UI and probabilities

[gnasher]

Consider this hypothetical situation:

 

East thinks for a while before bidding an invitational 3♠. West knows that he was thinking about either signing off in 2♠ or bidding 4♠.

 

West has a marginal acceptance of the invitation. If West knew that his partner was thinking of bidding 2♠, the UI would suggest passing. If West knew that his partner was thinking of bidding 4♠, the UI would suggest bidding.

 

If East's two possible hands were equally likely, presumably we'd say that the UI didn't demonstrably suggest one action over another.

 

Suppose, however, that West is able to make a good estimate of the relative probabilities East's possible hands, and that West knows that it's more likely that East was dealt a bad invitation than that he was dealt a good invitation.

 

That, in combination with the UI, now makes it more likely that pass is the right action than that 4♠ is correct. Does that mean that West is obliged to bid 4♠, or does it fail to pass the test of "demonstrably suggesting" the action? And does it matter how great the difference in probabilities is?

 

[Edited after TylerE's response to clarify what question I was asking.]

Edited September 27, 2009 by gnasher

[TylerE]

I think that there are enough variables in play that West can do whatever he wants at this stage. However, if he does something patently anti-percentage (e.g. passing with a 16 count), and it ends up being right, an adjustment may be in order.

[Vampyr]

Suppose, however, that West is able to make a good estimate of the relative probabilities East's possible hands, and that West knows that it's more likely that East was dealt a bad invitation than that he was dealt a good invitation.

I don't mean to derail your thread, Andy, but I wonder if it isn't also important to consider that you are pretty sure which types of hands your partner has more difficulty with (it is likely that a player would have some idea, from seeing which way partner tends to go wrong when faced with this kind of decision).

[gnasher]

Was this question just too dull to answer, or is it that I didn't explain it very well? Surely it can't be that no one knows the answer?

[Trinidad]

Was this question just too dull to answer, or is it that I didn't explain it very well? Surely it can't be that no one knows the answer?

No, it is a hard question to answer.

 

Let's put some numbers on this, to make the discussion easier: Let's say that 3♠ in an auction like 1♠-2♠; 3♠ shows 15-18. After the BIT, you know it will be either 15 or 18, not 16 or 17.

 

If the auction starts (Pass)-1♠-(Pass)-2♠; (Pass)-...3♠ you have two opponents that are quiet. In principle, you have the problem that you don't know whether partner thought of passing or of bidding game.

 

But if you know that your opponents are bidding on anything. You can exclude that partner has 15. Together with your 7 that would give you a combined 22 HCPs and the opponents would be in the auction.

 

On the other hand, against two solid, conservative opponents, you might have this auction: (1♦)-1♠-(Dbl)-2♠; (Pass)-...3♠ (let's assume that 3♠ is invitational). In that case it is more likely that partner has 15. If you have 7 and partner has 18, what were your opponents bidding on?

 

And then there is the case where both sides have found a fit and both sides are bidding like crazy. Who knows who can make what? You know that the HCPs will be 20-20, but partner may have been thinking about bidding game, based upon his distribution.

 

In other words, yes the odds that partner was thinking about passing or bidding game do matter. But it needs to be possible to somwhat quantify those odds. And it is very hard to quantify the opponents' style in these questions. I don't think that should be a factor in the decision.

 

On the other hand, there are some situations that are somewhat clearer, e.g.

 

Pass-1♣; 1♦-1♥; 1♠-2♠; ...3♠

 

The odds that a passed hand was thinking of shooting game in a known 4-4 fit are much lower than that he was thinking of passing. Nevertheless, I think it is very hard for players, who are not used to deal with UI, to pick that one up.

 

Rik

[bluejak]

Was this question just too dull to answer, or is it that I didn't explain it very well?  Surely it can't be that no one knows the answer?

I find theory questions like this one often difficult and with no sensible answer. So I moved on. I would much prefer an actual hand or two [invented if necessary] to answer.

[nigel_k]

In general you have to take into account the probability of partner holding various hands in deciding whether an action is demonstrably suggested by a hesitiation.

 

If it's a situation where he might pass, sacrifice or make a Lightner double, there are some auctions where a sacrifice is so unlikely that an unusual lead is demonstrably suggested by a slow pass and some where a sacrifice would be common and the slow pass would not suggest any particular lead was desired.

 

But in your pass, invite, or bid game scenario, I'm having trouble thinking of an example where the slow invite would demonstrably suggest one or the other,

[campboy]

The scenario is presumably when you know that partner tends to choose the overbid when he has hesitated. But in that case we can only really talk about the situation in terms of your personal ethics, since the probability is not something the TD can estimate.

[Vampyr]

The scenario is presumably when you know that partner tends to choose the overbid when he has hesitated. But in that case we can only really talk about the situation in terms of your personal ethics, since the probability is not something the TD can estimate.

No, the OP is making the observation that worse hands are more likely than better hands, so partner is more likely to have the former.

 

Suppose you have 14 HCP. The other players have 26, so 8.7 each. Partner, therefore, is more likely to be inviting on 9 or 10 points than on 11 or 12. Similarly, if you have 5 cards in a suit and partner has raised in a situation that does not promise or deny some number of trumps, he is more likely to have 3 than to have 4.

 

So the question is whether, if you have UI (which doesn't itself indicate one direction or another) but you can calculate the probabilities of the above and similar, are you constrained by this knowledge?

 

And I think that this question is very tough to answer, because while "yes" seems reasonable at first, it puts a bigger onus on those who are knowledgeable about probabilities and good at calculating them than on those who are not (but may be equally good bridge players). On the other hand, since the first sentence of this post is true, perhaps weaker hands should be considered the default when slow invitations are made. This tends to be the case in real life, after all.

[cherdanno]

Was this question just too dull to answer, or is it that I didn't explain it very well?  Surely it can't be that no one knows the answer?

I thought it obvious that actions "demonstrably suggested" includes actions that are, given the UI, demonstrably more percentage than before. I couldn't imagine any bridge player would think otherwise.

 

But then, I have really not much of a clue about the laws, and so assumed that the silent majority of posters with better knowledge about the laws than me had reasons for their silence.

 

Btw, if you wanted to construct an example, I would take an invitation by a passed hand, in an auction where a GF is barely possible. I guess you would have to make up the system somewhat :)

[gnasher]

OK, here's a made-up example. The bidding goes

1♣-1♥

1♠-1NT

2NT (slow)

 

1♠ denied a balanced hand and was non-forcing. 1NT was a good 6 to a bad 10. You are the 1NT bidder, and you have a marginal acceptance of the invitation.

 

You know that:

- With 6-4 or 4315, partner would usually have chosen a different invitation. Hence he is likely to be 4225, 4135 or 4144.

- Partner would raise 1NT to 2NT with any 17-count, 20% of 18-counts, and 20% of 16-counts.

- 16-counts occur roughly twice as often as 18-counts.

 

Hence it appears to be 2:1 that partner's hesitation was because he's at the lower end of the range rather than the upper end of the range. Does this mean that the UI demonstrably suggests passing over bidding?

 

What if your estimate were that the odds were 5:1, or 5:4?

[gnasher]

The scenario is presumably when you know that partner tends to choose the overbid when he has hesitated.

My original question was about how the a priori probabilities affect your obligations, but yes, the question applies equally to the probabilities after adjustment for partner's habits.

 

But in that case we can only really talk about the situation in terms of your personal ethics, since the probability is not something the TD can estimate.

Can't we talk about it in terms of what the Laws require? Your obligation to obey the rules isn't dependent on the TD's ability to enforce them.

 

In any case, I don't agree that the TD can't make this sort of estimate. If he needs to know something about your partner's style, he can ask you.

[campboy]

The scenario is presumably when you know that partner tends to choose the overbid when he has hesitated. But in that case we can only really talk about the situation in terms of your personal ethics, since the probability is not something the TD can estimate.

No, the OP is making the observation that worse hands are more likely than better hands, so partner is more likely to have the former.

 

Suppose you have 14 HCP. The other players have 26, so 8.7 each. Partner, therefore, is more likely to be inviting on 9 or 10 points than on 11 or 12. Similarly, if you have 5 cards in a suit and partner has raised in a situation that does not promise or deny some number of trumps, he is more likely to have 3 than to have 4.

 

So the question is whether, if you have UI (which doesn't itself indicate one direction or another) but you can calculate the probabilities of the above and similar, are you constrained by this knowledge?

 

And I think that this question is very tough to answer, because while "yes" seems reasonable at first, it puts a bigger onus on those who are knowledgeable about probabilities and good at calculating them than on those who are not (but may be equally good bridge players). On the other hand, since the first sentence of this post is true, perhaps weaker hands should be considered the default when slow invitations are made. This tends to be the case in real life, after all.

Oh, I see. But now it sounds like it is AI that is suggesting passing, since weak hands are more likely than strong ones with or without the hesitation. I don't think the UI itself suggests either course of action.

 

I suppose you could make an argument that if you wanted to accept opposite mid-range and maximum hands, the fact that mid-range hands are excluded by the hesitation suggests passing. But you could make that argument even if it were not true that minimums are more likely than maximums; indeed, if you wanted to pass opposite mid-range or weaker hands this argument would equally well apply the other way up.

[campboy]

Can't we talk about it in terms of what the Laws require? Your obligation to obey the rules isn't dependent on the TD's ability to enforce them.

No, but doing the right thing even when no-one will know if you don't is what I mean by "personal ethics" :)

 

I would certainly feel obliged to bid on if I had a clear feeling that partner was hesitating because he was at the lower end of his range. But I wouldn't necessarily be able to tell you why I thought he was, or assign a percentage to it. Mind you, that may just be because I haven't played enough boards with any one person. Older players with loong-established partnerships might have a much clearer idea.

[Finch]

This is an interesting idea, I must say I hadn't thought of it that way.

However....

 

In my experience, when someone thinks and then makes an invite, they are usually considering making some other sort of invite, not considering whether to make an invite at all.

 

A slow 1NT... 2NT (natural) contains one or more 4-card majors. A slow 1NT....2C (Stayman) - 2D - 2NT often has a 5-card major. A slow 2NT in your suggested auction (1C - 1H - 1S - 1NT....2NT) might be more likely to be considering bidding something else, with an unusual honour distribution (e.g. 6 bad clubs but good diamond stop, or 4135 with small singleton heart thinking about suggesting a diamond contract, or...)

 

So what I think is illegal is to cater for partner having an unusual hand over 2NT. If you have a choice of pass or 3NT, do whatever you want. But if you bid your doubleton club and catch partner with 6 clubs who passes for an excellent result, I would scent fish in the air.

[gnasher]

This isn't fair.

 

In my first post, I intentionally didn't give an exact sequence, because I wanted to avoid tangential discussions about what partner might have been thinking about. Then David said he didn't like theoretical questions and would prefer an actual example, so I spent ages making up a sequence and specifying conditions and agreements that would discourage any such tangential discussion.

 

Now Frances plainly understands my question, and even says it's interesting, but instead of actually answering what does she do? Yes, that's right: she takes my example question and initiates a tangential discussion about what partner might have been thinking about.

[lamford]

- Partner would raise 1NT to 2NT with any 17-count, 20% of 18-counts, and 20% of 16-counts.

- 16-counts occur roughly twice as often as 18-counts.

 

Hence it appears to be 2:1 that partner's hesitation was because he's at the lower end of the range rather than the upper end of the range.  Does this mean that the UI demonstrably suggests passing over bidding?

In addition to the fact that 16 counts do occur roughly twice as often as 18 counts, the fact that you have (presumably or there would be no problem) an 8-count, makes it almost three times more likely that partner is at the lower end, as he now needs to have 18 out of the remaining 32 points for three players, rather than 16 points out of 32.

 

A good example might be 2NT (20-22) - 4NT (slow) where the BIT is likely to be just a choice between 3NT and 4NT or between 4NT and 6NT. (Otherwise I agree with Frances that in general slow invites are quite likely to be considering making alternative invites).

 

Now, assuming that partner will be 10-12 balanced, he is around six times more likely to be at the lower end, so if you pass with 21, I think you are demonstrably using the UI. But I guess TDs would not draw these conclusions, so it is up to the player to be ethical.

[Finch]

This isn't fair.

 

In my first post, I intentionally didn't give an exact sequence, because I wanted to avoid tangential discussions about what partner might have been thinking about. Then David said he didn't like theoretical questions and would prefer an actual example, so I spent ages making up a sequence and specifying conditions and agreements that would discourage any such tangential discussion.

 

Now Frances plainly understands my question, and even says it's interesting, but instead of actually answering what does she do? Yes, that's right: she takes my example question and initiates a tangential discussion about what partner might have been thinking about.

You aren't being fair.

 

I didn't just look at a sequence you'd thought up; I was trying to make a general point. My general point is that in fact I can't think of a sequence where the 'pure' problem you are considering actually arises in practice.

 

Take Lamford's example of 2NT - 4NT

where the BIT is likely to be just a choice between 3NT and 4NT or between 4NT and 6NT

. Here are other things responder may have been thinking about: whether to look for a 5-3 major suit fit; whether to look for a 4-4 minor suit fit. Responder clearly has at least one 4-card suit and/or a 3-card major so has to take a decision whether to look for a fit in it or not.

[gnasher]

Even if the problem doesn't exist in its pure form, it still exists. The fact that partner might have been considering strain rather than level dilutes the effect I'm asking about, but doesn't render it irrelevant.

 

Revisting my example, suppose that if we think that partner will bid 2NT on any 5-4 17-count, 20% of 5-4 18-counts, 20% of 5-4 16-counts, 20% of 6-4 17-counts, 4% of 6-4 16-counts, and 4% of 6-4 18-counts. The effect of the a priori odds combined with the UI is still to reduce partner's average strength.

[StevenG]

I don't think these odds matter. It is the set of hands on which partner would hesitate, tthen bid 2NT which counts, not the set of all hands on which partner would bid 2NT.

[jdonn]

Was this question just too dull to answer, or is it that I didn't explain it very well?  Surely it can't be that no one knows the answer?

I thought it obvious that actions "demonstrably suggested" includes actions that are, given the UI, demonstrably more percentage than before. I couldn't imagine any bridge player would think otherwise.

Thinking about the question on my own I kept confusing myself which is why I didn't answer right away. However after reading this post, I think this answer was clear and obviously correct. Also I feel for gnasher a little in that I understood the question from the beginning, it clearly is a topic of potential interest (whether you think that is merely theoretical or not), yet it seems to be difficult to get people to answer what was asked.

[Trinidad]

I didn't just look at a sequence you'd thought up; I was trying to make a general point. My general point is that in fact I can't think of a sequence where the 'pure' problem you are considering actually arises in practice.

Suppose that your openings are fairly aggressive (all 12 counts, distributional 11 counts, occasionally a 10 count). How about:

 

Pass-1♣

1♦-1♥

1♠-2♠

...3♠

 

How high would you rate the probability that the other bid considered was:

Pass

4♠

Some bid at the three level?

 

My rough answers are:

Pass 79%

4♠ 2%

Some bid at the three level 19%

 

But I do agree that these pure auctions with a significant bias are rare.

(Pure auctions are not rare, just take any old invitational raise of a major: 1♠-...3♠, but then the bias is small.)

 

Rik

[bluejak]

Thanks for the example, which makes it clearer what you were asking, despite the myriad of off-topic answers. If partner makes a slow try, and it could be a good try or a bad try [or something else, but let's not worry about that] are you using UI illegally if you decide a borderline good try is more likely than a borderline bad try so you accept the try?

 

Yes, that is a breach of Law 73C, you have not made every effort to avoid gaining from the UI. Good question.

[Finch]

OK, let me try and answer what was asked.

 

I'm not very well today so may get confused, but I think it's important not to confuse UI and AI.

 

Partner's HCP distribution given the auction is AI (unless you need artificial aids to calculation in order to work it out). The UI does not necessarily change that.

 

Take your example where partner raises 1NT to 2NT and pretend that (i) there are no other possible calls other than pass, 2NT and 3NT and (ii) partner's 2NT bid shows 16-18 points.

 

Without any UI - with an immediate 2NT bid - you already knew that partner was, on percentage grounds, more likely (a priori) to be at the low end of the range than the upper end. Let's take your probabilities:

 

(i) Partner would raise 1NT to 2NT with any 17-count, 20% of 18-counts, and 20% of 16-counts

(ii) Within that range partner has a 16-count 50% of the time, 17 30% and 18 20% (these aren't exact but are roughly right)

 

So with no UI, partner's raise is

a 16 count 23% of the time

a 17 count 68% of the time

an 18 count 9% of the time (Bayes' theorem)

 

His expected HCP given a raise is 16.9

 

Now we are suggesting that the UI tell you that partner doesn't have a 17-count - he is either thinking of passing with a 16-count, or bidding game with an 18-count. Now he has a 16-count 5/7 of the time, and an 18-count 2/7 of the time, making his expected HCP 16.6

 

OK, there's a slight difference, but it's pretty small given the uncertainty in most of the other numbers. Particularly given the fact that partner will look at his pips, his honour distribution, his shape etc in deciding whether to invite or not, and I don't think anyone even knows the a priori and a postiori distribution for these.

 

I'm not at all convinced that the effect of the UI in this type of case is - generically - to give you any unauthorised information about partner's strength. I had to work through this example to to find out if he was weaker or stronger with the UI.

 

Certainly one can get auctions where the UI demonstrably tells you something about the strength of partner's hand, and this needs to be taken into account when considering LAs.

 

Suppose you play the 'normal' forcing pass approach where bidding at once is weaker than passing then bidding if partner doubles. If you think for a long time before making a forcing pass, the UI doesn't tell partner anything useful. However, if he now doubles and you bid, he has the UI from the auction that your action was marginal (assuming you couldn't have been thinking about alternative slam tries rather than a forcing pass).

[Finch]

Thanks for the example, which makes it clearer what you were asking, despite the myriad of off-topic answers. If partner makes a slow try, and it could be a good try or a bad try [or something else, but let's not worry about that] are you using UI illegally if you decide a borderline good try is more likely than a borderline bad try so you accept the try?

 

Yes, that is a breach of Law 73C, you have not made every effort to avoid gaining from the UI. Good question.

Just to be absolutely clear:

 

Are you using UI illegally if you decide a borderline good try is more likely than a borderline bad try so you accept the try?

 

Yes, but only if is a consequence of the UI that you believe a borderline good try is more likely; not if that is AI anyway.