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I think this is a good problem.

I 100% agree with the initial pass–come on, people, have some standards for opening bids: this is a crap 4333 12 count with only 1.5 quicks.

I have described my hand quite well with my PH jump to 2NT: 11-12 HCPs balanced hand ♠s stopped fewer than four ♥s (else a negative double) probably no 5+ card good minor (else 2m)

Therefore, I think the logical answer is to PASS now since partner presumably knows our hand almost exactly and yet took no action over (3♥).

So I applaud all with the discipline to PASS.

Yet, I *doubled*. When this works out poorly, I will have no defense against partner's charge that this represents the worst form of “bidding my hand twice.”

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I certainly wouldn't start with 1♦. 1♥ (better) wouldn't be my choice either. I like 2NT (unusual for reds) which we play as unlimited. If 4NT also showed these suits, that might be even better.

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If you like completely “abstract math”, i.e. no empirical numerical calculations, the analysis in my previous post can be continued to prove that R. Pavlicek's claim that for the finesse to be better than the “bang” East's “vacant spaces” must be at least twice West's “vacant spaces” is almost, but not quite, correct. The true result is: The finesse will be better than the “bang” if VSE > 2*VSW - 1

where “VSE” is the number of vacant spaces in East hand and “VSW” is the number of vacant spaces in West hand.

To prove this, continue on from my previous result that for the finesse to be better:

equation 1: P{2=4} > 1.5 * P{3=3}

(where P{2=4} is the probability of any 2=4 break and where P{3=3> is the probability of any 3=3 break.)

Now, there are 15 2=4 breaks (C(6,2)) and 20 3=3 breaks So introduce the terms P{sp 2=4} and P{sp 3=3} to represent the probability of one *specific* 2=4 break and one *specific* 3=3 break, respectively.

So, P{2=4} = 15 * P{sp 2=4} and P{3=3} = 20 * P{sp 3=3} Substitute these into “equation 1” and simplify to yield the result that the finesse is better when:

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This problem is easier to solve (quite easy, actually) if one considers only the cases where one line gains over the other, i.e. ignore cases where both succeed or both fail.

1. The bang gains vs. the finesse when (a) West has Jx (i.e. 1/3 of the 2=4 breaks) (b) West has Jxx (i.e. 1/2 of the 3=3 breaks)

2. The finesse gains vs. the bang when (a) West has xx (i.e. 2/3 of the 2=4 breaks)

The probability of 2(a) is exactly twice the probability of 1(a), i.e. 2/3 of all 2=4 breaks vs. 1/3 of all 2=4 breaks.

So for the finesse to be better, this extra 1/3 * P{2=4} must be larger than 1/2 * P{3=3} (i.e. the gain from 1(b))

Simplifying, the finesse is better than the bang IFF P{2=4} > 1.5 * P[3=3} or, if you prefer: P{3=3} < 2/3 * P{2=4}

Obviously, for this to be true, the “vacant space” differential must be very large (with East having many more vacant spaces than West), since with no special information about the distribution of *other suits*, at the point of decision: West has 12 VSs (having followed once in ♣s) East has 11 VSs (having followed twice in ♣s) thus: P{3=3} = 35.96%; P{2=4} = 21.58% very, very far from the conditions required for the finesse to be better than the bang.

Imagine an extreme situation where West has opened a weak 2 in a suit where we have 5 cards, so that suit can be assumed to be 6=2.

Now, at the decision point, East has 9 VSs, West 6. These conditions give: P{3=3} = 33.57%; P[2=4} = 37.76% still not enough to make the finesse better.

How about if West opened *3* of that suit, so we can assume it is divided 7=1? Now, at the point of decision in ♣s, West has 5 VSs, while East has 10. Finally, we now find that: P{3=3} = 23.98%; P{2=4} = 41.96% At last, the conditions required for the finesse to be better have been met since 41.96 > 1.5 * 23.98

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Interesting that in the Robson rules, one of the principle ones is that 2NT is almost always good/bad when advancing partner's take-out double with the opponents at the two level (a couple of minor exceptions, but this auction is definitely not one).

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What you described is the definition of “Good/Bad” 2NT. G/B is really the same convention as Lebensohl, just applied to more auctions (“Lebensohl” usually refers to the same convention played when they overcall our 1NT opening, and perhaps over our double of their 2M openings).

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Funny! I would be interested in a discussion, though, of whether it is better to play “good/bad” or “bad/good”. That is, should the immediate suit bid show the good hand or the bad one? Or perhaps it should be played differently depending on the exact details of the auction, thereby maximizing the partnership's chances of screwing it up (was partner's 2NT good/bad? or bad/good? or maybe scrambling? surely not natural?).

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Robson notes that the 2NT competitive raise showing 4 card support and ostensibly LR+ values can be “shaded” a bit in HCPs because that bid leaves “room” for partner to make a return game try below 3M.

So, if playing 2NT this way (which I believe is uncommon in the US, although I like it but don't actually get to play it), I think this hand *would* barely qualify for such a “stretch” 2NT 4 card LR+, particularly if RHO ♣ bid is supposed to be natural. But lacking the 2NT raise, I think a 3♥ “mixed raise” is a good desciption of this hand.

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I do not believe 2♥ shows extras. In my experience, it is losing bridge (particularly at matchpoints) to pass partner's 1M response with 4 card support just because we are minimum enough to doubt our side has a game.

Must raise immediately to make it harder for the opponents to come in, and to clue partner in that we have a real fit so he can better judge what to do later if the auction turns competitive.

We have plenty of tools available to investigate game after P-1m-1M-2M, so I do not see any need for opener's simple raise to promise “extra values.”

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Would not consider 1♥.

In practice, I'd probably open 2♥, but I can definitely understand a PASS at IMPs and this vulnerability because this hand doesn't have a very high “ODR”–two aces are good for defense (particularly when pard has a stiff ♥), and the ♥ suit is full of secondary holes that could spell a huge disaster if, say, RHO doubles and LHO leave it in.

My philosophy at IMPs is to do everything possible to avoid going for a number on partscore deals, and opening 2♥ with this hand could result in a big minus score without their side having a game.

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Although (as I stated) I would raise only to 2♥ with this North hand, I do not think 3♥ is ridiculous. Give responder a minimum hand with his honors better placed, say: xx-AQTx-T9xx-xxx

and 4♥ has some play. And certainly responder, even though a PH, could have considerably more than this, say: xx-AQTx-KT9x-xxx which makes 4♥ quite good, yet he won't move after P-1♦-1♥-2♥.

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I surprised myself by voting for “scramble” here because I'm a big fan of “good/bad” in many competitive auctions.

I tried to figure out a good reason for my vote (perhaps I'm just being inconsistent–I wonder if my partner would read this 2NT by me as “scrambling”, knowing what a big “good/bad” fan I am ?).

Perhaps my feeling favoring “scramble” is based on thinking that if partner had a good enough hand for a “good” 3♣ or 3♦ now, he likely would have acted over (2♥), probably with a negative double since 3m directly would be GF.

“Scramble” could be valuable when responder is 4=4 in the minors (and too weak for a negative double) to maximize chances of finding a 4=4 minor fit when opener is 5=1=4=3 or 5=1=3=4).

Nevertheless, I will acknowledge that there are probably hands responder could have up to, maybe, 9 HCPs that would have no convenient bid directly over (2♥) that would dearly love to be able to show some (perhaps surprise) values now by having “good/bad” available, thus avoiding having his 3♣ or 3♦ be totally ambiguous as to hand strength.

I should note that my competitive bidding guru, Robson, in his “Partnership Bidding….” clearly defines 2NT by responder on this auction type as “good/bad” (so that 3m is “good”), so I'm starting to think perhaps I should adopt this view, particularly as it will help in avoiding driving my partner completely mad when he has to guess what my competitive 2NTs mean.

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This wasn't a real deal for me–it arose from a discussion in another thread where this hand passed over (1♣), and LHO bid 3NT on a flat 11 count. Only a ♠ lead would have beaten the contract (dummy had ♠:Kx, and partner had S:87xx-♥:T-♦:Kxxxxx-♣:Qx and led a ♦).

On that thread, at least one respondant commented that a 1♠ overcall was clear with this hand. That seemed odd to me, since it is not even our longest suit. Anyway, I'm glad to see from the results of this poll that his is not a popular view.

I have no strong feelings between Pass, 1♥, DOUBLE, and a slightly off-shape Michaels bid (if the hand were a tad stronger, say ♣:AJ, I would like the Michaels bid more).

I'd probably have doubled, but think the Michaels call has more merit than the vote suggests. I know Mike Lawrence has advocated “weird Michaels” on hands with 4=5 majors, around opening bid strength, and lacking the unbid minor (making a DOUBLE less attractive), but also seem to recall that his advocacy of that call did not receive a lot of support either.

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Let's see- West has a 9 loser hand, no suit, slow winners in their suit. East has a 7 loser hand with ideal shape for a double of (2♥). And we're talking about how much blame West should get?

Only the unfavorable vulnerability gives any justification for East's pass over (2♥). If NV, DOUBLE would be clear. As it is, passing is quite conservative, but may be justified against opponents who are quick to double for that magic +200 (which is in fact available here).

As either West or East, I wouldn't criticize my partner's decisions on this deal even though they worked out poorly.

If I held the North hand, I would consider it strong enough for an invitational splinter if such could be shown (e.g. interchange North's minors, then 1♣-1♥-3♦ to show an invitational splinter raise of ♥s with short ♦s).

With the actual hand, I would probably content myself with the simple raise to 2♥, but only after considering 3♥.

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We use transfers starting with 1NT after 1M-(DBL) (but not after 1♥-(1♠)) *EXCEPT* when the 1M opening is in 3rd seat. In that situation, the value of Drury is so great that it is better to retain that convention.

Craig Zastera

I 100% agree with the initial pass–come on, people, have some standards for opening bids: this is a crap 4333 12 count with only 1.5 quicks.

I have described my hand quite well with my PH jump to 2NT:

11-12 HCPs

balanced hand

♠s stopped

fewer than four ♥s (else a negative double)

probably no 5+ card good minor (else 2m)

Therefore, I think the logical answer is to PASS now since partner presumably knows our hand almost exactly and yet took no action over (3♥).

So I applaud all with the discipline to PASS.

Yet, I *doubled*. When this works out poorly, I will have no defense against partner's charge that this represents the worst form of “bidding my hand twice.”

Sorry–I just couldn't stand it.

Craig Zastera

1♥ (better) wouldn't be my choice either.

I like 2NT (unusual for reds) which we play as unlimited.

If 4NT also showed these suits, that might be even better.

Craig Zastera

The true result is:

The finesse will be better than the “bang” if

VSE > 2*VSW - 1

where “VSE” is the number of vacant spaces in East hand

and “VSW” is the number of vacant spaces in West hand.

To prove this, continue on from my previous result that for the finesse to be better:

equation 1: P{2=4} > 1.5 * P{3=3}

(where P{2=4} is the probability of any 2=4 break and

where P{3=3> is the probability of any 3=3 break.)

Now, there are 15 2=4 breaks (C(6,2)) and 20 3=3 breaks

So introduce the terms P{sp 2=4} and P{sp 3=3} to represent the probability of one *specific* 2=4 break and one *specific* 3=3 break, respectively.

So, P{2=4} = 15 * P{sp 2=4} and P{3=3} = 20 * P{sp 3=3}

Substitute these into “equation 1” and simplify to yield

the result that the finesse is better when:

equation 2: P{sp 2=4} > 2*P{sp 3=3}

But since:

(a): P{sp 2=4} = VSW*(VSW-1)*VSE*{VSE-1)*(VSE-2)*(VSE-3)

and:

(b) P{sp 3=3} = VSW*(VSW-1)*(VSW-2)*VSE*(VSE-1)*(VSE-2)

(actually, each of the above expressions need to be divided by a denominator which is the same for both, so is ignored).

Substituting (a) and (b) into “equation 2” and cancelling like factors on both sides of the inequality gives:

VSE - 3 > 2 * (VSW - 2)

or (simplifying):

result: VSE > 2 * VSW - 1

as the exact expression for when the finesse will be a better percentage play than the “bang.”

Checking this formula against the examples from my previous post:

example 1: VSE = 9 ; VSW = 6 ==> 9 is not > 2*6 -1 (11)

so “bang” is better

example 2: VSE = 10; VSW = 5 ==> 10 > 2*5 - 1 (9)

so, finally, finesse is better.

Craig Zastera

1. The bang gains vs. the finesse when

(a) West has Jx (i.e. 1/3 of the 2=4 breaks)

(b) West has Jxx (i.e. 1/2 of the 3=3 breaks)

2. The finesse gains vs. the bang when

(a) West has xx (i.e. 2/3 of the 2=4 breaks)

The probability of 2(a) is exactly twice the probability of 1(a), i.e. 2/3 of all 2=4 breaks vs. 1/3 of all 2=4 breaks.

So for the finesse to be better, this extra 1/3 * P{2=4}

must be larger than 1/2 * P{3=3} (i.e. the gain from 1(b))

Simplifying, the finesse is better than the bang IFF

P{2=4} > 1.5 * P[3=3}

or, if you prefer:

P{3=3} < 2/3 * P{2=4}

Obviously, for this to be true, the “vacant space” differential must be very large (with East having many more vacant spaces than West), since with no special information about the distribution of *other suits*, at the point of decision:

West has 12 VSs (having followed once in ♣s)

East has 11 VSs (having followed twice in ♣s)

thus:

P{3=3} = 35.96%; P{2=4} = 21.58%

very, very far from the conditions required for the finesse to be better than the bang.

Imagine an extreme situation where West has opened a weak 2

in a suit where we have 5 cards, so that suit can be assumed to be 6=2.

Now, at the decision point, East has 9 VSs, West 6.

These conditions give:

P{3=3} = 33.57%; P[2=4} = 37.76%

still not enough to make the finesse better.

How about if West opened *3* of that suit, so we can assume it is divided 7=1? Now, at the point of decision in ♣s, West has 5 VSs, while East has 10.

Finally, we now find that:

P{3=3} = 23.98%; P{2=4} = 41.96%

At last, the conditions required for the finesse to be better have been met since 41.96 > 1.5 * 23.98

Craig Zastera

This is a perfectly sound, full opening bid with playability in 3 suits. Why would you want to distort the auction by making a weird opening bid?

Your hand is too strong to pass a semi-forcing 1NT response over a 1♠ opening–another reason not choose an abnormal call.

Craig Zastera

They always alert my competitive 2NT bids and explain “definitely not natural–after that, your guess is as good as mine.”

Craig Zastera

Craig Zastera

G/B is really the same convention as Lebensohl, just applied to more auctions (“Lebensohl” usually refers to the same convention played when they overcall our 1NT opening, and perhaps over our double of their 2M openings).

Craig Zastera

Craig Zastera

I would be interested in a discussion, though, of whether it is better to play “good/bad” or “bad/good”.

That is, should the immediate suit bid show the good hand or the bad one?

Or perhaps it should be played differently depending on the exact details of the auction, thereby maximizing the partnership's chances of screwing it up (was partner's 2NT good/bad? or bad/good? or maybe scrambling? surely not natural?).

Craig Zastera

So, if playing 2NT this way (which I believe is uncommon in the US, although I like it but don't actually get to play it), I think this hand *would* barely qualify for such a “stretch” 2NT 4 card LR+, particularly if RHO ♣ bid is supposed to be natural.

But lacking the 2NT raise, I think a 3♥ “mixed raise” is a good desciption of this hand.

Craig Zastera

Must raise immediately to make it harder for the opponents to come in, and to clue partner in that we have a real fit so he can better judge what to do later if the auction turns competitive.

We have plenty of tools available to investigate game after P-1m-1M-2M, so I do not see any need for opener's simple raise to promise “extra values.”

Craig Zastera

In practice, I'd probably open 2♥, but I can definitely understand a PASS at IMPs and this vulnerability because this hand doesn't have a very high “ODR”–two aces are good for defense (particularly when pard has a stiff ♥), and the ♥ suit is full of secondary holes that could spell a huge disaster if, say, RHO doubles and LHO leave it in.

My philosophy at IMPs is to do everything possible to avoid going for a number on partscore deals, and opening 2♥ with this hand could result in a big minus score without their side having a game.

Craig Zastera

Give responder a minimum hand with his honors better placed, say:

xx-AQTx-T9xx-xxx

and 4♥ has some play. And certainly responder, even though a PH, could have considerably more than this, say:

xx-AQTx-KT9x-xxx

which makes 4♥ quite good, yet he won't move after P-1♦-1♥-2♥.

Craig Zastera

I tried to figure out a good reason for my vote (perhaps I'm just being inconsistent–I wonder if my partner would read this 2NT by me as “scrambling”, knowing what a big “good/bad” fan I am ?).

Perhaps my feeling favoring “scramble” is based on thinking that if partner had a good enough hand for a “good” 3♣ or 3♦ now, he likely would have acted over (2♥), probably with a negative double since 3m directly would be GF.

“Scramble” could be valuable when responder is 4=4 in the minors (and too weak for a negative double) to maximize chances of finding a 4=4 minor fit when opener is 5=1=4=3 or 5=1=3=4).

Nevertheless, I will acknowledge that there are probably hands responder could have up to, maybe, 9 HCPs that would have no convenient bid directly over (2♥) that would dearly love to be able to show some (perhaps surprise) values now by having “good/bad” available, thus avoiding having his 3♣ or 3♦ be totally ambiguous as to hand strength.

I should note that my competitive bidding guru, Robson, in his “Partnership Bidding….” clearly defines 2NT by responder on this auction type as “good/bad” (so that 3m is “good”), so I'm starting to think perhaps I should adopt this view, particularly as it will help in avoiding driving my partner completely mad when he has to guess what my competitive 2NTs mean.

Craig Zastera

Only a ♠ lead would have beaten the contract (dummy had ♠:Kx, and partner had S:87xx-♥:T-♦:Kxxxxx-♣:Qx and led a ♦).

On that thread, at least one respondant commented that a 1♠ overcall was clear with this hand. That seemed odd to me, since it is not even our longest suit.

Anyway, I'm glad to see from the results of this poll that his is not a popular view.

I have no strong feelings between Pass, 1♥, DOUBLE, and a slightly off-shape Michaels bid (if the hand were a tad stronger, say ♣:AJ, I would like the Michaels bid more).

I'd probably have doubled, but think the Michaels call has more merit than the vote suggests. I know Mike Lawrence has advocated “weird Michaels” on hands with 4=5 majors, around opening bid strength, and lacking the unbid minor (making a DOUBLE less attractive), but also seem to recall that his advocacy of that call did not receive a lot of support either.

Craig Zastera

East has a 7 loser hand with ideal shape for a double of (2♥).

And we're talking about how much blame West should get?

Only the unfavorable vulnerability gives any justification for East's pass over (2♥). If NV, DOUBLE would be clear. As it is, passing is quite conservative, but may be justified against opponents who are quick to double for that magic +200 (which is in fact available here).

As either West or East, I wouldn't criticize my partner's decisions on this deal even though they worked out poorly.

If I held the North hand, I would consider it strong enough for an invitational splinter if such could be shown (e.g. interchange North's minors, then 1♣-1♥-3♦ to show an invitational splinter raise of ♥s with short ♦s).

With the actual hand, I would probably content myself with the simple raise to 2♥, but only after considering 3♥.

Craig Zastera

Craig Zastera

Craig Zastera