4 Suit Transfers & Minor Suit Stayman

[foo]

Recently my opponents produced the auction 1♥ - 2NT - 4♥ - 6♥. The explanations were that 1♥ was natural (five-card majors, 11-20 or so hcp), 2NT was a game-forcing heart raise, 4♥ showed a bad hand with no singleton or void, and 6♥ was to play. I held:

 

Jxx xx xxxx Txxx

 

What do I lead? How do I know? This is pretty much a pure guess, and I doubt that Meckstroth, Garrozzo, Hamman, Helgemo, Fantoni, or whoever else you want to name has a much better chance of going right here than I did. Turns out opponents are off a cashing AK in one of the suits, but if I don't lead it they have 12 top tricks. Sometimes blasting just works. Of course, if I had been on lead with the cashing AK they would have felt silly for not bidding more "scientifically..." but certainly if they had a cuebidding auction to the same 6♥ my chances of finding the right lead would improve dramatically. :)

Yep. We've all been there. Thankfully that sort of thing evens out in the long run.

(My guess is a D.)

 

Not so the rest of the discussion we are having.

 

Basically, the debate is between more accurate and constructive bidding where we risk telling Them more than we'd like VS less accurate bidding where We guess more often and hope They guess even more poorly. Particularly on Opening Lead.

 

It is a debate that has been going on in general a long time and I do not expect it to be settled in general any time soon. If ever.

 

Let's be clear that I completely agree that saying too much about the closed hand (and sometimes even about dummy) is a Bad Thing. However, like most other things there are extremes in both directions of the issue that IMHO are best avoided.

 

There is no way around or to "sugar coat" the fact that the "pass or blast" crowd, particularly in auctions that begin 1N, are counting on defensive errors to make up for lack of constructive bidding accuracy.

Also, there are plenty of contracts where the defense could be told =exactly= or =nothing= about what the declaring side had and it would make no difference. Some contracts are cold, and some contracts are doomed.

 

For the hands where it does matter, it is as it has always been: try like heck not to blow up a trick on defense. Flat hands opposite flat hands where the outcome is not foreordained usually have some significant work needed to bring them home.

Making Declarer work for all their tricks is usually the best the defense can do.

 

In addition, because "pass or blast" methods are "rolling the dice" more often than more constructive methods, there should be a vigorish in favor of the pair/team not using them when they compete against each other as long as the constructive side is not "wearing their cards on their sleeves".

[foo]

This concept needn't even be as extreme. In the mold of what Adam was talking about, 1NT p 2NT p 3NT, and you have xx KT8xx xx QJT9. You better believe I'm leading a club. The opponents probably will have to work for every trick and I intend to give nothing away. However 1NT p 3NT and I may well lead a heart that is riskier but has more upside, because of the likelihood that the opponents will otherwise have nine tricks too soon. If the opponents were overbidding 3NT on an 'invitational' hand, then you are likely to regret your risky lead. Keeping information away from opponents in close games is to your advantage.

Call me a simpleton, but w/ xx.KT8xx.xx.QJT9 I don't care whether they got 3N via 1N-3N or 1N-2N;3N, I'm leading the CQ.

 

The Hx rates to blow up the H suit way too often.

[jdonn]

This concept needn't even be as extreme. In the mold of what Adam was talking about, 1NT p 2NT p 3NT, and you have xx KT8xx xx QJT9. You better believe I'm leading a club. The opponents probably will have to work for every trick and I intend to give nothing away. However 1NT p 3NT and I may well lead a heart that is riskier but has more upside, because of the likelihood that the opponents will otherwise have nine tricks too soon. If the opponents were overbidding 3NT on an 'invitational' hand, then you are likely to regret your risky lead. Keeping information away from opponents in close games is to your advantage.

Call me a simpleton, but w/ xx.KT8xx.xx.QJT9 I don't care whether they got 3N via 1N-3N or 1N-2N;3N, I'm leading the CQ.

 

The Hx rates to blow up the H suit way too often.

Ok if you don't like the example, but you are totally missing the point, or at least skirting around it. When the opponents have an invitational auction that shows they have nothing extra, you usually want to make a safe lead and give nothing away. When the opponents have an auction that indicates extra values, you usually want to make an aggressive lead as your only hope of setting them before they have enough tricks.

 

If they blast 3NT on both types of hands, you can't lead as accurately.

[Stephen Tu]

BTW, this approach is NOT recommended for matchpoints. While you will steal some games, and pick up big chunks of mps when you do, you will overbid too many hands to make it a matchpoint approach.

 

I don't think this is true. One just blasts game more conservatively at MP to account for the odds being offered. Invites should be pretty rare anyway, over a std NT range the optimal invite range is something like 1 point wide at most. And most of this time you end up in the same contract. Certainly you will end up anti-field occasionally, but I definitely like my MP expectation when I am in 1nt and the field is in 2nt (freeroll, hope 2nt goes down because of bad breaks/losing finesses), or when in 3nt after 1nt-3nt rather than the field's 1nt-2nt-3nt or 1nt-2c-2?-2nt-3nt. I think anti-field is good if your expectation is positive, easier to win events that way. & this approach won't leave you in an anti-field contract very often anyway.

 

You just have to make sure the bid you gain gets you more MP than the occasional loss on your inv hands, if indeed you are losing anything in the net.

[bid_em_up]

.....but I definitely like my MP expectation when I am in 1nt and the field is in 2nt .....

 

 

Invites should be pretty rare anyway, over a std NT range the optimal invite range is something like 1 point wide at most.  And most of this time you end up in the same contract.

Herein lies the crux of what isnt being addressed. It is one point. A Jack for cryin out loud. Combine that with what you gain by not inviting on bad 8 counts (the field is in 2N going down) along with what you gain by bidding 3N directly on good 8 counts without giving away any information whatsoever, and you are waaaaaaaaaaaaaaaaaaaayyyyyyyyyyy ahead.

 

Additionally, given that according to foo's own figures:

 

15+8=44%

16+8=33%

17+8=23%

 

you will hold the values for game 56% of the time at a minimum and what you lack the other 44% will more than be made up from the lack of information passed in an invitational auction. It isnt a matter of blasting, contempt bridge, desperation, wanting defensive errors, or whatever else you choose to call it.

 

It is a matter of experience. It works, and it works well. It works at any level including the highest caliber. Try it and see.

 

Since the opponents do not know if they need to be passive or aggressive on 1N-3N auction, they will get it wrong more often than they get it right, which is more than can be said for any invitational sequence you care to construct. The invitational sequence is also at a big DISADVANTAGE when opener accepts the invitation, as now defenders know that dummy isnt that strong. It is also at the same disadvantage (or worse) when the invitation isnt accepted and 2N is passed out.

 

This is simply a fact of bridge, that even you appear to recognize.

 

Contrary to what is being argued, most expert theory that I am aware of these days is that it only requires 24 hcp for 3N to make. And that does not have to be 12 opposite 12, 16 opposite a good 8 works just fine. Any 25 pt NT game should be bid.

 

As I pointed out earlier, you should be able to tell from your hand when it is correct to bid 3N and when it isnt when holding an 8 count.

 

K10x 107x KQ1072 94, all day. (I would expect this to make > 85% of the time)

 

xx xx KQ97 QJ1042, all day (I would expect this to make > 65% of the time).

 

Q32 Q652 J32 QJ3, never (I would expect this to make 3N about < 15% of the time).

 

Kxx Qxxx Kxx xxx, no again (see above).

 

Once you learn to evaluate these hands properly, the odds of 3N actually going down DECREASE dramatically (I dont even remember the last time one actually went down, but I'm sure its happened in the last, umm, 6 months, year maybe??), while the odds of actually making it INCREASE as well (happens every day). Even when on 23 count.

 

Inviting with 9-10 is absolute and utter nonsense. The odds only improve. Bid the damn darn game already. You will be glad you did.

[david_c]

Contrary to what is being argued, most expert theory that I am aware of these days is that it only requires 24 hcp for 3N to make.

I wonder what it is exactly that you're saying here. If partner opens 1NT (15-17) and you have a random 9 HCP, then I believe it's right to bid game. However, if you bid 3NT and opener turns up with a 15 HCP minimum, then your expectation is now worse than it would have been if you'd passed 1NT (unless you're vulnerable at IMPs, in which case 1NT and 3NT are very close). 24 HCP does not make game good in this sense.

[foo]

Actually, 8 HCP + a 5card suit is a reasonable invite opposite a =16-18= NT.

 

The average 8 HCP w/ a 5card suit should not invite opposite 1N= 15-17 or weaker.

 

...I'll see if I can get the numbers to prove that 24 HCP split 15+9, 16+8, or 17+7 doth not usually a good 3N make.

[mikestar]

Doesn't this debate depend on what "15-17" really means to the partnership? If you liberally downgrade 15's and upgrade 17's then your effective range is 15 1/2 to 16 1/2 and there is no point in inviting. On the other hand, if you liberally upgrade 14's and downgrade 18's your effective range is 14 1/2 to 17 1/2 and invitations seem resonable in spite of the downside. Since most partnerships are some where between these extremes, it is a highly debatable question and niether side should be questioning the others rationality.

 

It is no question at all for those of us who use nominal 4-point ranges, for example 12-15 in Precision, allowing all our suit openings to be unbalanced. We need 2NT invitational or its equivalent. (I rather like 2♠ range ask.) The 4 point range loses a bit but there are compensating gains in the suit opening sequences--in particular, artifical or semi-artifical 1NT and 2NT rebids by opener can clarify many otherwise difficult sequences.

[mike777]

meckwell said it all, downgrade almost never, upgrade almost always. IF you accept on 23 hcp then the game seems to slow down and bidding seems easier. The game on every hand theory seems to make these decisions easier,yes, game on every hand.

[bid_em_up]

Contrary to what is being argued, most expert theory that I am aware of these days is that it only requires 24 hcp for 3N to make.

I wonder what it is exactly that you're saying here. If partner opens 1NT (15-17) and you have a random 9 HCP, then I believe it's right to bid game. However, if you bid 3NT and opener turns up with a 15 HCP minimum, then your expectation is now worse than it would have been if you'd passed 1NT (unless you're vulnerable at IMPs, in which case 1NT and 3NT are very close). 24 HCP does not make game good in this sense.

First of all, you must understand that I am not talking about casual or pick-up partnerships, but instead regular partnerships where you are aware of the others strengths, weaknesses and tendencies. Is partner a strong declarer? Is he a weak declarer? Is he the kind of partner who always accepts an invite no matter what he has? Is he prone to opening 14 counts 1N? All of these are, of course, factors in what I am saying. Given that I try to play with competent (at least, in my opinion) players, I expect partner to be reasonable about these things.

 

On the off chance that partner is on a bad 15 count, then yes, I am worse off. But if partner has enough sense not to open A53 A764 A32 K84 as 1N, (since it is better either for suit play, or if in NT, to have the lead going to the other hand), then I (usually) dont have much to worry about. If 3N goes down, it goes down.....but then again, I see 27/28 point NT hands go down as well.

 

Whenever partner is on a normal 15 count (a hand that actually has tenaces), then opposite any 9, 3N will usually have reasonable play (read as more than 50%). As long as partner is a competent declarer, there isnt much to worry about.

 

This doesnt even begin to include the mental energy the partnership saves over the long term by not agonizing over these decisions.

[awm]

I'm starting to lose track of the many boards partner and I have lost imps on when we avoided a no-play game only to find that the game was bid and made at the other table. Trust me, there have been a lot of such boards. Perhaps we need better teammates... but I suspect this is more a sign that defense can be a lot harder than declarer play.

[ArcLight]

>Contrary to what is being argued, most expert theory that I am aware of these days is that it only requires 24 hcp for 3N to make. And that does not have to be 12 opposite 12, 16 opposite a good 8 works just fine.

 

I asked Marty Bergen about this and he disagreed.

 

About responding to 1NT, he said:

 

pass 1NT w 8

bid 2NT w 9

bid 3NT w 10

[bid_em_up]

I asked Marty Bergen about this and he disagreed.

Unfortunately, if I were to respond to this the way I would like to, I probably could be held liable for slander, and I really cant afford it......

 

I knew there was a reason my profile says "NO BERGEN", I just couldnt remember why. Thanks for reminding me.

 

ROFLMAOWPIMP

[ArcLight]

>Unfortunately, if I were to respond to this the way I would like to, I probably could be held liable for slander, and I really cant afford it......

 

>I knew there was a reason my profile says "NO BERGEN", I just couldnt remember why. Thanks for reminding me.

 

 

I know Mike Lawrence is not a fan of Bergen raises, or using the LAW at high levels.

 

But you seem to be implying that Marty Bergen is not a good bidder (not talking about preempts) or player. Considering that he is a multiple national champion, that would imply he is a strong player. Another way to look at it is to ask "Is Larry Cohen a strong player"? I think the answer is yes. And why would Cohen have played with Marty Bergen for all those years if Bergen was not around his level (or at least in the ball park, even if not quite as good).

[jdonn]

>Unfortunately, if I were to respond to this the way I would like to, I probably could be held liable for slander, and I really cant afford it......

 

>I knew there was a reason my profile says "NO BERGEN", I just couldnt remember why. Thanks for reminding me.

 

 

I know Mike Lawrence is not a fan of Bergen raises, or using the LAW at high levels.

 

But you seem to be implying that Marty Bergen is not a good bidder (not talking about preempts)  or player.  Considering that he is a multiple national champion, that would imply he is a strong player.  Another way to look at it is to ask "Is Larry Cohen a strong player"?  I think the answer is yes.  And why would Cohen have played with Marty Bergen for all those years if Bergen was not around his level (or at least in the ball park, even if not quite as good).

Not that he wasn't a good player, but he is hardly the first person I would ask about this kind of theoretical point. In any case if he is so amazing, why does he not play in big tournaments any more? (perhaps there is actually a good reason, I really don't know, but my guess would be the best players just don't want to play with him any more)

 

Also let it be clear, the strategy he mentions of passing with 8 always or almost always is strictly a matchpoint strategy (not surprising coming from him). Lets say, hypothetically, your trick expectation with 8 opposite a strong notrump is as follows, and from the perspective of always bidding 3NT or passing but never inviting (mostly to simplify the analysis):

 

9+: 40%

8-: 60%

 

At matchpoints you would want to pass with your 8 because you will go down by bidding game, and thus ruin your score, over half the time. At imps you would want to bid 3NT since the gain for bidding game when it makes is 6 or 10, but the loss for going down in game instead of making 1NT+1 is -5 or -6, so you don't need to make the majority of the time to be gaining.

 

The actual analysis is more complicated when done thoroughly and without my simplifying assumptions, but it follows the same logic. My point is that these discussions in general don't pertain to matchpoints in particular, but I strongly suspect his advice does.

[foo]

Lets say, hypothetically, your trick expectation with 8 (presumably containing a 5card suit -foo) opposite a strong notrump (presumably 15-17 -foo) is as follows, and from the perspective of always bidding 3NT or passing but never inviting (mostly to simplify the analysis):

 

9+: 40%

8-: 60%

 

At matchpoints you would want to pass with your 8 because you will go down by bidding game, and thus ruin your score, over half the time. At imps you would want to bid 3NT since the gain for bidding game when it makes is 6 or 10, but the loss for going down in game instead of making 1NT+1 is -5 or -6, so you don't need to make the majority of the time to be gaining.

Unfortunately for the "blast or pass" POV, if one makes the default assumptions about 8 opposite 1N=15-17, the conclusion you state is dangerously wrong.

 

The reality is more like:

9+: ~13%

8-: ~87%

Since you need 25+ and a fit to have a positive expectation of making 3N or 4M.

 

The numbers above are only approximate, but the situation is so squewed that more thorough analysis is not going to change the odds enough to change the conclusion those odds indicate.

 

At IMPs, a >= 5/11 White game is a good game.

At IMPs, a >= 3/8 Red Game is a good game.

Both of the above assume you are never being X'ed.

At IMPS, assuming you make or go -1 you have to make >= 2/5 of your X'ed games.

At MP's or BAM, you want to always be bidding par or absolute par.

 

Even if the odds of 9+ were 2x higher (and that is extremely unlikely), you should not invite in this situation. If you are playing the odds, then the average 8 HCP containing a 5 card suit Responder should never invite opposite the average 1N= 15-17 opening.

Never. At any colors or form of scoring.

 

Doing so means either

a= you don't believe the math or

b= you don't respect the opponents or

c= you are desperate or

d= some combination of the above

[awm]

Where do these percentages to make a game with 8 opposite 15-17 come from?

 

Foo said: "9+ tricks 13% and 8- tricks 87%"

Josh said: "9+ tricks 40% and 8- tricks 60%"

 

Do either of these have any basis in fact or are people totally making them up?

 

It seems like there are three ways one can come across "real" numbers and each of them has some issues:

 

(1) Double dummy analysis. But the problem is, especially on an uninformative auction like 1N-3N leads are far from double-dummy. At the highest levels declarer play and defense are pretty good for the most part, but opening lead is still not an exact science. So I would expect declarer to do a little better than double dummy projections on 1N-3N auctions.

 

(2) Hand browsing based on BBO results. This takes the bad leads into account, but the level of play is not necessarily very high and you will get many results of people who are "trying to push bad players around" with varying degrees of success. This is not the best way to measure this approach in high-level play.

 

(3) Hand browsing from high level events. However, I strongly suspect that while good players may blast 3NT with SOME 8-counts, they will not do so (even at IMPs) with ALL 8-counts. Sampling these sorts of hands will tend to make blasting look better, because the hands where the blast actually occurred at some top flight tables will be 8-counts with five card suits and a bunch of tens.

 

Anyways, everyone knows that bidding slightly less than 50% games is good at imps and bad at mps. The relevent issues here are:

 

Suppose I have 8 points (or 9 points, or whatever you consider an invite). Are my chances of making opposite 17 substantially better than opposite 15? How much better?

 

Suppose I have the choice of blasting 3NT (1N-3N) or bidding stayman followed by an invite. The defense is obviously better placed on the second sequence (more likely to find a double if the contract is down, more likely to make a good lead, better able to count declarer's hand early on the defense). How many tricks is this worth on average? How much does it change my chances of making 3NT? Is trading the extra information for the knowledge that I will be in game opposite 17 (or good 16s) and not 15 a worthwhile exchange?

[bid_em_up]

I suspect that Marty no longer plays competively because it is more profitable for him to do otherwise. :D

 

I will not claim that he isnt/wasnt a good card player, but will instead just say that I am not a fan of the man, or his methods/theories. I agree with Josh that he is not the first person I would run and ask for advice regarding this kind of discussion (or any other discussion, for that matter, unless of course we happened to be discussing suicidal preempts). :blink:

[jdonn]

Where do these percentages to make a game with 8 opposite 15-17 come from?

 

Foo said: "9+ tricks 13% and 8- tricks 87%"

Josh said: "9+ tricks 40% and 8- tricks 60%"

He made them up and stated them as something like fact (and he is outrageously wrong). I clearly stated that mine were just a hypothetical example in order to demonstrate an analysis that Bergen's advice pertains to matchpoints. In any case, he is forgetting that you will actually make more tricks (and a significant amount more, it's a major factor) by blasting 3NT with these hands as opposed to inviting since

- they can't lead as accurately.

- they learn nothing about opener's hand compared to if you invite and opener accepts.

 

I even have an example from yesterday to prove my point! Justin was scheduled to play in the Cayne match but he had something come up and asked me to fill in for him, and I found myself in Garozzo's seat (there is something I never thought I'd say). One hand was as follows:

 

[hv=d=n&v=e&n=sq96hk973dak98ca8&w=sak7ha864d75c7542&e=st854hqjdt32cjt96&s=sj32ht52dqj64ckq3]399|300|Scoring: IMP[/hv]

 

Yes I realize responder has 9 not 8, but it's a pretty nondescript 9 that is worth more like 8 anyway and still proves the same point. Certainly you couldn't say it has a source of tricks.

 

Garozzo and I were east. At my table the auction went 1NT - 2NT - 3NT. Knowing even with my awful collection that the opponents had no values to spare, I made the safe club lead. Declarer (Versace, not the worst choice for best player in the world today!) won and despite having numerous winning lines, ran the heart ten into me and later hooked another heart into me, and thus went down two tricks.

 

At Garozzo's table the auction went 1NT - 3NT. Garozzo (not the worst choice for the best player in history!!) had no idea if the opponents had values to spare or not, and thus tried the riskier heart lead, letting the contract make. Blasting 3NT was worth two full tricks because the opponents, some of the world's best players in this case, know less about your hands, and thus make worse leads.

 

I'm not actually suggesting you blast 3NT every time you hold 8. But I completely agree with not inviting and instead blasting every time you hold an invitation, which to me is a good 8 or any 9. This isn't an abnormal example, this sort of result comes from it all the time.

[foo]

Where do these percentages to make a game with 8 opposite 15-17 come from?

 

Foo said: "9+ tricks 13% and 8- tricks 87%"

Josh said: "9+ tricks 40% and 8- tricks 60%"

 

Do either of these have any basis in fact or are people totally making them up?

Two ways,

 

1= Simulate. generate 100, or 1000, or etc boards where Responder has 8 average HCP w/ a 5card suit and Opener has 15-17 average HCP of the shapes you would Open IN= 15-17 (first pass would be 4333, 4432, 5m332, 5H332, some =2245, some =2425, some =2452)

 

2= Go ask top flight experts (and yes, Grant Baze, Marty Bergen, Larry Cohen would be among those who qualify)

They basically have a database in their heads of millions of boards they've encountered over the years.

 

As I have explicitly stated previously, I have =no= confidence that my casual analysis (which did not involve an accurate simulation) has generated accurate percentages.

 

OTOH, both the analysis and the opinions of people who have that database I mentioned in their head yield the same conclusion that the average 1N= 15-17 opposite the average 8 HCP containing a 5card suit does not make 3N or 4M often enough to be in it under almost all circumstances.

 

Danny Kleinman in _The NoTrump Zone_ not only mentions that average 8 HCP hands with a 5card suit should not invite opposite 1N= 15-17, he also mentions that he got the error on this point in the 5th ed of the Encyclopedia changed for the 6th ed.

 

Josh is doing me a disservice if he thinks I would "make up" such conclusions.

[jdonn]

I didn't say you made up your conclusions, I said you made up your data. And you seem to have admitted this. Which is fine, as long as we are all clear that it's opinion or hypothetical (as mine was), not fact.

 

You have, as usual, quoted me on something I never said.

[foo]

I didn't say you made up your conclusions, I said you made up your data. And you seem to have admitted this. Which is fine, as long as we are all clear that it's opinion or hypothetical (as mine was), not fact.

 

You have, as usual, quoted me on something I never said.

Apologies for inexactness.

 

"Josh is doing me a disservice if he thinks I would "make up" such data or conclusions."

 

My disclaimer about the percentages being accurate is based on the fact that I did not do accurate conditional probability calculations nor a rigorous simulation to get the percentages I did. I used nonconditional probabilities, and I know those are wrong.

 

However, the correction by doing it rigorously would not change the results significantly enough to change the conclusions.

 

Nor did I quote you.

 

I do not "make up" stuff I post, nor do I misquote people.

[jdonn]

EDIT: Decided some things just aren't worth the effort, so deleted my list of statements that were 'made up'...

[hrothgar]

Not that he wasn't a good player, but he is hardly the first person I would ask about this kind of theoretical point. In any case if he is so amazing, why does he not play in big tournaments any more? (perhaps there is actually a good reason, I really don't know, but my guess would be the best players just don't want to play with him any more)

 

Also let it be clear, the strategy he mentions of passing with 8 always or almost always is strictly a matchpoint strategy (not surprising coming from him).

Couple comments regarding Marty Bergen:

 

1. Bergen is (was?) a top theorist. A lot of the ideas that he developed and promoted represented very significant advancements compared to the standard methods of the day. I'm not sure that all the ideas that he promoted have stood the test of time, however, a lot of his philosophies have held up nicely.

 

2. These days Bergen isn't marketing himself as a "theorist". I think that he is deliberately dumbing down the complexity of the methods that he promotes in order to appeal to a broader audience. If you're trying to make money, this makes a lot of sense. (Better Bidding with Bergen v1 + 2 have been out for a hell of a lot longer than "Marty Sez". I'd be willing to bet dollars to donuts that Marty Sez has outsold BBwB by quite a lot.) However, this also means that you need to be quite careful regarding the advice that he gives...

[foo]

EDIT: Decided some things just aren't worth the effort, so deleted my list of statements that were 'made up'...

Since I seem to have been accused of something and on trial for it, here we go...

 

RED

10 -6

20 -12

20 -18

30 -24

30 -30 10*3 6*5 => 3/8

 

WHITE

6 -5

12 -10

18 -15

24 -20

30 -25

30 -30 6*5 5*6 => 5/11

 

X'ed RED

12 -8

24 -16

24 -24 12*2 8*3 => 2/5

 

X'ed WHITE

9 -6

18 -12

18 -18 9*2 6*3 => 2/5

 

1st column is Imps gained by bidding Game and making it when the other other table takes the same number of tricks in a partscore.

2nd column is Imps lost by bidding Game and going -1 when the other table plays a making partscore.

The 2nd two sets of figures involve the same calculations for X'ed contracts.

The result tells you how how often you have to make what you bid to at least break even playing IMPs.

 

In the Encyclopedia, the apriori odds of being dealt

15HCP is 44237/10^6

16HCP is 33109/10^6

17HCP is 23617/10^6

 

For a total of 100,963/10^6

 

The 1st simplification assumed is that the odds of any specific shape in this range is not affected by the HCP involved. This is incorrect if you want to get the numbers exactly right.

 

44247/100963= ~44%

33109/100963= ~33%

23617/100963= ~23%

 

The 2nd simplification is that Responder's hand is conditional on Opener's hand since Responder's hand can only be made from cards that are not already in Opener's hand.

I ignored this as well in my calculations for simplicity.

 

So, as I said these numbers are not exact. But they are close enough to exact and the decision is clear cut enough to give a valid conclusion.

If the odds were close enough to put the issue into doubt, then the more rigorous calculations would have to be made to make a justifiable conclusion.

 

OTOH, decisions that close in Bridge are often more strongly affected by non mathematical criteria like the skill and the emotional state of the people involved.