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2♣ is invitational or better, initially size-ask. 2♦ is minimum (11-12 in 11-14 range) without 5-card major, 2M is minimum with 5M, 2NT is any maximum (then 3♣ is puppet).

After 1NT - 2♣; 2♦, then 2♥ shows 4 hearts, scramble on the way to stop and play in 2M or 2NT.

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I think Nic is right. I intended to write a quick and dirty software monte-carlo simulation to proxy this cheating scenario, using different colored balls, but when visualizing the steps I would take, I decided the outcome was so obvious I don’t really need to write the program. Heh.

I start with a huge vat of balls … tanker load say … 15% (or whatever that should be, I will use Nic’s approximation) are red, representing the 5-heart hands, 20% (or whatever) are blue, representing the 4-heart hands, the balance black.

How many hands did BZ play? Say 150. So we draw at random 150 balls.

How often were they on defence, with Z leading, not having bid hearts, and trump not hearts? These are hands ‘with potential’ to cheat. Say 26. We draw down 26 balls.

For how many of those did B have the 5-heart or 4-heart condition? Say 12? Draw them down, call them ‘suitable’ hands.

Finally, how often did B signal? Let’s say 10 times, let’s say 5 times for 5-hearts and 5 times for 4-hearts. We draw down 10 final balls that represent those signals.

But wait, after doing all that drawing down, it’s obvious we really didn’t need to make all those draws for this exercise. If we had simply reached into the huge vat of balls and drawn 10, we arrive at precisely the same point.

(And note it doesn’t matter how many of the ‘suitable’ hands might also have had 5-hearts or 4-hearts and were not signalled, in our example 2 of them)

Now the signalling question becomes simply ‘in 10 tries, what are the chances of randomly drawing 5 red balls and 5 blue balls’? The answer has NOTHING TO DO with the sizes of the draws along the way. The ‘150’ hands played could be any number. The size of the ‘26’ potential hands could be any number. The number of ‘suitable’ hands doesn’’t matter. The calculation is independent of those draws … you arrive at the same place with one draw from the huge vat.

The answer is Nic’s calculation, approximately 1/ (0.15^5 x 0.20^5) or 1 in 40 million or so.

Another way to look at it. Instead of different colored balls, consider each ball (hand) as having no initial color, just a collection of potential colors. Those potentials do not change if you draw them down in stages. When the final 10 balls are selected, the probability wave collapses and a color pops up. 15/20/65% of the time it will be red/blue/black or 5-h/4-h/no-h. What are the chances, in 10 wave collapses, you will end with 5 5-hearts and 5 4-hearts?

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Kurt:

Presumably your ‘coin toss’ study is to examine the chances of a head (or series of heads) appearing. You toss 100, and record 45 heads.

You conclude a head will appear 45% of the time, but wonder if your sample size was too small. So you repeat for 1000 flips, and record 512 heads. Now it’s apparent where your study is heading.

If you stumbled upon a vast batch of BZ deals where BZ was playing the same dirty tricks, your N/n would approach 0.443 and your calculation would approach Kit’s. I’m repeating myself here, but I think you’re measuring two different things … results from a Specific Case subset, and Kit’s General Case.

Kit just commented below, saying approximately the same thing in a different way I think, but more eloquently.

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Since there are a few people out there who seem to know the PS methods (or think they do), feel free to PM somebody you trust who might post a ‘hey a birdy told me to look for such and such .. ’

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Steve:

Thanks for your explanation. I understand what you wrote. It’s just that I don’t understand your calculation. You said the odds are about 0.0015. I think that is 0.443 ^ 8. You used exponent ‘8’ because that is the number of remaining hands in the 12, after you used 4 hands to weed out other ‘similarities’ (I’ll refer to ‘4’ as the ‘weed number’, to be left with the one 5-property similarity.

It’s that exponent I have a problem with. It’s entirely possible (I think) to have different weed numbers based on a couple of things … (1) the order in which you select your hands, and (2) your definition of what is a similarity.

If I select hands beginning with deals 9, 11, 4, 3, I might get a totally different weed number (the ‘other’ similarities vanish or continue at a different rate) than the sequence 1, 2, 3, 4. Also if I loosen or tighten what I consider to be a ‘similarity’, my weed numbers would vary.

If my weed numbers change, so does the exponent and so do the odds, and I don’t understand why the order of hand selection or my subjective definition of ‘similarity’, should change the odds.

Put differently, maybe I’m asking why your exponent = 8 (and which is a function of what I think is a variable weed number) and not = 12. Why are hands in the weeding process not included in your odds calculation?

But I’m repeating myself and this topic is probably a snoooozefest for most, so never mind :-).

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Kurt:

Thanks for the explanation. I see what the difference is. You and Kit are calculating odds for different things. Kit is (correctly for his purposes) making the General Case, and you’re arguing for the much smaller Specific Case, a sample size of N, with n boards having the 5-property.

Or put differently, Kit’s General Case calculation is over all cards, so N and n are large. Say N = 1,000,000 and n = 443,000, you would say the chance the first card selected has a 5-property is 443,000/1,000,000, the chance for the second card is 442,999/999,999, etc, which will produce Kit’s number for large N.

Ummm say we wanted to study the results of flipping a true coin. Kit looks up the flip probabilities, and finds in general terms, we flip heads half the time.

We happen to have a sample of 100 coin flips that turned out to be 45 heads and 55 tails. Kit wants to know what are the general chances of flipping 5 consecutive heads. You use the sample to calculate that chance at 45/100 x 44/99 x … 41/96 to get .0162, and you’re right for the Specific Case of that particular sample. Kit says the chance is 0.5 ^ 5 or 0.0313, and he’s right for the General Case.

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Steve: Your calculation is partly a function of how many bell rings it takes to wring out all the similarities that one might find? On the first ring, if there was only the one similarity, the longest-suit-equals-5 situation, your calculation would be the same as Kit's I think, about 0.443^12 or 1/17000 or 0.000057. Your example rings four bells to reduce to one similarity, and the odds become 0.443^8 or 0.0015. But if I could liberally invent similarities to live through say 8 bell rings, the odds increase to 0.443^4 or 0.039.

And won't your calculation depend on the order of the hands you ring the bells? If you start hand 9 for example, good chance you'll reduce to a the special similarity in a number of rings not equal four.

I don't understand how subjective similarities, or the order you choose to look at the hands, have anything to do with this calculation.

Just curious, not a mathematician nor statistician.

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Let me first state I'm neither mathematician nor statistician.

Kurt I'm not following your explanation. The chance that any hand's longest suit is 5, is 44%. That chance is a constant, doesn't change.

When you calculate your 1 in 50,000 odds, with each additional card in the (k=12) group, your method changes the odds of the next hand having that 5-card property. You multiply n/N by (n-1)/(N-1) by … (n-11)/(N-11), decreasing the 5-property chances. You start with n = 44 and N = 100, so you’re claiming (correctly) the first hand has a 5-property 44% of the time, but the 12th hand just 37%.

I think the problem starts with your statement “On n of these boards B has a hand with a given property (e.g., longest suit is 5 cards)”, which should read “On ALL of these boards B has a hand with a 44% chance of a given property (e.g., longest suit is 5 cards).

I think your calculation defaults to 0.44^12, which agrees with Kit's calculation. However I stand to be corrected!

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Just for fun, I tallied the actual IMP results for the BZ hands where they have been observed to have signalled. There are (1) 12 hands where there were Gestures within 30 seconds of dummy coming down, and (2) 16 hands where Gestures were made later in the play. I was able to identify the hands in (2) by matching the published time of the Gesture to one of Nic’s spreadsheets. There were more than 16 events in the (2) hands, but for some hands there were multiple signals.

Anyway, the end result seemed to be a net gain for signalling of -7 IMPS in (1) and +36 IMPs for (2), for a total net IMP gain of +29 in 18 boards. Wow, cheaters do prosper!

But wait, there were some big swings, better take a closer look. For example, there was a +17 swing on a terrific sneaky B lead against a grand. That lead took place before BZ could get their signalling into gear. And wait, there is a +11 swing because of a phantom sac by Germany, and another +11 swing because Germany bid to 5NT down 1 (no details), and etc etc. By the time I remove all swings caused by differences in bidding (hence before any signalling takes place … 9 boards in total … and using my subjective judgement), the net gain for all those signals is down to, um, -6 IMPS.

-6 IMPs in 19 boards (28-9) is not a rousing success. Maybe it was a bad set for the system. Maybe the gain from knowing extra stuff about the hands (hey partner I got a 5-card suit!) is extremely incremental and requires a large sample to begin to show itself. Maybe it already does show itself and they’d be -25 IMPs without the cheating! Maybe they spend so much blood sweat and tears dealing with the signalling, their actual bridge playing suffers. Oh and I suppose it's possible the signalling isn't.

I have no answers, it just seemed an obvious question to answer. I apologize if any of my arithmetic is wrong.

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For randomly dealt hands, 44.3% should have a longest suit (or tied) of 5 cards. In that sample of 218 EBTC deals, BZ should have had 96 such hands whereas apparently they only were dealt 94 of them, so something seriously is not amiss.

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The showing of an open, spread hand to indicate possession of a 5-card suit, makes sense to me only if it is one signal in a battery of signals. If you were going to cheat about just the one thing (I have a 5-card suit somewhere), a smart cheater would signal in the safest most innocuous way. I don't know what precisely that way would be, but it wouldn't be awkwardly spreading out my open hand, inviting easy comparisons to my holding.

However if one was sending two or more signals, it would make some sense for the UI method to also be a memory aid. So if there is anything to the 5-card business, I’d wager something else is going on.

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I said pretty much the same thing in another thread. It seems an inefficient use of cheating resources to waste the signal on a confirmation (you can legally signal like or dislike), when you have other suits to exploit.

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I don't understand why B would be signalling how he feels about the suit that is led. Since he can signal legally how he likes that suit (more or less), why would he waste a good cheating opportunity on a mere confirmation signal? Wouldn't it be more useful to signal information for some brand new suit? Maybe, for example, the closest dummy suit to him that is unbid and unlead. That would also mix things up from hand to hand, making detection more difficult. I tried to check that hypothesis, unfortunately the video often/usually lacks sufficient detail on the layout of dummy's cards.

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What would add interest, at least for me, would to have deals at both tables played at the same time, with the Vugraph interface showing both tables. That would slow things even more, but would add drama and bypass the clunky having to bang a few keys to find out what exactly happened at the other table, if played.

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I love bridge, play it OK, but cannot watch these matches for any length of time because they are tooooo slow. Any casual onlooker would zzzzzzzzzzzzzzz very quickly. The BBO JEC matches (for example) are much more watchable at about 5 minutes per hand. If you want the world to watch, you'll have to dramatically speed up the game.

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Nic: I checked all the deals in that match where Z leads. The first board 17, the spades were flung carelessly quite close to B, too close, and I can see why he would want them moved (and should have asked) so he moved them lol.

The second board 19, the 6♦ hand, dummy placed the cards more carefully (maybe as a result of the earlier board) and not as close to B (but kind of closeish), and B takes some time before quite deliberately moving them as seen in the clip. I agree it now looks borderline suspicious … it was delayed and possibly with illicit purpose … but maybe too it's a bit of a, what, territorial dispute between dummy and B, or B thinks hey I moved them once I can move them again just to bug someone. I might be grasping for straws a bit with that. But is B good enough to scan that board in just a few seconds and see the danger of the squeeze and want partner to have precise count, dunno.

Next board 25, B had lotsa room.

Next board 26 heck I might have asked to be straightened, a little close and a lot messy, but B did not.

Next board 27 B had room.

So to answer your question did it help .. maybe a tad but I'm still unconvinced (although mind open). The mechanics of B's repositioning was totally as I would move them were I to flout convention.

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Melanie: Yes I have watched much material. I just finished watching some random matches to see how often ‘gaps’ and ‘spacing’ varied with ‘honest’ pairs, and they are allll over the place with their bid spacing. Narrow here, next deal wide, then wide-narrow. The very first match the very first hand (Ireland-Russia), a Russian was showing 3 widely spaced passes, then 3 narrow ones, on the same hand. Seems to me the more deliberation goes into the bid, the more likely the player places the bid thoughtfully and deliberately, tending to be narrow-normal. Looks to be normal behaviour with most/many of us (small sample I agree), to more or less randomly space our bids, so attempting to derive meaning from BZ spacing is probably futile. It's not unusual nor should it seem suspicious, to see varying gaps.

The clips of Balick positioning dummy cards look 100% UNsuspicious to me … make that 500%. Sure he should not be touching dummy's cards, so bad on him for that, but the movements look completely no-signal natural. Here is a few-second loop from board 19 Israel Poland.

There are four spades in dummy. They are widely spaced, spanning several inches. Of course he uses his full hand to move the suit as a unit, as a block. What is he supposed to do, poke away with one finger moving a card at a time? Looks completely unsuspiciously natural to me. Then he moves the shorter suits with fewer fingers! Omigod he must be revealing his distribution! I don't buy it, although I did buy it originally until I asked myself how would I move those cards, even if I shouldn't.

Also I don't see the point to watching the thing unspool at 0.25X speed … Z is seeing it at 1X speed and that's what we should be doing.

John: I think the players will have statistical ‘profiles’ and it's entirely possible, I'd bet on it, that a cheating BZ profile would be weird in a sense or two. I'd like to see anyway.

Doug Bennion

After 1NT - 2♣; 2♦, then 2♥ shows 4 hearts, scramble on the way to stop and play in 2M or 2NT.

Doug Bennion

I start with a huge vat of balls … tanker load say … 15% (or whatever that should be, I will use Nic’s approximation) are red, representing the 5-heart hands, 20% (or whatever) are blue, representing the 4-heart hands, the balance black.

How many hands did BZ play? Say 150. So we draw at random 150 balls.

How often were they on defence, with Z leading, not having bid hearts, and trump not hearts? These are hands ‘with potential’ to cheat. Say 26. We draw down 26 balls.

For how many of those did B have the 5-heart or 4-heart condition? Say 12? Draw them down, call them ‘suitable’ hands.

Finally, how often did B signal? Let’s say 10 times, let’s say 5 times for 5-hearts and 5 times for 4-hearts. We draw down 10 final balls that represent those signals.

But wait, after doing all that drawing down, it’s obvious we really didn’t need to make all those draws for this exercise. If we had simply reached into the huge vat of balls and drawn 10, we arrive at precisely the same point.

(And note it doesn’t matter how many of the ‘suitable’ hands might also have had 5-hearts or 4-hearts and were not signalled, in our example 2 of them)

Now the signalling question becomes simply ‘in 10 tries, what are the chances of randomly drawing 5 red balls and 5 blue balls’? The answer has NOTHING TO DO with the sizes of the draws along the way. The ‘150’ hands played could be any number. The size of the ‘26’ potential hands could be any number. The number of ‘suitable’ hands doesn’’t matter. The calculation is independent of those draws … you arrive at the same place with one draw from the huge vat.

The answer is Nic’s calculation, approximately 1/ (0.15^5 x 0.20^5) or 1 in 40 million or so.

Another way to look at it. Instead of different colored balls, consider each ball (hand) as having no initial color, just a collection of potential colors. Those potentials do not change if you draw them down in stages. When the final 10 balls are selected, the probability wave collapses and a color pops up. 15/20/65% of the time it will be red/blue/black or 5-h/4-h/no-h. What are the chances, in 10 wave collapses, you will end with 5 5-hearts and 5 4-hearts?

Doug Bennion

Presumably your ‘coin toss’ study is to examine the chances of a head (or series of heads) appearing. You toss 100, and record 45 heads.

You conclude a head will appear 45% of the time, but wonder if your sample size was too small. So you repeat for 1000 flips, and record 512 heads. Now it’s apparent where your study is heading.

If you stumbled upon a vast batch of BZ deals where BZ was playing the same dirty tricks, your N/n would approach 0.443 and your calculation would approach Kit’s. I’m repeating myself here, but I think you’re measuring two different things … results from a Specific Case subset, and Kit’s General Case.

Kit just commented below, saying approximately the same thing in a different way I think, but more eloquently.

Doug Bennion

I'm trustworthy :-)

Doug Bennion

Thanks for your explanation. I understand what you wrote. It’s just that I don’t understand your calculation. You said the odds are about 0.0015. I think that is 0.443 ^ 8. You used exponent ‘8’ because that is the number of remaining hands in the 12, after you used 4 hands to weed out other ‘similarities’ (I’ll refer to ‘4’ as the ‘weed number’, to be left with the one 5-property similarity.

It’s that exponent I have a problem with. It’s entirely possible (I think) to have different weed numbers based on a couple of things … (1) the order in which you select your hands, and (2) your definition of what is a similarity.

If I select hands beginning with deals 9, 11, 4, 3, I might get a totally different weed number (the ‘other’ similarities vanish or continue at a different rate) than the sequence 1, 2, 3, 4. Also if I loosen or tighten what I consider to be a ‘similarity’, my weed numbers would vary.

If my weed numbers change, so does the exponent and so do the odds, and I don’t understand why the order of hand selection or my subjective definition of ‘similarity’, should change the odds.

Put differently, maybe I’m asking why your exponent = 8 (and which is a function of what I think is a variable weed number) and not = 12. Why are hands in the weeding process not included in your odds calculation?

But I’m repeating myself and this topic is probably a snoooozefest for most, so never mind :-).

Doug Bennion

Thanks for the explanation. I see what the difference is. You and Kit are calculating odds for different things. Kit is (correctly for his purposes) making the General Case, and you’re arguing for the much smaller Specific Case, a sample size of N, with n boards having the 5-property.

Or put differently, Kit’s General Case calculation is over all cards, so N and n are large. Say N = 1,000,000 and n = 443,000, you would say the chance the first card selected has a 5-property is 443,000/1,000,000, the chance for the second card is 442,999/999,999, etc, which will produce Kit’s number for large N.

Ummm say we wanted to study the results of flipping a true coin. Kit looks up the flip probabilities, and finds in general terms, we flip heads half the time.

We happen to have a sample of 100 coin flips that turned out to be 45 heads and 55 tails. Kit wants to know what are the general chances of flipping 5 consecutive heads. You use the sample to calculate that chance at 45/100 x 44/99 x … 41/96 to get .0162, and you’re right for the Specific Case of that particular sample. Kit says the chance is 0.5 ^ 5 or 0.0313, and he’s right for the General Case.

Doug Bennion

And won't your calculation depend on the order of the hands you ring the bells? If you start hand 9 for example, good chance you'll reduce to a the special similarity in a number of rings not equal four.

I don't understand how subjective similarities, or the order you choose to look at the hands, have anything to do with this calculation.

Just curious, not a mathematician nor statistician.

Doug Bennion

Kurt I'm not following your explanation. The chance that any hand's longest suit is 5, is 44%. That chance is a constant, doesn't change.

When you calculate your 1 in 50,000 odds, with each additional card in the (k=12) group, your method changes the odds of the next hand having that 5-card property. You multiply n/N by (n-1)/(N-1) by … (n-11)/(N-11), decreasing the 5-property chances. You start with n = 44 and N = 100, so you’re claiming (correctly) the first hand has a 5-property 44% of the time, but the 12th hand just 37%.

I think the problem starts with your statement “On n of these boards B has a hand with a given property (e.g., longest suit is 5 cards)”, which should read “On ALL of these boards B has a hand with a 44% chance of a given property (e.g., longest suit is 5 cards).

I think your calculation defaults to 0.44^12, which agrees with Kit's calculation. However I stand to be corrected!

Doug Bennion

Anyway, the end result seemed to be a net gain for signalling of -7 IMPS in (1) and +36 IMPs for (2), for a total net IMP gain of +29 in 18 boards. Wow, cheaters do prosper!

But wait, there were some big swings, better take a closer look. For example, there was a +17 swing on a terrific sneaky B lead against a grand. That lead took place before BZ could get their signalling into gear. And wait, there is a +11 swing because of a phantom sac by Germany, and another +11 swing because Germany bid to 5NT down 1 (no details), and etc etc. By the time I remove all swings caused by differences in bidding (hence before any signalling takes place … 9 boards in total … and using my subjective judgement), the net gain for all those signals is down to, um, -6 IMPS.

-6 IMPs in 19 boards (28-9) is not a rousing success. Maybe it was a bad set for the system. Maybe the gain from knowing extra stuff about the hands (hey partner I got a 5-card suit!) is extremely incremental and requires a large sample to begin to show itself. Maybe it already does show itself and they’d be -25 IMPs without the cheating! Maybe they spend so much blood sweat and tears dealing with the signalling, their actual bridge playing suffers. Oh and I suppose it's possible the signalling isn't.

I have no answers, it just seemed an obvious question to answer. I apologize if any of my arithmetic is wrong.

Doug Bennion

Doug Bennion

However if one was sending two or more signals, it would make some sense for the UI method to also be a memory aid. So if there is anything to the 5-card business, I’d wager something else is going on.

Doug Bennion

Doug Bennion

Doug Bennion

Doug Bennion

Doug Bennion

Doug Bennion

Doug Bennion

Doug Bennion

The second board 19, the 6♦ hand, dummy placed the cards more carefully (maybe as a result of the earlier board) and not as close to B (but kind of closeish), and B takes some time before quite deliberately moving them as seen in the clip. I agree it now looks borderline suspicious … it was delayed and possibly with illicit purpose … but maybe too it's a bit of a, what, territorial dispute between dummy and B, or B thinks hey I moved them once I can move them again just to bug someone. I might be grasping for straws a bit with that. But is B good enough to scan that board in just a few seconds and see the danger of the squeeze and want partner to have precise count, dunno.

Next board 25, B had lotsa room.

Next board 26 heck I might have asked to be straightened, a little close and a lot messy, but B did not.

Next board 27 B had room.

So to answer your question did it help .. maybe a tad but I'm still unconvinced (although mind open). The mechanics of B's repositioning was totally as I would move them were I to flout convention.

Doug Bennion

The clips of Balick positioning dummy cards look 100% UNsuspicious to me … make that 500%. Sure he should not be touching dummy's cards, so bad on him for that, but the movements look completely no-signal natural. Here is a few-second loop from board 19 Israel Poland.

https://www.youtube.com/v/sZfhiMO_5lo?version=3&start=1592&end=1600&loop=1&autoplay=1&playlist=/sZfhiMO_5lo

There are four spades in dummy. They are widely spaced, spanning several inches. Of course he uses his full hand to move the suit as a unit, as a block. What is he supposed to do, poke away with one finger moving a card at a time? Looks completely unsuspiciously natural to me. Then he moves the shorter suits with fewer fingers! Omigod he must be revealing his distribution! I don't buy it, although I did buy it originally until I asked myself how would I move those cards, even if I shouldn't.

Also I don't see the point to watching the thing unspool at 0.25X speed … Z is seeing it at 1X speed and that's what we should be doing.

John: I think the players will have statistical ‘profiles’ and it's entirely possible, I'd bet on it, that a cheating BZ profile would be weird in a sense or two. I'd like to see anyway.