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All comments by Craig Zastera
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In the case of the 2/1 response, it is 100% clear to rebid 2.
Rebidding 2 doesn't show *anything* additional about opener's hand other than the inability to bid something else.
The 2 rebid shows that opener has 4+ s in addition to the 5+ s previously shown.

Not quite as clear after the 1NT(F) response.
Still, if opener rebids 2, he might play there in a 6-1 with an 8 or 9 card fit. So the s would have to be REALLY good and the s really poor before I would consider “hiding” the s in favor of rebidding the s.
Dec. 1, 2018
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John,
I am very skeptical about your claim that you make more tricks than “double dummy” result more than 17% of the time in 3NT contracts, unless you are playing in very weak fields.

Richard Pavlicek has compiled extensive statistics taken from very high level tournaments on how real-world declarer results compare to “double-dummy” results on the same deal.
His statistics are broken down by specific contracts.

For 3NT, actual declarers made 3NT about 4.3% more often than double-dummy results predict.

Pavlicek also includes statistics from these same high level events where the double-dummy play and defense begins *AFTER THE OPENING LEAD*. That is, he uses the *actual* real-world opening lead, but then uses double-dummy play and defense starting with the first play from dummy.

It turns out that the “real-world” declarer's advantage (vs. double-dummy play/defense) quoted above (4.3%) is *more* than entirely accounted for by the very much less than optimal choice of opening lead made by “real-world” defenders (!)

When one looks at the 3NT contracts using the actual real-world opening leads (instead of the “best” double-dummy leads) followed by double-dummy play/defense thereafter, the 4.3% “real world declarer advantage” cited above turns into 3.5% advantage FOR DOUBLE-DUMMY declarer over “real-world declarer's (!!!).

Thus, following something like your suggestion (of not using ”the best" opening leads) actually results in real-world declarers doing WORSE (on average) in 3NT contracts than double-dummy declarers.
Nov. 30, 2018
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I tried another (1000 deal) simulation where opener is given exactly *3* s *AND* a doubleton in one of the other suits
(still with 15-17 balanced).

I found that 3NT still outperformed 4H.
The actual results were:
3NT beat 4H on 535 deals
4H beat 3NT on 451 deals
3NT tied 4H on 14 deals

Thus, I am still favoring 1N-3N (if not looking for slam).

After alternate 1N-2-2-3NT, I do not expect my partner to be any more sophisticated or accurate in deciding whether to pass 3NT vs. pulling to 4 when s/he holds *3* s beyond perhaps passing with 4333 shape while pulling with a doubleton.

I tried another 1000 deal simulation where I gave opener
*4* s and a side doubleton.

On this simulation, the results were:
3NT beat 4H on 439 deals
4H beat 3NT on 557 deals
3NT tied 4H on 4 deals

So in this case, 4 did prove better than 3NT.

But what if opener is 3=4=3=3?

Another simulation for 3=4=3=3 openers gave:
3NT beat 4H on 654 deals (!)
4H beat 3NT on 343 deals
3NT tied 4H on 3 deals

An enormous win for 3NT in this case !!

But since we cannot find out if partner has 4 s *and* a side doubleton and play 4 only in those cases, it looks like a direct 3NT is still best.

If instead we Stayman and discover that partner has four s, we either have to bid 3NT or 4. Partner won't know to correct 3NT to 4 when he has a side doubleton but not otherwise since he won't even know that we have four s on that auction.
Nov. 29, 2018
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Jeff,
This is a good problem at matchpoints.

My *experience* suggests that this hand type should not bid Jacoby then 3NT because often 3NT will score better than 4 on deals where partner will pick 4.

In practice, I usually bid Stayman and choose 4 only if partner shows 4+ s.

But I did some (1000 deal) simulations with your hand.
I did use 15-17 for partner because I wasn't quite sure what to specify for “14+”.

Anyway, over all deals where partner has *3* s, 3NT was a big winner at matchpoints–it beat 4 on 606 deals while 4 won on only 387 deals (the remaining 7 were ties).

But even when partner had *4* s, 3NT narrowly beat out 4 (514 wins for 3NT, 482 for 4).

This suggests that on your hand, if responder is not going to look for *slam*, he will do best by just raising to 3NT *AT MATCHPOINTS*.

Note that at IMPs, the results were very different.
The same two 1000 deal simulations showed 4 winning handily over 3NT in both cases (i.e. even when opener has only 3 s).
This is because *many* of the matchpoint “wins” for 3NT were only by 10 points. But 4 goes down fewer times than 3NT, which is why it is better at IMPs.

I looked only briefly at slam possibilities.
I did a simulation giving opener 4 s and 17 HCPs and found 6 making a bit over 50% of the time. Of course, that is double-dummy (real world slams generally do not make as often as double-dummy results suggest).
On the other hand, I did not eliminate deals where we are missing 2 keys (or 1 key and Q). Doing that obviously would increase 6 make %age and should be easily achievable in the bidding.
A similar simulation giving opener 16-17 HCPs and 4 s dropped the 6 percentage slightly below 50%.

I will do a bit more simulation work to look more carefully at slam potential to try to see if considering that justifies bidding differently. My intuition is that this hand is not quite good enough to look for slam since even when partner has a “super-accept” (which will be relatively uncommon), slam is only marginal.
Nov. 29, 2018
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Or at least “not wrong.”

My thinking is that vs. good defenders, we can rule out the possibility that North has the 4th and South the :Qx.

If *South* has the 4th , then the 2nd round finesse is, mathematically, no worse than 50%.

That is because at the point of decision, North will be known to have 2 s and (by assumption) 3 s, hence *8* “vacant spaces.
Meanwhile, South's ”known“ cards are 1 and (by assumption) 4 s, hence also 8 vacant spaces.
Thus, in this case the finesse is just as good as playing for the drop.

But the other possibility is that North has the Q (perhaps with 4 s). He knows from the bidding, the play to the first 3 tricks, and looking at his hand that the only real chance for a 4th defensive trick is in s.

If he led the 4th (J) now, he knows that you would have little choice but to play him for the Q (by ruffing low).
The only alternative would be to ruff with A and hope to drop a stiff offside Q on the next trick. But that is such a low percentage shot that it is all but certain you would not choose it.

Thus, he switches to a to give you a ”losing alternative", namely to play to drop :Qx in the South hand.
Nov. 29, 2018
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What you are missing is that *partner* knows all this too.
Yet he passed (2).

If defending (2) is wrong when you hold this minimum hand with poor s and reasonable defense against s, it was up to him to do something directly over (2) to send that message.

Therefore, bidding again now with this hand is simply disrespecting partner. Perhaps your partner doesn't deserve respect. If so, go ahead and bid 3 (and then, perhaps, look for a new partner).
Nov. 29, 2018
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You can't specify the “ratios” between 15 vs. 16 vs 17 HCPs for opener in the abstract.

First, it depends on what the responding hand is.
The stronger the responding hand, the more likely it becomes that opener has only 15. Conversely, if responder is very weak, the chances opener has 16 or 17 inccrease.

Second, it depends on your exact requirements for the 1NT opener (and partner's tendencies to “upgrade” or “downgrade”).

For example, if you sometimes open 1M with 5332 hands with a 5 card major, that will affect the 15/16/17 ratios for your remaining 1NT openers.

That is because the most appealing hands for 1NT with a 5 card major are the 15 HCP ones. Those are a bit weak for the 1M-1N-2m-2M-2N strategy and also (perhaps) for inviting after 1M-2M.

Conversely, (many) 17 HCP hands with a 5 card suit can “stretch” to open 1, planning to rebid 2NT over a 1 response if necessary.

With 5 s, as long as the hand is good enough (generally 16-17) for the “2-step” over a (forcing) 1NT response (i.e. 1-1N-2m-2-2N), it is safe enough to open 1.

Good 2/1 GF methods handle 16-17 HCP balanced hands with a 5 card major easily after a 2/1 response–generally a jump rebid of 3NT is defined to show these hands.

The upshot of having a “mixed” strategy w.r.t. sometimes opening 1M and sometimes 1NT when holding a balanced hand with a 5 card major in the 15-17 HCP range is to *increase* the percentage of 15 HCP hands that are opened 1NT relative to 16 and 17 point hands.
Nov. 29, 2018
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John,
Your arguments are relevent to the downsides of having to go through Stayman to invite game in NT. But a simple 1NT-2NT would not suffer most of your objections (still allows opponents to know our side doesn't have considerable extra values, though).

My methods (still) require going through Stayman to invite game in NT and I hate it. If I could only figure out a way to eliminate that without giving up the ability to describe so many other hand types.

I have actually considered entirely giving up on having a balanced (NT) invite over partner's 1NT opening. I have done some simulations which suggest that perhaps VUL at IMPs that wouldn't be bad–it is very hard to find hands where a NT invite significantly outperforms just having responder decide himself between passing 1NT vs. blasting 3NT.

However, at *matchpoints* there is clearly a range of responding hands (OP hand here being an example) where a NT invite is measurably better than having responder decide on his own.

I've considered using the 2 “range ask”. Problem with that choice is that if it is to do “double-duty” as a NT invite *and* a transfer, then opener can't reply correctly for both–a “max” hand for NT purposes is not necessarily the same as “very good fit for s”.
Plus, 2 as a NT invite still gives opponents a bit more opportunity than would 2NT.
Nov. 29, 2018
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I would win A.
Cross to dummy, lead another and finesse if North follows low.

No certainty about who has the last , but if South had the Qx and only 3 s, surely North would have arranged a trump promotion with a 4th round of s.

That seems like enough of a clue to go for the finesse which is only slightly worse than playing for the drop with no information at all.
Nov. 28, 2018
Craig Zastera edited this comment Nov. 29, 2018
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Here we are on the other side of the coin.
No, this hand is too good to pass a 15-17 1NT opener.

If opener has 16-17 points, 3NT will make over 61% of the time–and that is double dummy.

Data comparing double dummy play and defense with real-world play/defense from high level events suggests real world declarer's in 3NT succeed about 4%-5% more often than double-dummy results.

But opposite 15 HCP openers, this hand makes 3NT only about 35% of the time. Even allowing for real-world declarer doing better, that is still too low to just blast 3NT.

An invitational raise to 2NT is “just right” with this hand.
Nov. 28, 2018
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Correct.
It is actually slightly worse than the average 9 HCP balanced hand in terms of its NT performance opposite a 1N opener.

An average balanced 9 count opposite average balanced 15 count makes 3NT a bit less than 40% of the time.

This dummy opposite average balanced 15 count makes 3NT about 35% of the time.
Nov. 28, 2018
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I wasn't arguing hard for 2NT–I said I picked 2.

*However*, so far 2NT has received *1 vote* while PASS has received 6.

In my view, 2NT is significantly better than PASS.
Nov. 28, 2018
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Hard for me to understand what there is about this hand to make me want to bid again.

I think I have said it all with my opening bid.
I do not believe in “bidding the same hand twice.”

Partner should expect me to pass out (2) unless I have something beyond what I've described either in the form of shape and/or high cards.

Knowing that, if he is not content to defend (2) opposite a normal, minimum range 1 opening with 5 s, it was *his* responsibility to have done something over (2).
Nov. 28, 2018
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My simulations strongly suggest that “just bid 3N” is very wrong at matchpoints with this responding hand.

I did a series of 5000 deal simulations.

Over all possible hands for opener (15-17 balanced), 3NT is right around 50%.
Whether it is slightly above 50% or slightly below 50% depends on secondary factors such as whether one opens 1NT with all balanced hands containing a 5 card major (in which case 3NT made 51% of the time) or chooses 1M with some of these.

My “simplified” criteria for whether to open 1NT with 5332 hands containing a 5 card major are:
* with 15, open 1NT
* with 17, open 1M
* with 16, open 1S with 5 s but 1NT with 5 s.

Obviously, in real life, this decision is more complex, but the above gives a reasonable approximation (for simulation purposes) of what I do without having to specify very complex criteria.

Anyway, with *those* assumptions, 3NT made 48.2% overall.
Intuitively, the drop is due to 15 HCP hands becoming relatively more frequent since all the 15s with a 5 card major are included, while all the 17s and some of the 16s are removed.

Refining the simulations (now sticking with including some but not all hands with 5 card majors as described above), I found the following:
Opener has 15 HCPs: 3NT made 35%
Opener has 16-17 HCPs: 3NT made 61.2%

I use the 15 vs. 16/17 as an approximate surrogate for whether opener would accept a NT game invite or not.
Again, real world criteria are more complex (if you have good hand evaluation skills) as some 15 HCP hands are as good as average 16s, while some 16s are as bad as average 15s.
Still, statisitically, for simulation purposes, I find the 15 vs. 16/17 to give a good approximation for “accept” vs. “decline” decision after a NT game invite.

The relative frequencies of 15 vs. 16/17 openers opposite the given responding hand was:
15: 47.3%; 16/17: 52.7%
(again, if you opened 1N on all balanced 15-17 hands with a 5 card major, the percentage for “15” would be somewhat lower).

Anyway, from the above data it should be obvious that inviting with 2N wins big AT MATCHPOINTS vs. blasting 3N.

When opener has 16/17, it doesn't matter which strategy you choose, because you will play 3NT either way.

But when opener has *15*, he will decline the invite.
In those cases, 2NT beats 3NT 65% to 35%.
Combining that result with the relative frequencies, shows that overall, inviting (2NT) beats blasting (3NT) by:
0.473 * 65% = 0.527 * 50% = 57.1%
at matchpoints. That is a considerable win for the invite.

Since OP problem specified matchpoints, I will not include here the IMP analysis (which I have done), except to say the results are quite different (particularly when VUL).
Nov. 28, 2018
Craig Zastera edited this comment Nov. 28, 2018
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I picked 2 like almost everyone else.

But 2NT is IMO a reasonable enough alternative to merit significantly more than the 1 vote out of 40 that it has garnered so far.

There is a *lot* of ambiguity on this auction about East's strength and shape. 10-18 HCPs. He might even have only four s and five s (or the other way around, or 5=5, or maybe he rebid 2 on a 3-bagger with good 3 card support and extra values).

Because of all that ambiguity, “stretching” slightly for a 2NT rebid with this hand type can be the winning choice.

The “stretch” on this OP hand with 9 HCPs, two working 10 spots and that big 9 is not huge, I think.
Nov. 28, 2018
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I'll have more comments later after I've finished some simulations.

But I must say I looked up this deal as I was interested in what sort of hand South might have held for his (to me) rather unusual vulnerable actions of first passing in 3rd chair and later volunteering 2 over a (usually game invitational or better) Stayman 2 from his RHO.

It turns out that South's actual hand was:
97 AQJT95 97 864

It seems to me that perhaps many players would have methods permitting some sort of 3rd seat opening with this hand, no?
Nov. 28, 2018
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If you prefer a game in which some decisions are significantly more important than other (as I do), then IMP pairs is probably your choice.

If think every correct decision should be rewarded equally and every mistake equally expensive, then matchpoints (or, better, BAM) would be your preference.
Nov. 28, 2018
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Wish you would have included question about opener's holding in responder's (major) suit.

Traditionally, I believe the 3NT bid was supposed to have a singleton in responder's suit. I believe I have seen Eric Kokish in print advocate this as being quite important (virtually a requirement).

It seems that many players are (much) less strict about this, though.
Nov. 27, 2018
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The most likely shape for 2 overcall followed by later TO double of (4) is 1=3=6=3 with maximum overcall values. Or, possibly, 0=3=6=4 .

Therefore, on this auction, I do not think 5 from south is more reasonable than 5, although you might argue for 4NT.
Actually, among those three, I think I prefer 5, 4NT second, 5 last.

Of course, best choice by that point of the auction would be to pass (4X) and “take the money” since any game is far from certain.

Much better for North to start with 2NT to show is two strong minors. Maybe he will later get a chance to double (s) to suggest his 0=3=5=5 shape.
Nov. 26, 2018
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Since this problem is largely about tactics and perhaps judging what your specific opponents are likely to do under pressure, I won't pretend that computer simulation can be of much value here.

Even generating random deals and looking at them “by hand” to try to determine what might happen if you open 1 vs. 5 is not very productive because on many deals it is very hard to say what the other three players will do (lots of shape around the table).

However, I thought it might be of some interest just to ask, statistically speaking, how many tricks North is likely to make playing in s over a large number (I chose 5000) of random deals.

Here are the double-dummy results for tricks makeable in s by North over 5,000 random deals with given North hand:

13 tricks: 295 (6% cumulative)
12 tricks: 989 (26% cumulative for 12+ tricks)
11 tricks: 1476 (55% cumulative for 11+ tricks)
10 tricks: 1259 (80% cumulative for 10+ tricks)
9 tricks: 710 (95% cumulative for 9+ tricks)
8 tricks: 266 (99.9% cumulative for 8+ tricks)
7 tricks: 5 (100% cumulative for 7+ tricks)

Those numbers make the 5 opening look pretty appealing since most often that is actually the best contract for our side, and it puts maximum pressure on the opponents.
Nov. 26, 2018
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