Hello Mr Wolff

The opening lead should be Club Ace/King and not Club Jack. The card play of ruffing fourth club small in dummy is fantastic.

best regards

Shantanu Rastogi

Hi Shantanu,

Apologies for the unexplainable jack of clubs, said, by the hand diagram, to have been led.

Yes, since this hand is all about what can be called, double dummy play, it can only be justified by citing “table presence”.

No doubt, West, whoever he happened to be,
either learned to hold his hand up or, at the very least not to appear so interested in the bidding as to give his trump holding away (especially to such a great player).

Balicki first divined out where the cards were, and then he did what he needed to do to score his contract up. That is what top level players do, so all an opponent can counter is to try and give away as little as possible by one’s table action.

About the thought-provoking BWTA item:
Your sage advice surprised me (middling intermediate Club player) at first. But a rough calculation suggests opener is in fact likely to have four Spades more often than not. Why? Well, assuming Opener has at least two for a known combined holding of at least six, there are seven more on the loose. Over the long run. the remaining seven Spades should divide evenly amongst the other three hands; i.e. 2 1/3 in each hand; so on average Opener will have at least 4 1/3 Spades.
Is my rough estimate correct? Is this why, as you said “it feels right to use Stayman”?
If so, seems your advice would apply not only at IMPs but also at matchpoint Pairs.

Clarksburg –

Interesting math argument. Possibly, one could add to it that North has more of the missing 9 spade HCPs than E-W, as North has 20-21 of the missing 38 HCP, while E-W have only 17-18.

The real answer is closer to 35% according to Pavlicek’s companion hand calculator.
http://www.rpbridge.net/cgi-bin/xch1.pl
f<5 (how freaky are you willing to get on a 2C-2D-2N sequence?), s<6, h3
Considering that making 3NT without a fit is plausible but not likely, giving it a shot seems reasonable but it is close.

h3? Not sure where that came from. I meant to say:
s<6 h1 h>1 c>0 d>0 HCP 22-24
Query s>3

If you categorically disallow singletons on a 2C-2D-2N sequence the number drops a couple of percent. Perhaps this is one to pass in Matchpoints and press on in IMPs.

OK the site is definitely doing something funky with my GT/LT symbols. Hopefully you get the gist.

Hi Clarksburg,

While numeracy is somewhat in a small way related to mathematics, it is directly related to being or become a whiz of a bridge player.

Instead of higher mathematics (the expected knowledge of a real mathematician), instead, the game of bridge favors a person whose mind is constantly thinking about the application of everything numerical, e.g the time of day to a businessman or woman, but instead to the playing of bridge, constantly adding (and subtracting) the number 13 (number of cards, around the table) in a suit, number of tricks necessary for success, distribution of the 3 unseen hands as well as the first thought when one’s own hand is picked up and inspected.

It also applies in sports when in American football, the quarterback always knows exactly how many yards till the next first down, how many seconds left on the play clock, how many time outs left in the half, when in the lead, how much time may be left for the opposition to score, also wide receivers where they need to get to before the next first down and the whole defensive team trying to insure against the opposite, allowing the opponents an easy first down, particularly so on their 3rd down when the ball is located in the far side of the field, but also 4th down when possible field goals are in the air or the ability to risk not having to punt on 4th down.

In basketball the shot clock is involved on every possession both for the offense and the defense, but NOT in baseball, which is not a timed event.

The above represents numeracy and its important applications, nothing highly analytical but ultra important, especially in the game we love.

Others have presented what I think are valid answers to your thought assumptions about divisions of cards. I can only add that since the sequence given usually shows a HCP total of 22-24, not the 2NT opening of 20-21.

In addition while playing real bridge (rubber or IMPs) an extra undertrick is usually not to be worried about and sometimes the opponents opening lead helps declarer, giving the bidding of close games an unseen advantage.

Another thought, at least to me, is real and that is simply a usual relaxing exercise to defend a part score while playing an important bridge match, but not so defending a game or higher. This leads to being a tough opponent for your side when you constantly are bidding close games making your opponents life as difficult as such bidding can do.

All in all, keeping in mind that bridge is no where near an exact science, it then follows that the more pressure a partnership can put on their worthy opponents the more chance they have to win that particular event.

And all the above, just in case partner does not have 4 spades along with you, usually placing your partnership hands about where is necessary to have approximately a 50-50 chance at a spade game.

Hi Jim2,

Your thought about, because of the known division of HCP’s perhaps the strong hand is more likely to have the A,K,Q than are the other players, will have to be thought about and accurately analyzed before I will comment, but in any event thanks for your effort.

Hi Slar,

Thanks for your contribution. My top of the head immediate thought would make 35% absolutely the highest percentage likely in finding a 4 card spade holding with the good hand, mainly because 4 of the possible 13 spades are already accounted for of the 52 card deal. However I, still favor a Stayman inquiry hoping for either lightening to strike or optimistically something good to happen.

Different reasons for different bridge players, but leading to the same conclusion.

BTW, Richard Pavlicek has my complete respect since what he has always brought to the table, a great bridge game, complete with a highly ethical and positive manner toward the game itself without, to my knowledge any minuses. A hearty recommendation, but one I feel totally secure in offering.

The spade honor probabilities are even better with the 22-24 count, letting E-W have only 14 – 16.

As for spades in general, Clarksburg’s point that North should have at least two certainly is valid. South has four, so seven remain. North has 11 open slots and E-W have 26 open slots for a total of 37 slots into which the seven spades can be dealt. That seems using simple math only that the expected value for North spade length would be 2 + 77/37 or about four cards.

The math is likely more complicated than the above because North has so many HCP and most of the HCP unaccounted for are NOT spades. Figure, 38 missing, but only 9 are in spades. That is, North must have many slots filled with non-spade honors.

I’m stopping here. I’ve already had too many ibuprofen this week!

I’ve decided that if I was playing matchpoints, I’d bid 3C, pass a 3D response, and raise 3H to 3NT. With a maximum of 4 hearts, a NT contract could run into all sorts of problems. I think partner would be more likely to go 3D= or even 3D+1 than 3N=.

Thanks to all. This was educational and fun.
About estimating Opener’s expected Spade length, my simple back-of-an-envelope estimate was 4.33; Jim2’s estimate was “about four cards” (Actually 2 + 77/37 = 4.08).
Just purely out of curiosity I’m going to nail this down with the help of a probability and statistics expert (a priori, Opener’s Spade length is at least 2 and up to 5 but can’t be 6 or 7; what are the probabilities of the holding being 3,4 and 5?
Back to Earth, for practical purposes what I’ve learned, from Mr. Wolff’s sage advice, combined with the simple-arithmetic estimates is that:
1) Opener’s Spade holding will likely be longer than many would intuitively expect
2) In future I’ll be bolder with similar responder holdings; for me, a brand new insight.
A good day on the Blog!

Clarksburg –

If accuracy is the intent, the HCP element would need to be addressed. That is, most of the “missing” spades are NOT point cards and the North hand must include at least 22 HCP. Thus, many non-spade point cards must be in the North hand.

Another way to put it would be that the 11 open slots in the North hand do NOT have a true random chance of being a spade, since most of the missing spades are spot cards and each card in the North hand must be – on average – almost 2 high card points.

Bobby, I am friendly wth a Canadian genie named John who upgraded your Club Jack to the Club King as the opening lead. Amazing what the right connections can do!!

For what it’s worth…a further note on the estimate of how many Spades to expect in your no-trumper-Partner’s hand when you hold four, assuming Opener has at least 2. May be of interest to SLAR and Jim2.
From the most-recent Bridge Encyclopedia, there’s a Table of Distribution of Cards in Three Hidden Hands (Table 3, page 577), Using the data, and throwing out the not-applicable cases where Partner has one, six or seven of the missing seven, I found that the percentage for Opener holding four or five is about 37/38 percent… very close to Mr. Wolff’s instinct and what SLAR found using Pavlicek’s calculator.
My initial rough estimate, assuming the missing seven cards would tend to divide equally amongst the three hands, was that Opener would be likely to hold 2 + 7/3 = 4.33 as a many-hands average. Why was this simplistic estimate so wrong? No doubt because it is essentially analogous to expecting four missing cards to normally divide 2-2 in the two opponent hands! Duh!

Hi Clarksburg,

First, your (and others) interest in the arithmetical feature of our game bodes well
for the likelihood of your ascendency up the ladder to however good you intend to get.

Second, it is probably wrong to expect the statistics of bridge to get a free pass away from mathematical probabilities which have long since ruled our planet. The law of averages, that immutable phenomena, has seen fit, especially in my now home city of Las Vegas, to create out of sight expensive structures to dot our skyline with constant reminders of what a relative small edge in gambling will reek.

With that as a backdrop, and with bridge as a sample, it seems logical that the more of a suit which is in one hand (including both honors and small cards) the fewer of which, when dealing with a finite number (13), to be located in any other one hand among the other 3.

Yes, there is some logic out there, as well as perhaps voodoo reasoning, to suggest that when partner has specifically 22-24 HCPs (unless he has upgraded with a good 5 carder, probably not a major, which would materially downgrade that hope) he is more likely to have honor cards than others (and we have only one Jack in the key suit, but only one other honor card, also a Jack), but how that sways the percentage number in favor of, in this case spades, I’ll leave it up to our elite group and other mathematicians, to educate and thus convince me.

Mr. Wolff,
Many thanks for checking in again on this one.
When I referred initially to the BWTA item being “thought-provoking”, that went (unwritten) beyond the single question of how many Spades the No Trumper would be likely to hold.
Things like: how risky is the 3NT game with a lopsided 24 / 26 HCP? Is the likelihood of finding a 4-4 Spade fit enough to justify revealing part of our shape to the opponents? Lacking a Spade fit, can I fall back on the expectation that Opener will probably have a two-out-of-three combination of an adequate Heart stop, and fits with my minors? etc.
A year or two ago, I would never have been thinking in terms of such aspects of “how to compete”; it is being learned by visiting this Blog every day.
Thanks

Hi Clarksburg,

This episode of “True Confessions” is not the least bit surprising. All you are saying is what and how so many very intelligent people have approached becoming a real bridge player, with much healthy competition and logical thinking to match, straight ahead.

My advice to you is play as much as you feel like among your friends, business acquaintances, and, of course, family, if appropriate, but at the same time be serious about learning more and more about the majesties inherent within the game itself.

Bridge will never let a true lover down, although at times you’ll question whether it is worth it, but never will it disappoint you in its challenges.

My guess is that your desire is firm, your temperament conducive to learn as much as you can and, at the speed which makes sense.

Those attributes usually fit in well with what bridge has to offer, since between you and your favorite partner, (still possibly to come) it will be a fun journey to get there from here.

Although it is better to remain polite to all who try and help, it is better to just write down what seems important to ask and between the fine players (not to mention, very intelligent upstanding, appreciative bridge lovers on this site to chime in), you’ll be headed in the right direction to make a big splash any given year that fate allows you to.

Not the easiest of trips, but I can vouch for it being well worth it, and maybe, as Humphrey Bogart said so many years ago, “This may be the beginning of a beautiful friendship”.

Good luck to you in however you decide to stay in touch and, at the same time, advance through the bridge stages, directly ahead of you.