EricK

I don't think I'd open it - the singleton A is quite a big defect and probably counteracts all the features which caused you to upgrade the hand. If I were to open, I would definitely go with 1♣ - planning to raise 1♦ or 1♠ and bid 1NT over 1♥.

But at what level? Last time I held a similar hand on this sort of auction I bid 4♥ and it worked out well. [Anecdote]I knew it would work out well as I remembered the hand from the previous week. Apparently the people on the first table had omitted to shuffle and deal the cards at the start of the evening. As we only got to the hand towards the end of the evening, after many pairs had already (re)played it, I didn't think it worth the hassle to point this out to anyone.[/anecdote]

Boys are more prone to die than girls for a number of reasons. eg They are more likely to be involved in violent incidents. They are more prone to various genetic disease (because they only have one X chromosome and where a girl might be able to compensate for a defective gene on one X chromosome with a normal gene on the other, a boy can't) They are more prone to risk taking They are genetically programmed to spend less resources on repairing the body and more resources on being vigorous in youth and middle age (essentially for the reasons above) Because of this, although men outnumber women at birth, women end up outnumbering men in almost every age range. Where a society has a surplus of men, it is always because of female infanticide (whether after birth, or via selective abortion)

This was really my point. The fact that they gave the answer of 1/7 means they had a certain interpretation in mind. However the fact that they didn't make all the assumptions clear in the problem means that there is a fair chance they don't understand what assumptions underlie their answer and why they are important. And that is worrying if this question came from someone trying to teach probability.

It isn't clear to me that the "natural" interpretation of the problem is "we choose a family at random from all the 3-children families which have at least one boy" rather than "we choose a random child from all the families which have 3 children and it turns out to be a boy"

Assume you find out that a family with N children has at least B boys because you ask the question "do you have at least B boys?" and get the answer "yes". Then, letting P be the probability that a random family with N children has at least B boys, the probability that this family has N boys is 1/(P*2^N) P will equal to (C(N,B )+C(N,B+1)+...+C(N,N))/2^N where C is the standard Combination function (http://en.wikipedia.org/wiki/Combination) On the other hand, if you find out the family has at least B boys because you see B children at random and they all turn out to be boys, then the probablity that they are all boys is simply 1/(2^(N-B )) Note that this relates to restircted choice because the play of a bridge hand is more like the first scenario than the second - i.e. players don't play cards at random.

There is no unique answer to the question as you need to make some assumption as to how you came by the knowledge that (at least) one child is a boy. Consider these scenarios: 1. You ask a person who has 3 children "is at least one a boy?" and he answers "yes".. 2. You ask a person who has 3 children to tell you the sex of one of his children. He says "male". In the first scenario the probability that all his children are boys is 1/7 (assuming he was telling the truth!) In the second scenario the probability that he has 3 boys is 1/4 (again assuming he isn't lying)

This looks like a rather obvious game try.

Almost the same thing happened to me once. Although in my case I genuinely psyched a WJO with a strongish hand opposite a passed partner because I had a feeling, correct as it turned out, that it would cause the opps to overbid. I also got ruled against.

Most people are not capable of thinking in such convoluted ways, so it would just add a layer of confusion for no real benefit to the vast majority of players.

3♥

The only suit which looks obviously wrong to lead is ♦. And a ♣ looks as good, if not better, than the others.

This looks like a 2NT rebid to me. 2♥ seems quite likely to put us into a 5-1 fit (when partner bids two suits, he usually has a singleton, and with a 1354 hand he would probably (or do I mean hopefully?) raise to 2♥ instead of bidding 2♣).

After the 2NT rebid, you know that partner has at least 2♥, and he knows you know it. Hence if you bid checkback, discover partner has 4♠ and 2♥ and still just bid 4♥, you are showing that your checkback bid was some sort of slammish move (otherwise you would just have rebid 4♥ straight away). Because of his control rich hand and excellent support (in context), I think partner should have made some move after 4♥.

My love of 4m pre-empts persuades me to bid 4♣.

I pass first time. I hope to then bid ♦ and then ♠ (unless opps show particular length in these suits).

More seriously though, I just don't think my hand screams playing diamonds instead of NT. (Thanks for the ♥T, dealer!) Also, possibly having to ruff with trump honors doesn't work so well unless it is partner who has the intermediates. It doesn't scream anything except "whatever we play it would probably be better being played from partner's side". I am not that great at constructing hands etc, but it is hard for me to see how raising ♦ here (presuming partner is aware of the possibility) is going to lead to a worse result than bidding NT. You are right that trumping with honours is potentially bad; but it is seems unlikely in this scenario (assuming partner also makes "sensible" bids") that: a. we end up in ♦ b. partner does not have a good ♦ suit (i.e. at least 5 and some intermediates) c. NT plays better.

I don't like bidding balanced hands as if they are non-balanced, and I very rarely do it. In fact I am more likely to bid semi-balanced hands as if they were balanced because it looks like NT will be the right contract - especially played by me. Perhaps this comes down to a question of bidding philosophy. Should the sequence 1♣ 1♦ 1NT be analagous to the conversation "I have an opening hand, clubs might be a good trump suit" "Well I have a few points too. Might I suggest diamonds as a trump suit?" "I have a minimum hand and fancy playing NT" Or should it be closer to "I have an opening hand and at least 3 clubs" "I have a few points and at least 4 diamonds" "I have a minimum balanced hand" And similarly, ought 1♣ 1♦ 2♦ suggest "I have an opening hand, clubs might be a good trump suit" "Well I have a few points too. Might I suggest diamonds as a trump suit?" "I have a minimum hand. I agree diamonds might be a good trump suit" Or alternatively "I have an opening hand and at least 3 clubs" "I have a few points and at least 4 diamonds" "I have a minimum hand with 5 clubs and 4 diamonds"

This hand isn't nearly an upgrade to 1NT - the nine points in diamonds aren't pulling their full weight, and both majors are completely unstopped. So it is a 1♣ opener for me. The trouble with hands like this is that NT from partner's side could easily play 3 or 4 (or more) tricks better than from yours. When partner responds 1♦ this does nothing to alleviate those concerns - in fact, it heightens them. So I think those who rebid 1NT are making a safe position for themselves in the post mortem ("1NT shows 12-14 balanced. That's what I've got!"); but I'm not convinced that bidding this way maximises the expected score on the hand. If you bid 2♦, partner with any extras will be still look for NT; and if he doesn't have extras, 2♦ is almost certain to be very playable. The same can not be said for a NT contract unilaterally bid by, and played from, your hand. 2♦ is better than a 2♣ rebid, though, as partner will pass 2♣ with most mediocre hands with 1 or 2 ♣ even with long ♦, and will even pass with some strongish hands with a singleton ♣. Similarly, I would raise a 1♥ response to 2♥. However, I would rebid 1NT after a 1♠ response.

1♦ 2♠ playing WNT; SJS 3♠ 4♣ support; cue 4NT 5♠ RKB; 2+Q 5NT 6♦ Specific King ask;♦K 6♥ 6NT ♥K ask; yes 7NT

This reads as if you have stopped playing it. If that is the case, why?

4♠ is very unilateral. South is right to the extent that because of the ♦ fit, there could easily be a game in ♠ on. The trouble is, he doesn't yet know if there is a ♠ fit or not! A 3♠ bid is surely enough.

It's unlucky really. You might say that 3♠ is an overbid, but give south ♦AKQJ and you still have 4 top losers! You might also say that North should devalue his ♣KJ. But they actually turn out to be good cards (as is probably frequently the case when the 1♣ bid is Polish)! Swap South's red suits, and we might, under slightly different circumstance, have got an "ATB for missing game" thread.

Because its important for a developing player to first recognize what suit key card applies to, and then learn later on that this isn't a key card auction at all, but rather quantitative. This is how most people learn bridge. I suppose there are prodigal types that can immediately appreciate the need to play auctions like this as quant. but they are few and far between. My point is not that they might be a prodigal type who can immediately realise that it should be quantitative, my point is that in order for them to learn that it should be quantitiative, they need to see people play it as quantitative! And because people, by nature, pay more attention to their own auctions than their opponents', this is a perfect time to teach them. Conversely, if you reinforce people's mistakes it will be harder for them to correct them later.

I hate answers like this! If you assume it is RKB just because the perpetrator is a beginner, or choose to bid it yourself as RKB just because partner is a beginner, then how will a beginner ever learn that this should be quantitative? Without discussion, the bid is quantitative, and if someone, beginner or not, bids it as RKB without discussion then they have misbid.