[rbforster]

I'm interested in what the average number of tricks one can expect to take in NT with a given level of combined high card points. Say you have 22 points - is that 7 tricks, 8 tricks, 7.3 tricks or what? I'd like to know so I can think about (mathematically) whether it makes sense to play a weak 1NT (8-10, 10-12,12-14?) and also if I should maybe raise a weak NT to 2NT or 3NT with very weak hands (if I think the opponents will be missing their game).

We've all heard the basic rules about how many points your side should have to bid various NT contracts (25 or 26 for 3N, 33 for 6NT, 37 for 7NT), but these rules certainly don't guarantee that you will make those tricks as many unlucky declarers can attest. Besides at IMPs especially your probability of making game doesn't need to be that high to justify bidding it. So maybe 25 points for 3N is really only 8.5 tricks on average?

One might imagine that the number of tricks for your side with X points is simply related to the number of tricks your opponents make, like maybe this equation:

(Our tricks with X points) = 13 - (their tricks with 40-X points)

While simple, this doesn't include factors like the declarer's playing advantage (from being able to plan the play better) or the defense's advantage of getting the opening lead. Often times both sides (or neither!) can make 1NT depending on who declares it. As an extreme example, with 38 points the declarer will almost always find a way to make 7NT. What if one of the opponents psyched 1NT with their balanced 2 count and plays in 1NTX? The defense might accidentally give declarer a trick since it's harder to executing squeezes as defenders, etc. If a declarer with a weak hand tends to make an extra trick relative to what his side would take on defense, this would certainly be an argument in favor of weak NTs.

Is this the sort of question that the bridgebrowser(?) software might be able to answer?

[ArcLight]

3 additional factors to consider -

1 - spot cards, having a few extra 10's and 9's can make a huge difference

2 - are the points all in one hand, or does dummy have some entries. Opening 2NT with 20-21 and having a 0 HCP dummy means no finesses. Opening a 17 HCP 1NT and dummy has 3 HCP can also mean no finesses. Compared to a 15 HCP hand opposite a 6 HCP hand with 2 entries.

3 - length - is there a side suit than can generate an extra traick or two?


Its not just a simple matter of 21 HCP = 7 tricks. There are other factors to consider.

[jtfanclub]

There's also the split issue- you're supposedly more likely to make with 12 across 12 than with 19 across 5.

[pbleighton]

Quote

I should maybe raise a weak NT to 2NT or 3NT with very weak hands (if I think the opponents will be missing their game).

No.

In general, what your questions are lacking is the importance of a source of tricks in the responder's hand, as well as intermediate cards. As an example, let's say your partner opens a 15-17 NT. Here are some hands to evaluate. For convenience, none of them have a 4 card major or a huge minor suit, so you are talking about a raise to 2NT or 3NT:

1. K32-K42-Q753-Q62
2. K102-K92-Q1093-Q102
3. K2-64-KQJ103-J102
4. K10-109-KQJ107-1092
5. J10-109-KQJ1072-109

The fist three hands are all balanced aceless 10 counts, but have big difference in playing strength. 1 has no shape, no intermediates, and no honors working together. I would downgrade it to 9 and bid 2NT. 2 has a bunch of intermediates, and will probably take a trick (or even two tricks) more than 1. I would feel happy to raise this to 3NT. 3 has a source of tricks in the diamond suit. I like this even better than 3, in spite of the missing heart stopper.

4 has only 9 points, but is a clear raise to 3NT because of the intermediates and suit.

5 has only 7 points, but I would raise to 3NT (some wouldn't) because of the intermediates and good 6 card suit. It may not be *worth* 3NT, but with hands with long suits, experience shows that most of the time you will either score big with the suit and make 3 (or more), or the opps will run a suit and you will make 1 (or less).

Peter

[mikeh]

This thread is based upon an erroneous but hidden assumption: that counting points is a precise valuation method. The sad truth is that hand evaluation is far, far more complex than point counters realize. Other than in straightforward, balanced hand opposite balanced hand, I know of no good player who pays a great deal of attention to how many points they hold... and, even then, good players still look at a number of other factors....

While BridgeBrowser will undoubtedly tell you that 12 opposite 12 resulted in an average of 8.371 tricks (I made this up...don't take it seriously), that really has little useful to tell us...and focussing upon this type of question diverts one's attention from learning how to go beyond counting points.

Without trying to be exhaustive, some factors that affect trick-taking potentials of given hands include (not in any particular order than their occurence to me as I write):

In and Out valuation: hands in which the high cards are in the long(er) suits are generally more powerful than the converse situation

Combining cards: hands in which honours are combined are generally more powerful (consider AQxx AQxxx xx xx and Qxxx Qxxxx Ax Ax)

Interior spot cards: the work point count (4321) gives no weight to 10's, 9's etc. Spot cards matter.

Controls: Aces and Kings are undervalued in the 4321 count and Queens and Jacks overvalued. Hands lacking controls are often referred to as 'soft' and soft hands are not as powerful as control-rich hands

Positional values: hands become more or less attractive based on the auction: including bids by the opps as well as by partner. Locking in on the initial point count prevents one from listening to the auction.

Shape: a huge factor...especially combined with in and out valuation. Anyone who has played a lot of bridge will know of hands on which slams have been made on 15 hcp or so....in my experience, usually bid as a sacrifice BTW, I know that many (all?) teachers suggest adding points for distribution, and in fact I learned that approach myself... but I doubt that any good bridge player does it.... in the sense of coming up with a number.

And of course a major problem with BridgeBrowser results is that the vast majority of players appear to be very weak.... but the bias, if there is one, is probably in favour of over-estimating trick taking potential. This is because defence is more difficult than declarer play. There are, at most tables, two weak defenders and only one weak declarer, so the defence is twice as likely to screw up.... and this ignores the fact that defence requires understanding of the partnership style (signalling methods, etc) that simply doesn't exist in a casual on-line partnership.

Point counting is a good way into the topic of hand evaluation, but it is only the beginning of the learning curve... and it is essential to understand that all of the data-mining in the world, if limited to 'how many points' is not going to help anyone become a better bidder.

[rbforster]

Perhaps my original post wasn't clear. I certainly am aware of and agree with the various valuation issues raised so far - spot cards, split points between hands, long suits, etc. It would interesting to study for example how the distribution of values between the two declaring hands effects trick-taking ability (due to communication issues, etc). These are all important issues in constructive bidding, but this wasn't what I had in mind.

I am thinking about this in the context of how to continue after a weak NT opening, when to psych, etc. If partner bids a 10-12 1NT and I've got a flat 2 count, they are on for 3NT most of the time. If they haven't doubled yet, can I bid 3NT to scare them out of game? What fraction of the time do I have to be doubled to make this a bad gambit? If I do this with all 15-19 point hands (to make, but not interested in slam) and also all 0-3 counts (preempting their game), what should 4th hand do with his random 13 count after 1NT(10-12)-P-3N-? Is it more likely that I've psyched and he should double (when his partner has a similar 12-14 count), or that I've bid 3NT to make and he's double will work out really badly since it's his partner rather than me that's got the bust hand? One advantage of a Kamikaze weak NT of 8-10 is that there's a wider range of weak responding hands where you can be sure the opponents have game and try some trickery to talk them out of it. Heck, if you played 1NT as 5-7(!) you'd have them missing slam sometimes which means that even getting doubled off might be a matchpoint top at favorable as long as you can take that one trick...

Obviously to answer these questions, it's important to know about how many tricks you can make with a given strength level as declarer. Your sacrifices can't go down too many too often after all. I wanted to run some simulations, work out the common psychs and when to chance doubling them, etc. But as inputs to the simulation, I'd need to know what the likely number of tricks each side would take, which is something that depends more on real players and real defense, rather than double dummy analysis. I was hoping to get some idea if, on average, it was right to play a 8-10 NT or just give up and play something more normal. A lot of precision people like a weak NT, and if a weak NT is good (as a preempt), would a weaker NT be better?

[awm]

It doesn't seem like the number of tricks here really matters. If partner opens 1NT (weak) and I raise to 3NT on nothing, and opponents find a double... does it really matter if I go for 1100 or 1400 or 1700 into their game? The IMP scale is logarithmic after all, so the difference in the value of my huge minus score is not necessarily all that much. This will also depend a lot on play and defense -- bridgebrowser won't help because the sample size of hands where we are playing in 3NT holding 10-15 hcp is fairly small. GIB won't help because the play and defense on these hands is likely to be far from double-dummy.

The more interesting question is probably "how often will they find a double"? But this also depends on a number of things such as: (1) What were their methods in direct seat over the weak NT? (2) Do they know how frequently you "psych" these raises? (3) How much do your opponents like to double 3NT holding a random balanced 17 after 1N-P-3N?

I've seen this kind of raise work, but I've also seen it backfire spectacularly. Usually it's "safer" if you hold a long suit to run to.

In any case, this situation is rare. Far more frequent opposite a weak NT is a situation where neither side has a clear "high card point" game. Even opening 8-10, your side has close to half the expected strength. Rather than considering "how often can I psych the opponents out of game by bidding 3NT and going down six, versus how often will they get me?" it would be better to consider factors like:

(1) How often will my side be down two doubled opposite no game for the opposition?
(2) How often will my side go down three undoubled opposite no game for the opponents?
(3) How often will I get doubled for more than the value of their game at 1nt or 2x?
(4) How often will my opening 1NT or pass help the opponents in the play of their contract?
(5) How often will one side or the other fail to find its best fit due to the 1NT opening?
(6) How often will my super-light NT opening wrong-side a 3NT game for us?
(7) What is the effect on the rest of my system from playing this notrump range?

I know you seem obsessed with the idea that somehow it is right to bid a lot on lousy balanced hands. Various posts have suggested opening 1NT on 5-7 points, opening lorenzo-style twos on balanced hands or playing a forcing pass with a 2♣ fert. I think there's pretty strong evidence that in any reasonable field, this is losing bridge. Even the once-popular 10-12 notrump range (relatively tame by your standards) is very much on the decline in the expert game. The fact is that weak balanced hands offer very little safety, and opening (or not opening) them at some level gives the opponents a lot of help in what is likely to be their contract. I don't think adding frequent psychic raises of your weak notrumps is going to help much in this department.

[kenrexford]

IMO, if you elect to operate after a weak 1NT opening, the best long-term tactic is subtlety. 1NT-P-3NT on trash can work, and it looks funny. More subtlety, like Stayman, or inviting game (2NT perhaps), or suit-inhibition (transfer to a three-card suit) even, has greater chances of recurring success.

[rbforster]

awm, on Jun 4 2007, 03:39 PM, said:

bridgebrowser won't help because the sample size of hands where we are playing in 3NT holding 10-15 hcp is fairly small. GIB won't help because the play and defense on these hands is likely to be far from double-dummy.

I agree about GIB, but I would think bridgebrowser could shed some light on the issue I originally raised - how many tricks in NT on average does your side take if you have X combined points? It doesn't have to be 3NT on 10-15 hcp, it could be 1NTX on a similar range (say if a weak NT got opened)... the result still says something about how many tricks got taken. There will be slight issues as to what the defense knows and how they defend, but these are secondary considerations.

Quote

it would be better to consider factors like:

(1) How often will my side be down two doubled opposite no game for the opposition?
(2) How often will my side go down three undoubled opposite no game for the opponents?
(3) How often will I get doubled for more than the value of their game at 1nt or 2x?

Sure these are also good things to think about and knowing how your average strength level translates into tricks taken would be useful. You can have some idea for how much you might go down, how likely you are to make, etc.

Another place this sort of information could help is in testing/designing a defense to a weak NT. If your opponents play a 11-14 NT and you play a penalty double, how strong a balanced hand should you have to double? 12? 15? You can ask what people normally do, but you'll get a range of answers. Doing some math on the conditional probabilities of the remaining high card points you could get some idea about the minimum strength required and a more sound basis for your defense. What about to sit for your partner's penalty double after 1NT(11-14)-X(13+bal)-P-? How strong do you need to be to pass? Since your partner could have extra values, it might not be just a question of having enough values opposite partner's minimum... you might be able to pass with a little less since often partner will have at least some extras for you.

Quote

I know you seem obsessed with the idea that somehow it is right to bid a lot on lousy balanced hands. Various posts have suggested opening 1NT on 5-7 points, opening lorenzo-style twos on balanced hands or playing a forcing pass with a 2♣ fert. I think there's pretty strong evidence that in any reasonable field, this is losing bridge. Even the once-popular 10-12 notrump range (relatively tame by your standards) is very much on the decline in the expert game.

Well the 2♣ NV fert was Richard relating some older forcing pass system, but I'm just willing to be open-minded about things. The fact that Meckwell played 9-11 or 9-12 NT when NV (and outside the US) does seem to suggest that fairly weak NTs aren't a completely awful idea. Besides, if playing weak NT were just "bad bridge" you wouldn't think the ACBL would have all these restrictions legislated against them. I mean they don't forbid you to open 4♦ on a weak hand and a 5 card suit - they just figure you'll learn the hard way pretty quick and move on to a better idea. I'm much more inclined to think that anything the ACBL opposes is probably either a good idea or at least interesting and worth considering (like assumed fit preempts or 2♥ multi).

Getting back to the original question, I'd love to see the results of a study of any NT contract, doubled or otherwise, and the aggregate results of how many total tricks it took compared with the declaring side's total strength. Something like:

20 pts .... 7.5 avg tricks
21 pts .... 7.8 avg tricks
22 pts .... 8.1 avg tricks, etc

[P_Marlowe]

Hi,

as the weak NT was developed, they studied how
may points are needed to make 7 tricks, the answer
was that a weak NT is enough.
The main problem is, that they most likely assumed
that the relevant partner holds on avg. 8 ponts.

If you open a 10-12 NT and face 0-3HCP, the only
tricks you will make are your fast tricks (i.e. your
Aces and Kings), i.e. I would say on avg. you make
2 tricks (+1-2 they may present you through the lead,
it may well be that you wont score your King.

The above should be fairly obvious, assuming that
the defenders are reasonable competent, and we are
not talking about old poor guys, you beat anyway,
... and using your suggested tactics against those is
...

With kind regards
Marlowe

[pdmunro]

Have you thought of using Richard Pavlicek's database of double-dummy-solved hands to answer your question?

Look for RP Deal Finder    http://www.rpbridge.net/rpbr.htm#11

[bid_em_up]

I (vaguely) recall someone, possibly Ben?, posting the results of a BridgeBrowser query showing the number of tricks made when balanced hands opposite balanced hands contain varying number of HCP, i.e.

12 vs. 12
12 vs. 13
12 vs. 14
13 vs. 10
13 vs. 11

etc.

Unfortunately, I can't find it at the moment.

I also think its meaningless, because of where the result are obtained from.

A skilled declarer will (normally) make the best usage of his cards, therefore he will make more tricks on average than a weak declarer. Since the results of any BrBr study are derived from BBO or OKB hands, the results tend to be skewed towards the weaker players. In other words, if such a study were to show that, on average, most declarers managed to take an average of 8.32 tricks on 12 vs. 12, the average for skilled declarers will be much higher than that, imo.

And of course, as others have said, there are still a wide variety of factors that influence any such result.

[FrancesHinden]

Rob,

The short answer to "Is this the sort of question that the bridgebrowser(?) software might be able to answer?" I would say is no.

I understand what you are asking, and I don't think you can take the inferences you want to take from slightly different data. I've had a lot of experience with a mini NT and would observe that:

- it's almost unknown for it to go mini NT P to me when I have a balanced 2-count. Much more common is 4-8 HCP or so, when you aren't entirely certain if they are making game or not, which changes the odds from your potential psyches.

- the correct approach as responder depends on oppo's methods. If they play double of Stayman/xfer etc as lead-directional, there's more to be said for it to sow confusion. If they play it as showing a strong balanced hand (quite a common treatment against weak/mini NT) the 3NT psyche may work better.

- if 1NT is doubled, partner may have an escape suit, which you have pre-empted.

- the exact number of tricks you are making in a silly contract (3NTx on a combined not-very-many) is not really relevant, particularly at matchpoints. Just say 'it's a bottom' and concentrate on comparing how often it will happen compared with other approaches as responder.

- I agree the one useful question is how many tricks you make in 1NTx, but this has to compare with how many tricks they make if they declare. That's a handy question: if we have 10 opposite 4, say, are we better in general playing 1NTx or defending 3NT? Clearly at favourable you'd rather make 4 tricks in 1NTx than concede 9 in 3NT, but the opening leader will have an advantage. Against that declarer has a big advantage as he knows his combined assets; the auction 1NTx all pass can be harder to defend.

- My long experience with the mini is that the gains/losses are not really from this area at all. The gains are when 1NT buys it, or when the opponents miss their obvious game (being unsure about their values for overcalling), or misdefend 1NTx (taking 100 instead of making their partial in particular), or you bid 1NT-3NT and they have to lead blind, or you pre-empt their 4-4 fit when they both have balanced hands. The losses are the very occasional large penalty (really, very rare playing 10-13 NV) but much bigger losses are - at matchpoints, going for 300 against a partial, or responder being pre-empted and the final contract wrong-sided, or playing 1NT instead of a 4-4 fit; at imps the losses come from helping oppo play the hand when they then bid to game and know the HCP layout, or going for 300/500 against a non-making game.

[cherdano]

Jlall, on Jun 5 2007, 09:34 AM, said:

21+ points=game
19- points=defend game
20 points=race to 1N.

In a recent bulletin article recalling some hands from the Cavendish I learned 19 = defend 1NTX, collect 500, though.

[helene_t]

Jlall, on Jun 5 2007, 05:34 PM, said:

21+ points=game
19- points=defend game
20 points=race to 1N.

I once did a statistical analysis of the GIB DD database. The purpose was hand evaluation, but the number of tricks required for a given number of tricks rolled out as a by-product.

The optimal coefficients were, rather than 4-3-2-1:
A=3.96
K=2.79
Q=1.79
J=0.99
T=0.46

The low value of queens is probably an artifcat of the double-dummy thing: if declarer knows where the queen is, it has less value for the defense.

The number of points required to make 3NT with 50% of hands is 24.35.

The formula guesses when to bid 3NT with an accuracy of 91.7%, as opposed to 91.5% for the "4-3-2-1-points">24 criteria.

[SoTired]

helene_t, on Jun 5 2007, 11:55 AM, said:

The optimal coefficients were, rather than 4-3-2-1:
A=3.96
K=2.79
Q=1.79
J=0.99
T=0.46
<snip>
The number of points required to make 3NT with 50% of hands is 24.35.

The formula guesses when to bid 3NT with an accuracy of 91.7%, as opposed to 91.5% for the "4-3-2-1-points">24 criteria.

You Got Me Good! ... I was trying to memorize those 3 digit numbers until I reread the 91.7 vs 91.5...