[Jlall]

Cascade, on Aug 29 2009, 11:40 PM, said:

Not that I am suggesting that 2NT is ideal it is far from that but the 1minor openers have two problems:

1. The auction may end at a very low level in not your best fit

Why is this a problem if your other option is to play 2N? I guess it's possible 2N is better sometimes but I would rate playing 1m (especially clubs) to be right way more often. It's not like you can magically get to 3 of your best fit after opening 2N.

[Cascade]

Jlall, on Aug 30 2009, 05:25 PM, said:

Cascade, on Aug 29 2009, 11:40 PM, said:

Not that I am suggesting that 2NT is ideal it is far from that but the 1minor openers have two problems:

1.  The auction may end at a very low level in not your best fit

Why is this a problem if your other option is to play 2N? I guess it's possible 2N is better sometimes but I would rate playing 1m (especially clubs) to be right way more often. It's not like you can magically get to 3 of your best fit after opening 2N.

I don't think I said that. I think I acknowledged that 2NT was not ideal.

[awm]

Jlall, on Aug 30 2009, 12:23 AM, said:

awm, on Aug 29 2009, 11:02 PM, said:

But with that said, is this a winner on frequency grounds? 21+ hcp hands only come up maybe once every two-three sessions

Really? Kinda surprised by this, maybe it's because my memory lumps in very strong playing hands that are equivalent to 21+ as in that group also when obviously they aren't.

Hands with 21+ actual hcp have a frequency of 0.8% or 8/1000 = 1/125. So I expect to hold such a hand about once every five sessions. Of course, we need to add in the times that partner has a hand in this range too, so the partnership has one about once every 2.5 sessions. Occasionally someone opens in front of us (albeit less frequently when we have a big hand, but they could open a preempt or something). So the opportunity to use our specialized methods for 21+ hcp hands will be pretty infrequent. It may also be worth mentioning that of these 21+ hcp hands, more than half are balanced (under a strict definition where balanced hands contain no singleton or void and at most one doubleton).

For comparison, the frequency of holding a weak two in diamonds (under a fairly strict definition where only six card suits are allowed) is about 2.4%. Combined with partner, one of us has a weak 2♦ bid on average more than once a session. Of course, some of these our opponents will open ahead of us (and such is substantially more frequent than when we hold the big hand), but it's still a good bet that weak 2♦ openings outnumber 21+ hcp hands substantially. Keeping in mind that a fairly high percentage of 21+ hcp unbalanced hands are easy to bid without special gadgets, my numbers shouldn't be too far off.

[Jlall]

awm, on Aug 30 2009, 01:35 AM, said:

Keeping in mind that a fairly high percentage of 21+ hcp unbalanced hands are easy to bid without special gadgets, my numbers shouldn't be too far off.

Yeah, I agree with your totally point and I didn't doubt your numbers, was just surprised because if you had asked me "how often do you or your partner have 21+HCP" I would have said once every 20 boards or something lol. Again, I just think it's my brain associating other very strong hands with less HCP as being in that range.

[fred]

awm, on Aug 30 2009, 06:35 AM, said:

For comparison, the frequency of holding a weak two in diamonds (under a fairly strict definition where only six card suits are allowed) is about 2.4%. Combined with partner, one of us has a weak 2♦ bid on average more than once a session. Of course, some of these our opponents will open ahead of us (and such is substantially more frequent than when we hold the big hand), but it's still a good bet that weak 2♦ openings outnumber 21+ hcp hands substantially. Keeping in mind that a fairly high percentage of 21+ hcp unbalanced hands are easy to bid without special gadgets, my numbers shouldn't be too far off.

Hi Adam,

How did you come up with 2.4%? You sure that is right?

The reason I am asking is that the next version of the web-client will have the ability to make computations like this. I asked it the odds of a hand with:

- 0 to 3 cards in each major
- 0 to 4 cards in clubs
- exactly 6 diamonds
- between 5 and 10 HCP

The answer I got was 1.33%.

I am not completely confident that the algorithm I designed to solve such problems or the code I wrote to implement this algorithm is correct. That's why I am wondering how you got your number and if you have strong reason to believe that is correct.

By the way, I agree with the basic point you are making - the purpose of this post is to try to make sure I don't have a bug

Thanks,

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[nigel_k]

I also got 1.33% for a weak 2♦ using Fred's conditions. I quite often have a 5 card suit nonvul and sometimes a 4 card major which increases the frequency but also open 3♦ with a 6 card suit sometimes.

For hands with 21+ HCP I got 0.80%, the same as Adam.

Of course, the real issue is not just the frequency but how many IMPs you gain or lose. Some may disagree, but I find the weak 2♦ is quite effective as a preempt, both when I use it and when it is used against me. However I wouldn't be surprised if Ken is able to come up with a more profitable use for it in accurately bidding strong hands.

[awm]

The differences in calculation are:

(1) I'm allowing a range of 5-11 hcp. While this is only one point difference, 11 hcp is a very common number to have.

(2) I'm not disallowing a four-card major, or a five-card club suit.

My real-life tendency is to open 2♦ quite frequently on hands which are 5-4 or 5-5 in the minors (and to usually open 3♦ with 6-5 in the minors). Probably this makes my 2♦ openings more frequent than what's simulated here. As for four-card majors, there is some requirement of relative suit qualities that is hard to model.

[gwnn]

Anyway you should divide the 21 hcp hands by something between 2 and 4. I am not sure what the probability is that a hand contains 4+ spades. Is there an easy way to calculate it? (and does this probability depend on hcp)

[fred]

awm, on Aug 31 2009, 12:05 AM, said:

The differences in calculation are:

(1) I'm allowing a range of 5-11 hcp. While this is only one point difference, 11 hcp is a very common number to have.

(2) I'm not disallowing a four-card major, or a five-card club suit.

My real-life tendency is to open 2♦ quite frequently on hands which are 5-4 or 5-5 in the minors (and to usually open 3♦ with 6-5 in the minors). Probably this makes my 2♦ openings more frequent than what's simulated here. As for four-card majors, there is some requirement of relative suit qualities that is hard to model.

Thanks for clarifying. My program returns 2.38% if I define 2D as you did.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[Cascade]

gwnn, on Aug 31 2009, 12:07 PM, said:

Anyway you should divide the 21 hcp hands by something between 2 and 4. I am not sure what the probability is that a hand contains 4+ spades. Is there an easy way to calculate it? (and does this probability depend on hcp)

P(4+) = 1 - P(0) - P(1) - P(2) - P(3)

These latter probabilities are easy to calculate.

P(0) = combin(13,0) * combin(39,13) / combin(52,13) = 0.012790948

P(1) = 0.08006186

P(2) = 0.205873354

P(3) = 0.286329607

P(>=4) = 0.41494423

Those numbers are without reference to the HCP.

Yes the HCP vary according to the distribution. This is easy to see e.g. a

13=0=0=0 has P(0) of having most numbers of HCP.

Therefore you know that if you have 11 HCP you have probability zero of having a 13-card suit.

[Cascade]

fred, on Aug 31 2009, 12:14 PM, said:

awm, on Aug 31 2009, 12:05 AM, said:

The differences in calculation are:

(1) I'm allowing a range of 5-11 hcp. While this is only one point difference, 11 hcp is a very common number to have.

(2) I'm not disallowing a four-card major, or a five-card club suit.

My real-life tendency is to open 2♦ quite frequently on hands which are 5-4 or 5-5 in the minors (and to usually open 3♦ with 6-5 in the minors). Probably this makes my 2♦ openings more frequent than what's simulated here. As for four-card majors, there is some requirement of relative suit qualities that is hard to model.

Thanks for clarifying. My program returns 2.38% if I define 2D as you did.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

Does your program do a brute force calculation or is there something more clever?

[kenrexford]

awm, on Aug 29 2009, 11:02 PM, said:

It seems pretty obvious that by devoting more openings to strong calls (i.e. Romex) you can do better on some awkward strong hands like this one.

But with that said, is this a winner on frequency grounds? 21+ hcp hands only come up maybe once every two-three sessions, and a lot of them are easy to bid with a standard 2♣/2NT opening (for example all the balanced ones). Even when you get an awkward pattern like this one, opening one of a minor will work most of the time. It seems like the strong hand method is getting a very small number of pickups. In the same time period that you wait for an awkward big hand that you can bid accurately with this method and not otherwise, you could've probably opened a weak 2♦ a dozen times and picked up substantially more IMPs.

From my own investigation of vugraph records, this does not actually bear out. Largely, this is because of two major factors. First, strong hands yield more IMP swings more frequently, such that dedicating extra tools for these auctions pays more per occurrence. Second, better methods for handling strong hands means lower minimums for strong-hand openings, means more occurrence; the flip of this is that more use of strong openings and lower minimums means lower maximums for other openings and hence less strain in weird areas (like responding with garbage because partner might have a freak and the sets that occur because of reaching too high with the yarbs).

If doing pure math, then, you would want to calculate the likelihood of having an unbalanced hand that is about 9+ winners without any real concern about suit quality or "weird" shapes. That occurs much more frequently. And, the IMP yield potential is high, as to swings.

[fred]

Cascade, on Aug 31 2009, 12:59 AM, said:

Does your program do a brute force calculation or is there something more clever?

It figures out the total number of hands that meet the specified constraints and then divides by the total number of possible hands.

I was not able to figure out any particularly clever way to do this, but it is not as if I spent a lot of time trying. Not sure if I would call my algorithm a "brute force" approach (probably it is), but it does seem to be "computationally intensive".

However, CPU cycles are sufficiently cheap these days that the degree to which my program is computationally intensive is not going to matter much in practice (I think). In other words, if it takes 1/10th of a second to solve a difficult problem and a more elegant program would take 1/20th of a second, I don't think anyone will notice let alone care.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[mike777]

kgr, on Aug 29 2009, 04:46 AM, said:

With 4=1=4=4 or 1=4=4=4 , singleton A in S or H, and points in your 2NT opening range.
Do you open 2NT or do you prefer to open 1C / 1D?
Yesterday I opened 2NT with 4=1=4=4:

Dealer: South Vul: ???? Scoring: MP

♠ Q8xx ♥ xx ♦ xxx ♣ 987x ♠ AKxx ♥ A ♦ KTxx ♣ AQJT

2NT was down on a Heart lead and ♣K wrong, while 4♠ would make.
 
My concern: When you open 2NT with a singleton then either partner will insist to play in that suit with length OR opps will lead it against 3NT.

non expert reply:



if we are nv then:

1c=1s(basically i reply on nothing)
4s


if vul then:


1d=p

I do not reply on nothing over 1c vul.....

[awm]

My impression was that the idea is to split the standard 2♣ openings into 2♣ and 2♦ depending on whether they have four spades. This also allows you to open a few hands with awkward shapes like 4441s that are "strong enough for 2♣" with the strong opening.

The point is that hands which are strong enough for 2♣ only come up about once every five sessions per player. And "regular" bidders do get to the right spot on these hands sometimes (actually fairly often). Even on the hard to bid ones (like a big 4144) you can survive by opening 1m most of the time. If you're changing your standards for one-level responses because "partner might have a 22-count 4441" then you'll get a lot of bad results, but that's not really what people are advocating. The idea is that yes, sometimes you open 1♦ on a big 4441 and you miss game because partner passes... but if partner finds a response you are well-placed and sometimes when partner passes you win because you get to play at the one-level in a making contract.

It seems reasonable to believe that standard bidders won't have a disaster on a hand in the strong 2♣ range more than one hand out of six or so. Keep in mind that half the hands in this range are big balanced hands anyway (usually not too hard to bid) and some of the others are one-suiters and such (also pretty easy). Even the "tough" ones like the big 4441 it's not like you get a bad result every time, just sometimes. Assuming this is true, it seems like playing the artificial 2♦ gets you about one big win per 15 sessions. Typically this win is about 10 IMPs (bid a slam they miss at the other table, or get to a making game instead of a failing game). So the strong 2♦ wins you 2/3 of an IMP per session by making strong hands easier to bid.

But during the same 15 sessions, my partner and I have opened a weak two in diamonds about 10 times. A lot of these times it didn't make much difference, but it wouldn't surprise me if over 10 weak 2♦ openings, we find a couple of good sacrifices (say win 5 apiece) and jam the opponents into missing slam or picking the wrong game once (say win 10). We might also go for a number opposite no game once (say lose 6), and we will have a lot of push boards. Still, it seems likely that opening 2♦ weak picked up more than 10 IMPs for us over ten openings.

Of course, if you're seriously lowering the requirements for your artificial strong opening (rather than just including "awkward shapes" with the usual playing strength) then the wins and losses will be substantially different.

[kenrexford]

That's a lot of math for a lot of seems-likes.

When I have done my consideration of various ideas, I have taken vugraph records as a sample of the real world (adjusted for high-level play of a specific variety) as a base, and then run through hands. On hands where, for example, a 2♦ opening as weak was available, I either rely on the real table results, if 2♦ weak was opened at at least one table, or extrapolate based on my assumptions of the bidding and play. I the get a net result of the bid.

When doing this for weak 2♦, an oft-repeated task because I have considered many other meanings for 2♦, I find 2♦ to be sometimes volatile but averaging out for little real impact. In other words, almost all gains are eaten by losses.

2♦ as a weak opening is a pure study, in that there are no real effects caused on alternative auctions, except perhaps some alleviation of very low-end 1♦ sequences.

Artificial 2♦ openings of the intermediate or strong variety, are more difficult to analyze, as the impact is more intertwined elsewhere. Make 2♦ Flannery, for instance, and you have impact on 1♥ opening structures, and impacts there that are more difficult to track.

A two-way strong structure is somewhat easy to track as to "when it occurs" analysis. Even that, however, assumes a different standard for opening strength requirements and some thought experiments.

That mathematics is difficult, obviously.

However, here's a more basic idea. Many people give up weak 2♦, either for system (many systems need 2♦ for something else) or for toys (Mini-Roman, etc.). As a general rule, then, weak 2♦ calls are becoming rare to use. There seems to be a group-think reason. My more detailed analysis suggested to me that this group-think is right. Each should decide for themselves, I suppose.

[rduran1216]

kgr, on Aug 29 2009, 12:03 PM, said:

Thanks all for the answers!
For those who prefer 1m above 2NT:
Is that a preference with this particular example hand or is that a general preference with a 1-4-4-4 hand a a singleton A?
 
We normally open 1D with 4-4 in the minors and we also play T-walsh. I think I would open 1C on this particular hand.

I will always open a 4-4-4-1 hand 1 of a minor, because a reverse is forcing, and I can gauge my partner's strength and shape fairly quickly

In this particular hand if I open 1C, my partner will pass, and thats fine. If I open 1D, my partner will pass. Even with 21 points, if my partner doesn't have enough to respond, playing 3NT or some other contract would be very difficult.

So I open 1D. opening 2NT is a bad lie because of shape concerns, and you most certainly dont want to play 2 or 3NT if ur partner turns over 4-5 points.