a maximum for his point range. He wants to make a "strong" double.

The video:

Notice howBalickiplaces his double card far from the edge of his previous bid.

vs. ESTONIA, board 25. Zmudzinski is South.

Zmudzinski has a Yarborough. He wants his partner to shut up. He wants to make the weakest pass he possibly can.

The video:

Notice howZmudzinskiplaces his pass almost right on top of his previous pass.

vs. ISRAEL, board 17. Zmudzinski is West.

Zmudzinski has a very strong 4♥ preempt. He could be a lot weaker. He knows that North may compete to 5♠, and he would like his partner's cooperation if that happens. He wants to make a "strong" pass.

The video:

Notice howZmudzinskiplaces his pass card far from the edge of his previous bid.

For each of the above hands, the player made a narrow bid-placement when he had a weak hand in the context of what he has already shown, and he made a wide bid-placement when he had a strong hand in the context of what he has already shown.

These examples illustrate that Balicki and Zmudzinski are not consistent with their bid placement. Other than that, these four hands by themselves prove nothing. They are four hands chosen from 14 matches B/Z played in the 2014 EBTC.

Is the narrow vs. wide matching weakness vs. strength on these four hands a coincidence? Or is this pattern of narrow for weak hands and wide for strong hands a pattern which B/Z follow consistently throughout the tournament? This question is answered in the following pages.

The hypothesis regarding the bid spacing of Balicki-Zmudzinski is as follows:

On the second round of bidding or later, when the bid is placed on the tray with a wide space between the current bid and the previous bid, that indicates a good hand (within the context of the auction). When the bid is placed on the tray with a narrow space between the current bid and the previous bid, that indicates a bad hand.

There are two difficulties involved with verifying this hypothesis:

1) Observation. There may be a dispute about whether there is a wide space or a narrow space. The picture on the video is not always ideal for determining this. Also different people may have different views about what is wide and what is narrow.

2) Evaluation. One person's good hand may be another person's bad hand. Thus, there may be a dispute about whether or not the hand in question is what is indicated by the bid spacing.

It was important to examine every hand from every match B/Z played in the EBTC. Choosing only a few matches or hands would potentially create bias, since the excluded hands might indicate the opposite conclusion.

I examined every bid from every auction that B/Z made in order to eliminate bids where it was clear that signaling the suggested information would be of little or no value. For example, auctions where B/Z passed throughout, or bids where a player is placing the contract or determining what his partner has so he can place the contract. I did this without looking at the videos or the cards held. I was just looking at the bidding sequences. This would avoid wasting time examining videos which couldn't matter. Most of the potentially meaningful bids occurred on the second round of the auction, although there were several which occurred on later rounds. I took a liberal view on which bids to include, since if I included a bid where no signal would be given it wouldn't make any difference -- the bid spacing would presumably be normal and it would be ignored. There were over 200 bids which needed to be examined.

Next, I enlisted the help of several volunteers to examine the videos and determine what the bid spacing was for the bids they observed. Each volunteer examined between 30 and 40 bids. The observers had no idea what the hand was. They only looked at the videos.

The reason for these observations was to find bids where the bid spacing was definitely wide or definitely narrow. Each bid was evaluated as one of the following:

• Clearly wide
• Somewhat wide
• Normal
• Somewhat narrow
• Clearly narrow
• Couldn't see

Four observers independently examined each bid. To accept a bid as definitely wide or definitely narrow, I required at least 2 of the observers saying that the bid was clearly wide or narrow, and those who didn't, to say that it was somewhat wide or narrow. If the observations of the bid did not meet these standards, I didn't use the bid. The observers found 65 bids which qualified. If they were signaling it is certain that some bids where they signaled would have been missed, but that isn't important. What is important is that every bid in the study was either clearly wide or clearly narrow.

As further verification of these observations, Rui Marques measured the actual distance from screenshots of the bids. All of the bids which the observers said were narrow had a distance of less than 1 1/2 inches from the previous bid, usually much less. All but one of the bids which the observers said were wide had a distance of greater than 1 1/2 inches, usually much greater. Considering the difficulties involved with these observations and measurements, these are remarkably consistent results. There can be no dispute about the spacing of these bids.

It is important to understand that these 65 bids were not selected bids which satisfied the hypothesis. They were chosen in a totally objective manner, with no knowledge of the actual hand. The only basis upon which these bids were chosen was that the observers found the bid spacing to be clearly wide or clearly narrow.

The key question is whether or not these spacings could be predicted. Could one look at the actual hand held by the bidder and the auction, and predict whether the spacing would be wide or narrow? If this prediction could be made consistently, that would be solid evidence that B/Z were signaling.

I put together an expert panel to independently make the following decision: For each of the 65 bids, if they were permitted to signal in such a manner would they place the bids with wide or narrow spacing? These experts are:

• Sabine Auken
• Tony Forrester
• Chip Martel
• Fred Stewart
• P.O. Sundelin

For each bid, the majority choice was compared to the actual spacing.The panelists had no idea what the spacing actually was. They were looking only at the hand and the auction.

If there were no signaling, the spacing would have no relationship to the hand. That would mean whether or not the signal chosen by the panel matched the actual spacing would be just by chance. It would be expected that the signal chosen would match the actual spacing roughly half the time.

If the signal matched the spacing substantially more than half the time, that would be strong evidence that there was signaling. It could happen by chance, of course. But the greater the percentage of matches, the less likely it would be to happen by chance.

One might expect that if B/Z were signaling the signal chosen by the experts would always match the spacing. However, there are several reasons why this is not the case:

• B/Z might disagree with the evaluation of the experts. Bridge opinions do differ. Also, the parameters which B/Z are using for their evaluation might not be exactly the same as the parameters used by the experts.
• B/Z might have chosen not to give a signal in the particular situation, and the bid might have been placed wide or narrow randomly.
• B/Z might have been careless with how they placed their bid. This happens with any illegal signaling system.
• B/Z might have been unable to place their bid the way they want. This can happen if they are E-W and their screenmate is moving the tray as they bid.
• B/Z might have chosen for personal or other reasons not to signal vs. a certain team or teams.
• The observation of the spacing might have been inaccurate even though all observers saw it the same way. The camera angles can be tricky, and what appeared to be a wide or narrow bid might have actually been a normal bid placement.

The above happenings will not occur often. But they will occur occasionally, which is why we cannot expect a 100% agreement if they are signaling.

The actual results are as follows:

Out of the 65 clearly irregularly-spaced bids, the majority choice of the expert panel matched the actual spacing 56 times. When the expert panel was unanimous (40 hands), they matched the actual spacing 38 times.

To put this in perspective, assume the gaps have no meaning. If the gaps have no meaning, then the expert panel should have no correlation with the gaps. The experts’ choice of spacing would be completely independent of the observed bid spacing and, in theory, would match about 50% of the time by pure chance. What is the probability of 56 out of 65 matches? Or 38 out of 40? With a 50% chance of being right for each bid, the probability of this occurring by chance is minuscule.

The rest of this article will cover the panel's vote on each of the 65 irregularly-spaced bids.

Here are the exact instructions that I sent to the expert panel:

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For each problem you are given a bidding sequence and a hand, and you are making the final call. You must decide whether you would signal with a narrow spacing or a wide spacing when making this call. Definition of what is a narrow spacing and what is a wide spacing is as follows:

Everything is in context of what has already been shown. This includes what is shown with the bid made at this turn.

For bids other than pass or double:

• At 1 and 2-levels, the emphasis is on strength. Narrow means weaker. Wide means stronger.
• At higher levels, the emphasis is on interest in bigger things (game or slam). Narrow means little interest. Wide means real interest.

For doubles:

• At low levels: If the double is a penalty double, narrow means really want to defend here -- Wide means not so clear. If the double is a takeout double, narrow is weaker and wide is stronger.
• At higher levels: It is mostly a matter of offensive vs. defensive orientation. Narrow is more defensively oriented, suggesting partner pass if close. Wide is offensively oriented, suggesting partner bid if close.

For passes:

• At low levels: If the strength of the passer has not been defined, narrow means weaker and wide means stronger. If the strength has been defined, narrow is a suggestion that partner not compete and wide is a suggestion that partner should compete.
• At higher levels: It is mostly a matter of offensive vs. defensive orientation. Narrow is more defensively oriented, suggesting defending. Wide is offensively oriented, suggesting competing.

In general, if the decision looks borderline it is probably right to choose the narrow bid-spacing.

Another way to look at the evaluation might be as follows: Suppose you are playing without screens and you are allowed to be unethical with huddles. A quick action is like a narrow bid-spacing. A slow action is like a wide bid-spacing.

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(Editor's note: Kit's original article included all 65 hands. In the interests of conciseness, we have displayed the hands from only one of the 14 matches, POLAND vs. DENMARK, so you can get an idea of what the expert panel saw. If you are interested, thefull list of 65 boards, along with other data relevant to the investigation, can be found here.)

Each board is labeled with a three-letter code indicating the opponent, the board number, the player making the unusual spacing, and which round the unusual spacing occurred. The final call in each auction is always highlighted and was observed with an unusual spacing in the video. If you put your mouse over the highlighted bid, you will see what that spacing was observed as.

27. Den 18 z 2

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28. Den 25 b 2

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29. Den 26 z 2

1♣ = Strong, artificial

1♥ = 2suiter, same shape (or any 3-suiter), 8-15

1♠ = Pass or correct

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30. Den 26 b 2

1♣ = Strong, artificial

1♥ = 2suiter, same shape(or any 3-suiter), 8-15

1♠ = Pass or correct

Dbl = Good hand, diamonds and spades

A full summary of each hand's spacing along with the panel vote is available on the next page.

Here are the actual spacings for each of the 65 hands with clearly irregular spacing, along with the votes of the panel of experts. Many of the votes were unanimous, although as one might expect there was some disagreement. The majority vote was deemed to be the signal which would be given.

The panel of experts was, in order of the votes:

• Fred Stewart
• Tony Forrester
• Sabine Auken
• Chip Martel
• P. O.Sundelin

The number in parentheses in the consensus column indicates how many of the five panelists voted for the majority choice.

The majority choice matched the observed spacing on 56 of the 65 bids. The bids for which the majority choice did not match the observed spacing are in red.