[barmar]

Basic assumptions: partner only opens 1♦ with 3 diamonds when she's exactly 4=4=3=2 and outside the range for an opening NT bid. Your shape is 2=2=6=3. She opens 1♦, you make an invitational 2♦ raise (denying a 4-card major), and she bids 2NT (promising stoppers in the majors). What's the probability that she has only 3 diamonds? Does the fact that the opponents are silent make it more likely (since her major length leaves fewer majors for them to preempt with)?

[Free]

The chance depends on a lot of things. For instance, do you open 1♦ with 4-4m? What about any 5-4m? Because with such holdings, opener can still have stoppers in both Majors, but these hand types decrease the chance of partner having exactly a 3 card ♦.

I'll leave the calculation of the exact odds to someone else

[helene_t]

that she has stoppers in both majors only increases the chance slightly as given the circumstances she was odds-on to have stoppers in both majors anyway.

But the fact that opps are silent changes it quite a bid, I would think, especially if they are nonvulnerable.

[billw55]

I read an analysis somewhere that put it at 5% based on the opening bid only. So, I adjust my expectation from there based on the current circumstances. Partner holding stoppers in both majors and silent ops, both mildly suggest that partner has length in the majors, and so increases the odds of the key shape (4432). But I would not think very much, I would still put it at less than10%.

Is 2NT forcing / unlimited? That might matter, as it would help explain silent ops.

[fromageGB]

Don't ask me about statistics, but here's a stab. The probability of a 4432 shape(any) is 21.6%, so a quarter of that has 3 diamonds, and a third of the reduced amount has doubleton club. So I reckon a 4432 is 21.6/12% of hands. "A" = 1.8%

Now, how often do you open 1♦? You play 5 card majors, and a 5+ card suit is held about 64% of the time. When not the right strength for 1NT, you will open a major about 32% of the time, the remainder split between the minors depending on your methods (longer? which if equal? clubs with balanced hand and diamonds is unbalanced?) but assume ♣ is twice as often as ♦. Then you open 1♦ 68/3% of the time. "B" = 23%

The probability that a 1♦ open is 3 cards is therefore A/B or 7.8% Does this seem plausible?

[jogs]

I don't know and I don't care. Your pattern is probably
more important than whether pard has 4 diamonds.
6322 in flat and unlucky. 6331 is better. 6430 is even
better.

[PhilKing]

My guess is that the opponent's silence >>>>> significant than any calculations about partner's combinations, so the chances of 4432 has gone way up. And it depends on the oppo style - one partner of mine will overcall 100% of hands containing a five-card major when non-vul versus vul (even the nut low - 65432 and a zero count is on record).

[fromageGB]

fromageGB, on 2013-August-07, 11:23, said:

The probability that a 1♦ open is 3 cards is therefore A/B or 7.8% Does this seem plausible?

As nobody has torn holes in this yet, continuing with the bidding, presumably partner would not rebid 2NT but would bid 3m with a 6 card suit or a xx55 (and of course, opponents bid a major on these) so 1/3 of the 23% can be ruled out. That makes the chances of 4432 distribution 12%.

Further, let us say that when opener has this shape opponents will bid 10% of the time, when he has 4 diamonds in a {4432} 30% of the time, and when he has 5 diamonds 50% of the time. (I know plenty of people who would not overcall with a 5 card major unless they have 10 hcp, or 12hcp over my 2♦.) So on these assumptions, the chance of partner having a 4432 with the bidding as it has been coming back to you becomes 16%. So 84% possibility of 4 diamonds or more.

Do I get a coconut?

[mycroft]

It also depends what "outside the NT range" means. There are more (11)12-14 4=4=3=2s than there are 15-17 4=4=3=2s, for instance.

[FrancesHinden]

fromageGB, on 2013-August-07, 11:23, said:

Don't ask me about statistics, but here's a stab. The probability of a 4432 shape(any) is 21.6%, so a quarter of that has 3 diamonds, and a third of the reduced amount has doubleton club. So I reckon a 4432 is 21.6/12% of hands. "A" = 1.8%

Now, how often do you open 1♦? You play 5 card majors, and a 5+ card suit is held about 64% of the time. When not the right strength for 1NT, you will open a major about 32% of the time, the remainder split between the minors depending on your methods (longer? which if equal? clubs with balanced hand and diamonds is unbalanced?) but assume ♣ is twice as often as ♦. Then you open 1♦ 68/3% of the time. "B" = 23%

The probability that a 1♦ open is 3 cards is therefore A/B or 7.8% Does this seem plausible?

No, because you have 6 diamonds. That clearly affects partner's possible diamond length.

[fromageGB]

FrancesHinden, on 2013-August-09, 02:15, said:

No, because you have 6 diamonds. That clearly affects partner's possible diamond length.

Of course it does, silly me. Isn't life complicated?

[barmar]

FrancesHinden, on 2013-August-09, 02:15, said:

No, because you have 6 diamonds. That clearly affects partner's possible diamond length.

That was the whole point of my question.

Specifically, this is what I saw:

---

We play 15-17 NT, and I assume she usually opens 1{DI] with 4-4 minors (it was a first-time partnership, we hadn't discussed this).

Should I be expecting that we have a 10-card fit in diamonds, or is a 9-card fit more likely because of my extra length? The opponents did have 5-card suits (South was 5-5 in the majors, North had 5 clubs), but the vulnerability kept them silent.

I drove to 6NT, but it turned out that 5 was the limit in both NT and ♦. Partner's shape was 3=3=4=3, with a loser in each side suit, but one of them could be disposed of. It was matchpoints (the 2nd qualifying session of the Wernher Pairs), so I was right to stay in NT, but I pushed too high and we got a poor board.

[JLilly]

barmar, on 2013-August-09, 23:49, said:

[T]his is what I saw:

---

We play 15-17 NT, and I assume she usually opens 1{DI] with 4-4 minors (it was a first-time partnership, we hadn't discussed this).

Should I be expecting that we have a 10-card fit in diamonds, or is a 9-card fit more likely because of my extra length? The opponents did have 5-card suits (South was 5-5 in the majors, North had 5 clubs), but the vulnerability kept them silent.

My intermediate sense is: Your partner would have misbid if she had had only three diamonds.

2NT from her is an invite to 3NT if you have better than minimal values. If her hand suggests to her that the partnership should look for a suited contract she'll name a 4+ major, will respond with clubs if she has no 4-card major and is 3-5+ in the minors, or will raise your diamonds with 4-card support. 3-3-3-4 would be a hand that bids NT in response to your 1D opener. So any scenario in which she had 3 diamonds would be covered by major, NT, or clubs bids.

[barmar]

JLilly, on 2017-March-12, 23:07, said:

My intermediate sense is: Your partner would have misbid if she had had only three diamonds.

2NT from her is an invite to 3NT if you have better than minimal values. If her hand suggests to her that the partnership should look for a suited contract she'll name a 4+ major, will respond with clubs if she has no 4-card major and is 3-5+ in the minors, or will raise your diamonds with 4-card support. 3-3-3-4 would be a hand that bids NT in response to your 1D opener. So any scenario in which she had 3 diamonds would be covered by major, NT, or clubs bids.

I think you're confused about who "I" and "partner" are in the scenario. I'm responder with 6 diamonds, she is the one who opened 1♦.