[jallerton]

West is on lead against 3NT. If West finds a spade lead this will trivially beat the contract by 1 trick. If West finds any other lead the contract is bound to make exactly 9 tricks.

West asks about the N/S auction before leading. Based on the explanations received, he judges that there are two plausible opening leads: a spade and a heart. He cannot decide which to choose, so mentally tosses a coin. He fishes out a heart lead and declarer claims 9 tricks. The TD agrees that on the given explanation, it was 50/50 whether West chose a spade or heart lead.

However, it transpires that there was misinformation.

Scenario 1. If West had been correctly informed, the reasoning behind West's choice of lead would have been somewhat different. West contends (and the TD agrees) that it was still 50/50 between West leading a spade and a heart.

Ignoring "sympathetic weighting" for the moment, is it correct to:

(a) leave the table result to stand, on the basis that West was no more likely to find the winning lead given the correct explanation; or
(b) adjust the score to 50% of 3NT= + 50% of 3NT-1 on the basis that this "would have been the expectation had the infraction not occurred"?; or
(c) something else (please specify)?


Scenario 2. If West had been correctly informed, West contends (and the TD agrees) that it was 50/50 between West leading a spade and a diamond.
Ignoring "sympathetic weighting" for the moment, is it correct to:

(a) leave the table result to stand, on the basis that West was no more likely to find the winning lead given the correct explanation; or
(b) adjust the score to 50% of 3NT= + 50% of 3NT-1 on the basis that this "would have been the expectation had the infraction not occurred"?
c) something else (please specify)?


Scenario 3. If West had been correctly informed, West contends (and the TD agrees) that he would have been 75% likely to have led a spade and 25% likely to have led a heart.

Ignoring "sympathetic weighting" for the moment, is it correct to:

(a) adjust the score to 25% of 3NT-1 and 75% of 3NT=, on the basis that West was 25% more likely to find the winning lead given the correct explanation compared with the explanation actually received; or
(b) adjust the score to 75% of 3NT-1 + 25% of 3NT= on the basis that this "would have been the expectation had the infraction not occurred"?
(c) something else (please specify)?


What is the correct reasoning in each of Scenarios 1, 2 and 3?

[campboy]

In 1 and 2 there is no damage as defined in 12B1. In neither case did NOS score badly "because of an infraction"; the bad score was entirely due to bad luck.

In case 3 there was damage, since the bad score was partially due to the MI (and partially due to bad luck, but damage either exists or does not; we can't say it 25% exists). I would adjust to 75% of 3NT-1, since that was the expectation without the MI.

[hrothgar]

Please note:

This is what makes logical sense to me. I don't claim that this is consistent with typical rulings. Nor do I believe that this methodology necessarily work if you can't provide good estimates of the prior and posterior probabilities.

I define the "prior" as the probabilities given the incorrect information
I define the "posterior" as the probabilities given the correct probabilities.

From my perspective, the critical issue is whether probabilities shift in the non offending side's favor.

In your first two cases, the odds have not shifted.
The non offending side got unlucky when they flipped a coin, but those is the breaks.

In the third case, non offending side was definitely damaged by the misinformation.
In this case, the world resets completely.
The original coin flip never happened.
The adjusted score is based on a new theoretical coin flip that would "win" 75% percent of the time and lose 25% of the time.

[sailoranch]

I'll take a stab at this. In scenario 1, West would attempt a 50/50 mixed strategy with or without the correct explanation. His attempt at randomization at the table resulted in a heart lead. Is there any reason to believe that he would vary his randomization process based on the different explanation?

I think expectation in 12B1 is conditioned on West's actual lead of a heart. If you think that there is a perfect correlation between the misinformed lead and the corrected lead, then no adjustment. If they are independent, you would adjust to 50% making, 50% -1. Good luck ruling if you think it's somewhere in between.

For what it's worth, I would lean toward no adjustment as it's hard to actually play randomly, and unless West is choosing his lead based on some parity in the nth word of declarer's explanation, I have doubts that the choice would be different.

In scenario 2, I think it's clear to adjust, because the actual table result is worse than the expected 50/50 in spades and diamonds. The difference is that the actual play of a heart when misinformed was no good under the correct explanation. It doesn't make a difference that the two mixed strategies would yield the same expectation when resulting.

In scenario 3, if I think that West would play a spade 75% of the time and a heart 25%, I would adjust to 75% 3NT-1 and 25% 3NT=. Again, the table result of 3NT= is worse than the expectation. But if West is claiming a 75/25 mixed strategy, I would be skeptical. He's judged the utility of each suit to be the same, so it wouldn't matter if it's 50/50 or 75/25 or 100/0.

[mink]

In szenario 1 I assume that the misinformation affects the decision what to lead (the process of the decision is different), but, by chance, the odds of the well-informed decision are the same as the odds of the mis-informed decision (which is hardly true in reality, but anyway). So I cannot see any difference between scenario 1 and szenario 2.

Law 12B1:

Quote

The objective of score adjustment is to redress damage to a non-offending side and to take away any advantage gained by an offending side through its infraction. Damage exists when, because of an infraction, an innocent side obtains a table result less favourable than would have been the expectation had the infraction not occurred – but see C1(b).

What table result do we expect if West got the correct information? For sure, this cannot be something weighted, as there would be no adjustement without misinformation. What we expect is 3nt= or 3nt-1. In one of the expected cases, there is damage. This is true no matter what the odds for 3nt= and 3nt-1 are.

When possessing the correct information, West's thinking process takes a different route, and only at the end of this process the mental coin is flipped. With the correct information the coin is tossed differently, because you never toss a coin exactly the same way.

In scenario 1 and 2 I therefore adjust 50:50.

In scenario 3 no coin is tossed. Rather, if West is able to see that the odds are 75:25 in favor of the successful lead, he will always chose this. Therefore the adjusted score is 3nt-1.

Karl

[campboy]

jallerton, on 2012-October-19, 11:46, said:

(a) adjust the score to 25% of 3NT-1 and 75% of 3NT=, on the basis that West was 25% more likely to find the winning lead given the correct explanation compared with the explanation actually received;

It just occurred to me that there is a simple proof that this is wrong. Consider two cases: i) West receives correct information ii) West receives misinformation, then calls the director who rules on this basis.

In i) (no infraction) West's expectation before choosing a lead is simply 75% of 3NT-1 and 25% of 3NT=.

In ii) West's expectation before choosing a lead is 50% times (result if he leads a spade) plus 50% times (adjusted score if he leads a red card). If he leads a spade he gets 100% of 3NT-1 and if he leads a red card he gets 25% of 3NT-1, so this works out at 62.5% of 3NT-1 and 37.5% of 3NT=.

If we rule in this manner, then, West expects to lose by the infraction even taking into account the adjustment, which must be wrong.

[jallerton]

mink, on 2012-October-20, 03:13, said:

In scenario 3 no coin is tossed. Rather, if West is able to see that the odds are 75:25 in favor of the successful lead, he will always chose this. Therefore the adjusted score is 3nt-1.

Karl

If West is able to see that a spade lead has a 75% chance of success and a heart lead has a 25% chance of success, then yes he would always choose a spade lead. However, my scenario 3 is based on a player not being sure what card he would have led given the correct explanation, but with his instinct suggesting that it is probable, but not certain, that he would have led a spade.

If you prefer, imagine that the probabilities for scenario 3 are determined as follows. The TD finds 20 peers of West who agree that the opening lead on the explanation originally supplied was a toss-up between a spade and a heart. He asks these 20 players what they would lead on the correct explanation. 15 say that they would lead a spade and the other 5 say they would lead a heart.

campboy, on 2012-October-20, 11:32, said:

It just occurred to me that there is a simple proof that this is wrong. Consider two cases: i) West receives correct information ii) West receives misinformation, then calls the director who rules on this basis.

In i) (no infraction) West's expectation before choosing a lead is simply 75% of 3NT-1 and 25% of 3NT=.

In ii) West's expectation before choosing a lead is 50% times (result if he leads a spade) plus 50% times (adjusted score if he leads a red card). If he leads a spade he gets 100% of 3NT-1 and if he leads a red card he gets 25% of 3NT-1, so this works out at 62.5% of 3NT-1 and 37.5% of 3NT=.

If we rule in this manner, then, West expects to lose by the infraction even taking into account the adjustment, which must be wrong.

Using this logic, are you advocating that the Scenario 3 adjustment should be to 50% of 3NT= + 50% of 3NT-1?. That way the expectation of a successful lead becomes 50% plus (50% of 50%), a total of 75%

[Vampyr]

jallerton, on 2012-October-21, 16:38, said:

If West is able to see that a spade lead has a 75% chance of success and a heart lead has a 25% chance of success, then yes he would always choose a spade lead. However, my scenario 3 is based on a player not being sure what card he would have led given the correct explanation, but with his instinct suggesting that it is probable, but not certain, that he would have led a spade.

But the player did not get the chance to make the informed choice of a spade, so it seems unfair that he should receive some percentage of not having led it.

[sailoranch]

Vampyr, on 2012-October-21, 20:21, said:

But the player did not get the chance to make the informed choice of a spade, so it seems unfair that he should receive some percentage of not having led it.

I think this is just the nature of weighted rulings. The NOS didn't get the chance to make the most favorable action. Any adjustment with less than 100% of that action is going to be worse.

Quote

Using this logic, are you advocating that the Scenario 3 adjustment should be to 50% of 3NT= + 50% of 3NT-1?. That way the expectation of a successful lead becomes 50% plus (50% of 50%), a total of 75%

You adjust to the expectation without the MI, not to some weighting that will make the expectation of the result (possibly adjusted, possibly not) equal to that without the MI.

[StevenG]

sailoranch, on 2012-October-22, 00:18, said:

I think this is just the nature of weighted rulings. The NOS didn't get the chance to make the most favorable action. Any adjustment with less than 100% of that action is going to be worse.

Thr corollary is that the offenders are guaranteed a better score than they would reasonably likely have got at the table. This cannot be right.

[iviehoff]

campboy, on 2012-October-19, 17:19, said:

In 1 and 2 there is no damage as defined in 12B1. In neither case did NOS score badly "because of an infraction"; the bad score was entirely due to bad luck.

Jeffrey's examples are carefully designed to expose what "damage" actually means. You have correctly assessed that there is no damage in an objective sense. But it is not the sense in the laws.

12B1: "Damage exists when, because of an infraction, an innocent side obtains a table result less favourable than would have been the expectation had the infraction not occurred". (This is the useful part of 12B1. The first sentence of 12B1 really ought to be deleted, because it doesn't actually do anything beyond express a pious hope, and is of no use to the practitioner except as a distraction.)

So we see, quite clearly, damage is calculated by the comparison of the table result, and the expectation of a result had the infraction not occurred. You cannot say "it was a 50/50 shot either way, so no damage". You have to compare the table result with the 50/50 shot.

Jeffrey's examples are carefully designed to demonstrate the difficulties with this definition of damage. Consider the following example, which illustrates the issue even more starkly.

(1) With misinformation, a heart lead is near certain. Declarer has to make two 50/50 choices which are a toss up, and needs to get them both right to make his contract. The contract is 25% on a heart lead. By misfortune (from the defender's point of view), he gets them both right and it makes.

(2) With correct information, a spade lead is near certain. This resolves one of declarer's two choices, so now declarer only has to make one choice. The contract is 50% on a spade lead. We do not know the outcome, because this didn't happen.

Ex ante, ie, before the hand was played to a result, it is clear that the misinformation was no damage at all, it actually encouraged the defender to make a lead that was not in declarer's interest. However, ex post, there is damage. The defender had a 50/50 expectation with the correct information, and, in comparison to the table result, which is the calculation we are instructed to make, this is damage. Thus damage can exist in a legal sense even in a situation where objectively there was actually quite the reverse of damage.

I am sure this definition of damage has been adopted in order to reduce the number of calculations the director has to make. he director can see the table result, and only has to calculate an expectation for the case with correct information. In an objective assessment of damage, he has to calculate expectations in two cases.

[campboy]

jallerton, on 2012-October-21, 16:38, said:

Using this logic, are you advocating that the Scenario 3 adjustment should be to 50% of 3NT= + 50% of 3NT-1?. That way the expectation of a successful lead becomes 50% plus (50% of 50%), a total of 75%

No. We should not adjust in a manner which leaves NOS worse off on average, but it is perfectly fine to adjust in a manner which leaves them better off on average.

I would adjust to 75% of 3NT-1 because I believe the objective is to adjust based on what might have happened "had the irregularity not occurred". Unfortunately that phrase is in 12C1e (which does not apply), not elsewhere in 12C1, and "equity" (as in 12C1c) is not precisely defined. However, I think that given the wording of 12B1 and 12C1e it makes most sense to interpret "equity" as the expectation had the irregularity not occurred.

[campboy]

iviehoff, on 2012-October-22, 04:17, said:

So we see, quite clearly, damage is calculated by the comparison of the table result, and the expectation of a result had the infraction not occurred. You cannot say "it was a 50/50 shot either way, so no damage". You have to compare the table result with the 50/50 shot.

This is not true. There is no damage, according to the law you quote, unless the bad score is "because of the infraction".

Suppose that in fact West is 50% to lead a spade without the MI, but 75% to lead a spade with MI. He tosses two (imaginary) coins; they both come up tails so he leads a heart. Is there damage?

[c_corgi]

I hope campboy is right, because otherwise the score will be significantly different if the chance of a spade lead without MI was 50% or 51%: if it is 50% the table score stands, if it is 51% the NOS gets his losing guess back.

[iviehoff]

campboy, on 2012-October-22, 04:57, said:

This is not true. There is no damage, according to the law you quote, unless the bad score is "because of the infraction".?

Yes, it is true. All sorts of things can happen after an infraction to change the result. Some of these are random, some of them good or bad decisions. But in general we say that the table result which actually occurred is the table result "because" of the infraction, except when those happenings are SEWOG. We don't make changes for the numerous decisions and chance events that happened between the infraction and the actual table result. When have you ever seen a judgment ruling based upon the expected result immediately after the infraction, as opposed to the table result? Answer, never. This is because it is not a valid procedure. Every time, we use the table result, regardless of the occurrences in between, so long as they aren't SEWOG.

In reality, you know this perfectly well. It is just you are now choking on it because you have been given an extreme case where it is straightforward to see the difference between objective damage and damage as made procedure in the laws.

campboy, on 2012-October-22, 04:57, said:

Suppose that in fact West is 50% to lead a spade without the MI, but 75% to lead a spade with MI. He tosses two (imaginary) coins; they both come up tails so he leads a heart. Is there damage?

Now you have introduced something that is potentially SEWOG. If someone did mentally toss two coins and as a result deliberately chose a 25% line, we would call that "gambling", and treat that as SEWOG. That is the reason for the different approach in this case.

I gave you an example at the end of my previous post, in which the 25% outcome occurred by chance, rather than deliberate gambling. Legally, there is damage, even though objectively there was not.

If the 25% outcome occurred simply because the player played badly, that is not SEWOG. And the table result is indeed the table result "because" of the infraction, despite the various things on the way between the infraction and the table result that affected the result.

I'm sure you know this really.

[iviehoff]

c_corgi, on 2012-October-22, 05:35, said:

I hope campboy is right, because otherwise the score will be significantly different if the chance of a spade lead without MI was 50% or 51%: if it is 50% the table score stands, if it is 51% the NOS gets his losing guess back.

The thing you hope to be true requires campboy to be wrong, I think. It is campboy who is advocating comparing the expected results immediately after the infraction with the expected result without the infraction. This is what results in the 50%/51% sensitivity. You avoid this by doing what the law says instead, ie, comparing the table result with the infraction to the expected result without the infraction.

[campboy]

I'm not even sure any more what you are claiming that I know perfectly well. Let me outline what I believe a little more clearly than perhaps I did before.

In order for there to be damage you need both

i) the table result was worse than the expectation immediately before the infraction
ii) this was caused, at least in part, by the infraction.

You seemed to be saying that we only need i), and since i) was clearly satisfied there was damage. This is not true: we also need ii) and in my opinion ii) is not satisfied unless the correct information would have made West more likely to find the correct lead.

It is in my experience completely normal in MI cases to rule that "correct information would not have made <successful action> any more likely, therefore there was no damage".

[campboy]

c_corgi, on 2012-October-22, 05:35, said:

I hope campboy is right, because otherwise the score will be significantly different if the chance of a spade lead without MI was 50% or 51%: if it is 50% the table score stands, if it is 51% the NOS gets his losing guess back.

This sensitivity exists no matter who is right. If the chance of a spade lead was 51% without MI then (I hope) everyone would adjust; if the chance of a spade lead was 49% without MI then (I hope) no-one would adjust, so whatever you do when it is 50% there must be a point where 1% makes a difference.

In practice of course there is no way you can distinguish between the three cases. Unless I was confident that the chance of finding the right lead was greater with the correct information than without I would not adjust.

[campboy]

iviehoff, on 2012-October-22, 06:24, said:

Now you have introduced something that is potentially SEWOG. If someone did mentally toss two coins and as a result deliberately chose a 25% line, we would call that "gambling", and treat that as SEWOG. That is the reason for the different approach in this case.

No I haven't. The original post asked us to consider a case where West is not sure what he would have done with correct information, but estimates that he would have chosen a spade 75% of the time. This is a perfectly plausible scenario. It is not the same as "West calculated that a spade lead had a 75% chance of being successful", and I don't understand why two responses seem to have interpreted it as such.

[iviehoff]

campboy, on 2012-October-22, 07:01, said:

No I haven't. The original post asked us to consider a case where West is not sure what he would have done with correct information, but estimates that he would have chosen a spade 75% of the time. This is a perfectly plausible scenario. It is not the same as "West calculated that a spade lead had a 75% chance of being successful", and I don't understand why two responses seem to have interpreted it as such.

OK, I understand what you meant now, and now I agree your case isn't SEWOG, it is like my case which you did not comment on.

Now please look at this case again. I'll now re-present it in a slightly different way, so it looks like a normal every day case.

-With MI, a heart lead is near certain. An objective person who bothered to make the complicated calcualtions would say the contract is 25% on a heart lead, though at a glance this is far from obvious. However owing to a complicated sequence of events, poor decisions by both sides, and the outrageous slings and arrows of fate, but nothing SEWOG, the contract makes.

-Without MI, a spade lead is near certain. The contract is, on careful consideration, about 50% on a spade lead. We do not know the outcome, because this didn't happen.

In this case, we routinely say there is damage. We discounted the outrageous slings and arrows, we discounted the poor decisions, we simply looked at the result. We justify this by saying these are slings and arrows and decision points that simply would not have occurred in the different situation without without MI. But essentially this case is no different from the ones that Jeffrey has constructed, he has simply made the location of the slings and arrows particularly transparent and particularly close to the moment where the MI makes a difference.