Wednesday, September 29, 2010

More thoughts on defensive signaling

I was a little disappointed to get no response, comments, whatever on my earlier contribution to defensive signaling: Show and Tell – More on Defensive Strategy.  Indeed the only reaction I got was from my own favorite partner who thought my idea was all wrong.

Yet, we had just suffered a bad result where, if we had both been following my ideas, we might have averted disaster.  The scene was a pickup game against the GIBs: this was the hand.  The opponents were in 2C doubled after my rather pushy negative double was left in.  It turns out that they can always make 2C but there was just a chance that maybe we could get a heart ruff provided the HJ was led at trick 3.  I led my trump to the 9, T and Q.  At trick 2 declarer played a small club to partner's J on which my discard was the S9.  According to my "show and tell" ideas, this card was purely informative (show in this case because there was no apparent defensive urgency).  After all, I had to pitch something and I certainly had plenty spades to spare.  Partner thought it was a more active signal (a "command") to switch to spades.  Nothing really bad happened: according to GIB, we were never setting this contract.  But partner was convinced that a H switch would have got us a ruff (and the setting trick). 

So, what is it really that distinguishes between show and tell.  In my previous blog I suggested it was all about distribution and level.  The more distribution and/or higher level, the more urgency exists (and therefore telling is most effective). 

But now, I'm thinking perhaps it has more to do with the dummy.  Assuming that dummy is where the ruffs, if any, are going to occur (not always the case after a transfer or in the case of a dummy reversal), the dummy pretty much dictates the type of hand.  If dummy has a good long suit with entries, or will be able to do some ruffing (bearing in mind that declarer may be able to throw dummy's losers on his own good suit and then ruff in the now short suit) then "tell" signals should prevail.  The level of urgency has been increased by an "active" dummy.

Either way, in the hand in question, dummy was pretty much rubbish and would have required a few thousand volts to make it in any way active.  So, signaling should be to show assets rather than directing the defense.

Now, does anyone have any comments?  If I'm oversimplifying something, then let me hear it!

Friday, September 24, 2010

Responding 1NT to a minor-suit opening

Generally speaking, we have so much confidence in our notrump hand evaluation that we are able to limit the ranges shown by notrump bids quite severely. Typically, an opening NT bid shows a range of just three points, rarely four (though I've known five!). As we go higher, the NT ranges become smaller (usually 2): 18-19 typically for the 2NT rebid; 20-21 for the opening 2NT, etc.

What about responding bids? Invitational bids are often 11-12. Game responses (3NT) are often played as 13-15 (or 13-16). A wider range here is OK, because most of the time, opener will simply pass. He won't go looking for slam unless he himself has 17+ (or 16+).

The tricky part arises with the 1NT responses to 1♣ or 1. Playing a 15-17 notrump (or 16-18), you can be confident in the knowledge that, if partner has a balanced hand, it will be in the 12-14 (or 12-15) range. In which case, you can bid 1NT with 6-9 (a four-point range) knowing that there is no biddable game. When playing 15-17, you can even bid 1NT with a 10 count, and probably not miss game. You might want to do this, for example, when partner opens 1 and you aren't strong enough to bid 2 or 2♣ (and you lack a four-card major).

However, playing a weak notrump of say 12-14, opener is likely to have a balanced 15+ when he opens a minor (he might also have an unbalanced hand but that's another story). If your range for 1NT is 6-9, you will miss some games unless opener stretches to raise with, say, a good 16 or 17, which can easily put you too high if responder has a minimum. The Kaplan-Sheinwold solution is to respond 1NT with 5-8 but that requires some other adjustments. The K-S solution of course was the inverted minor suit raise, defined as showing 9+ hcp, no four-card major and at least four cards in support. Note that the inverted minor concept required a little adjustment when it became applied to the "standard" bidding structure. The truly scary bid in the K-S system is the 2♣ response to 1. Not only does it not force to game, it isn't forcing to 2NT either. In theory, according to the book, you can respond 2♣ to opener's 1 even with ♠x Kxxxxx ♣QJxxxx!

I began to ponder all this after a hand at the club this week on which my partner and I, playing 12-14 notrumps, scored a big fat zero. I held ♠AJ4 A92AJ84 ♣QJ3 and opened 1. Partner responded 1NT and I had to decide if it was possible we could be missing game. Given that I had 17 hcp, including three aces (even at notrump evaluations 4 points doesn't quite do justice to an ace), I felt it might qualify for a 2NT rebid. Given that partner was relatively short in the majors, I thought my hand looked quite fine: major-suit aces that could be held up twice and fillers in the minor suits where at least seven of partner's cards would lie. I therefore rebid 2NT and partner promptly passed.

As it turned out, partner held a decent 6-count: ♠T92 J84QT74 ♣K75, but which was tragically mirrored by my hand. The opening lead was a low club and partner set about trying to find an eighth trick. Regrettably, it couldn't be done. The K and the ♠KQ were all offside. My LHO, a grand-life-master observed that our system had caused us to overbid. I wasn't convinced. A balanced 23-count will, on average, take 7.6 tricks at notrump (according to Matthew Ginsberg). Often, declarer's advantage of seeing all his resources will push the total up to 8. I had a feeling that the problem was either the expert defense, or possibly the wrong-siding of the contract. Studying the results and the hand records later confirmed this. Only 7 tricks can be taken from whichever side declares. However, every other N/S pair had taken 8 (or even more) tricks in notrump (or 9 tricks in diamonds in one case). I don't know if every other pair had played it from the strong side (this seems unlikely) but I do know that even if I had passed 1NT and partner had made his contract, we'd still be getting a zero!

In truth, it's all about the opening lead. What do you lead from ♠653 K75395 ♣A962? I would probably lead the 3, on the grounds that if I found either A or Q in my partner's hand all would be well. I'd want to reserve my certain trick (♣A) to help cash those hearts. Not so the opening leader at our table. Any heart (or the ♣A) gives away the eighth trick, even though partner has the QT6. Any of the other 8 cards is fine. From the other side, the more "normal" opening lead, the hand is: ♠KQ87 QT6K32 ♣T84. There are only five winning cards this time, none looking particularly appetizing: 32 ♣T84.

Nevertheless, the hand prompted me to take another look at the details of the Kaplan-Sheinwold system, especially the 1NT response to 1m. Some of my partnerships have monkeyed around with this system such that we don't play it exactly as it was designed (admittedly, they too, made modifications and I think eventually stopped playing it). Yet, when you look at it, it really is an incredibly well-thought-out system.

Thursday, September 23, 2010

Gosh, what a hand!

Back in the day, there was no problem picking up a hand like ♠KQ76 KQT542AK7 ♣– and hearing RHO open 1♣.  You simply bid 2.  No problem.  But then we realized a jump overcall was much more frequent (and useful) if it showed a weak hand.  So that left a problem: what to do with a good one-suited hand (GOSH)?  To qualify as a GOSH, the hand should probably have a decent suit and 18+ hcp or a very good suit and 16+ hcp. 

I learned a simple rule from the excellent Robson and Segal book mentioned previously in this blog: if, having already doubled, you next make a new suit bid that, if you had bid it immediately would have been a jump overcall, you are showing a GOSH.  Although this bid isn't forcing on a partner with a Yarborough and a misfit, it is surely highly encouraging.

A few examples should clarify:
  • 1♣ X p 1 p 2: a GOSH with hearts (nothing to say about the other suits)
  • 1♣ X p 1NT p 2: ditto
  • 1♣ X p 1NT 2♣ 2: ditto
Note this last one.  It could be made perhaps on a good hand with hearts but not necessarily a true GOSH because partner has shown signs of life over there and RHO has bid again.  Still, I think it should be forcing, given that partner has significant values.

A raise of partner's suit can't be a GOSH, obviously (unless perhaps you double-raise).
  • 1♣ X p 1♠ 2♣ 2♠
  • 1♣ X p 1♠ p 2♠
The first one shows a non-minimum takeout double and confirms four spades and wants to compete.  The second (no competition) shows a hand that might still make game even though partner is limited to about 7 or 8 hcp.  Not necessarily a GOSH, though.

When is doubler's new suit not a GOSH?  This really needs to be discussed with your partner first.  But suppose the auction proceeds:
  • 1♣ X p 1 p 1: the classic "equal-level conversion".  You haven't raised the level of bidding but you're saying that you don't really have diamonds – you have a hand with both majors which is not suitable for a Michael's bid.  Perhaps something like ♠KJxx AQTxx xx ♣Ax or ♠AJxx AQxx xx ♣Axx.
  • 1 X p 1♠ p 2♣: you basically have a decent hand with clubs and hearts, perhaps with only two or three spades.  ♠Kxx AQJx xx ♣AQxx.  Similar to the equal-level conversion situation except that we have raised the level so it's not equal-level any more.  This one definitely needs to be discussed with partner.
I held the hand mentioned at the top the other evening at the club.   The auction proceeded 1♣ X p 1NT 2♣ 2, as described above.  Unfortunately, my partner didn't consider my bid to be forcing and he passed 2.  I made 5 for almost a bottom.  Possibly, my bid wouldn't be considered forcing by others.  But I can't quite picture the hand that would bid this way where we wouldn't want to play at least 2NT.

    Monday, September 20, 2010

    The gift box

    One of my partners likes to talk about the gift box being open.  There's no sense in being presented with a gift if you're not going to accept it.

    Here's an example from last week's instant matchpoint game.  Nobody was vulnerable and I dealt myself ♠KJT3AK6KJ4 ♣J54.  As we were playing a 12-14 notrump, I opened 1♣ and LHO bid 1♠.  Partner doubled and this was passed back to me.  I had just been handed a gift, but the box wasn't open.  I woodenly bid 1NT, partner raised to 3NT and I made 400 (the par score).  However, this did not matchpoint well, as others made four.  I played the hand assuming the overcaller had the missing high cards.  She didn't.  The overcall was based on a balanced six-count with five spades to the AQ8.  All I had to do was pass the double.  Surely, whether I can take 7 tricks in notrump (opposite a balanced six count with four hearts) or 9 tricks (opposite a 10-count), this looks like a hand to defend.  100 (versus 90) perhaps in the former case, 500 (versus 400) in the latter.  Admittedly it's a close call.  Still, I had been offered a gift but the box wasn't open.

    Let's spend a little more space thinking about the role (and importance) of gifts at the bridge table.  There are usually more ways to break something than there are to fix something.  This is the reason, for example, that most genetic mutations are short-lived: they probably cause something to work less well.  But every now and then a mutation improves survival for an organism in a specific environment and it gets retained.

    What has all this to do with bridge?  Well, there are more ways to bid/declare/defend a hand badly than there are ways to do it well.  Let's imagine that to bid and make 6♠ successfully on a particular board, there is really only one reasonable pathway.  Making a different bid at some point, or making a different play in the declaration will result in a lower score.  Some of those mistakes will result in a score of, say, 650 and some will result in 230 or -100.

    If you're one of the good players at the club, you will make your 6♠ along with two or three others.  The field will score less.  But you're unlikely to get a clear (unshared) top, unless you're a contender for a Bols Brilliancy Prize.  Other good players will do the same as you.  Occasionally, 6♠ might make an overtrick on a esoteric squeeze which will be missed even by the other good pairs.  But my experience says that this doesn't happen very often.

    But what if your opponents bid 7♠, missing the ♠A, you double and they manage to go down 1.  You've almost certainly "earned" a clear top.  See my comments below on earning bottoms - in this case, it was the opponents who thoroughly deserved their zero.

    My point is that good play can earn you good scores, but not tops.  To get tops, you need gifts.  And, of course, the "gift box" must be open.

    Unfortunately, along with gifts, there are fixes.  Fixes and gifts are the yin and yang of duplicate bridge.  It's hard to precisely define a fix, but let me try.  A fix happens when your opponents make a poor decision in the bidding or play but it turns out well for them.  Examples abound but here's the sort of thing.  You are playing two intermediate players and it's clearly their hand.  They sail past 3NT without really thinking and land in 4♣.  Perhaps they're not really familiar with the concept of fourth-suit-forcing.  All the average and good pairs bid the normal 3NT (plus a few that bid ♣).  You guessed it: 3NT and 5♣ fail on an unusually foul lie of the cards and 4♣ makes exactly.

    So every gift is potentially nullified by a corresponding fix.  In what follows, I will define the number of "gifts" as the net of gifts and fixes.

    What about bottoms?  I am confident that the converse is true.  You can quite easily generate zeroes on your own account, while fixes are unlikely to give you a clear bottom (there's usually two or three tables where the fix occurs).  An example of a self-inflicted zero?  That's easy: making a close double and then allowing them to make.

    A score over about 60% is almost certain to have benefited from (a net of) several gifts, unless you're Zia filling in at the local intermediate/novice game.  I estimate that the gift factor at your local club is about 15% (plus or minus 7.5%).  Let's say a good pair plays reasonably well and doesn't make too many silly errors.  With no net gifts let's say they will score 50%.  But if the opponents are generous, they might score 65%.  Everything depends on the gift factor.  In the Life Master Pairs, the gift factor is somewhat less, but still significant.  I'd guess something like 4% either way.

    By contrast, a score of less then 40% (the Mendoza line of duplicate bridge) is almost certain to have benefited (if that's the right word) from several own goals.

    Bridge is such a fascinating game!

    Sunday, September 19, 2010

    Poet Laureate of Bridge

    Did you know that I am the reigning Poet Laureate of bridge?  I thought not.  It hasn't been well-publicized.  But I have a certificate from the ACBL to attest to the fact.

    At the Reno tournament this year, a limerick contest was set up as the entertainment on the evening that was St. Patrick's Day (March 17th in case you come from a different planet).  Whether or not the limerick is a truly Irish form of poetry is very much open to question.  The form was popularized by the Englishman Edward Lear (1812-88).  In any case, you can learn more on Wikipedia.

    I decided to enter the contest after reading about it in the Daily Bulletin at the start of the tournament.  I got a little carried away and submitted five entries, although I admit that the first one I came up with was the best.  The judges apparently thought so too and I successfully challenged all comers to win the prize of $60 and the certificate, at least until next St. Patrick's Day.

    Here is my winning entry:

    This game of bridge is a breeze,
    I bid six notrump as a tease,
    I sure got my kicks
    When I wrapped up twelve tricks,
    Lucking into a stepping stone squeeze.

    In future blogs, I may share with you some of the others too.

    Saturday, September 18, 2010

    Hoist with his own petard

    If I were a bridge teacher, one of the lessons I would emphasize for my students is to avoid being hoist by their own petard.  Before explaining exactly what I mean by this, let me digress a little.

    A petard was an early form of small bomb or grenade.  Its etymology is fascinating, as is Shakespeare's coining, in Hamlet, of the phrase that forms the title of this piece.  You can read all about it on Wikipedia.  The essence of these forms of ordnance is that they are used at relatively close quarters, unless you have a launcher, as in an RPG.  But if you're going to use it on a nearby target, there are two essential steps: arm it; throw it.  If you fail to do the first, nothing happens.  If you fail to do the second, everything happens, but you will know nothing about it. 

    If you'll forgive a further digression, my father was in the Grenadier Guards, one of Britain's elite regiments, and spent most of World War II as a small arms and weapons instructor.  They were doing live ammunition training when one of the recruits pulled the pin from the grenade and then froze.  My dad had to grab it and chuck it or they both would have gone poof!  And I wouldn't be here writing this.  He got a mention-in-dispatches for that.

    In my bridge analogy, the act of thinking about bidding a suit on the next (or later) round is pulling the pin.  Throwing it is when, on the next round, you realize that if the suit wasn't good enough to bid before, it isn't good enough to bid now.  Being hoist by one's own petard is bidding the suit later when you know it isn't a good idea, getting doubled and going for a number.

    I discussed one example of this in one of my earliest blogs called Daytime Bridge.  Here's another which happened the other evening in the instant matchpoint game.  An opponent held ♠ J43 KQT62 T2 ♣ AJ8 and all were white.  If RHO dealt and opened 1♣ or 1, you'd probably bid 1, right?  I think so.  Maybe not everyone would bid 1 but I think most would.  What if RHO opened 1♠?  You have to bid at the two-level now if you want to get your suit in and you have three quick losers in RHO's suit (the "death" holding).  Against that, partner might have either a good hand, three hearts, or both!  In fact, you could have a game!  Nevertheless, to my mind, this is not even a close decision.  I would pass every time.  If partner has the right hand, he may well get a chance to do something.

    Now, how about this scenario?  Partner deals and passes, RHO passes and you "pull the pin" by thinking that you have a nice heart suit that you'd like to mention but you decide you don't have a good enough hand to bid 1.  LHO bids 1♠, partner passes again and RHO bids a semi-forcing 1NT.  Is there any incentive in the world that could make me bid 2 now?  A gun to my head perhaps.  Bidding 2 now is the military equivalent of forgetting to throw the damn grenade!  If the hand was not good enough to bid in third seat and now, with the opponents advertising no fit, and partner showing nothing, how could it possibly be good enough to bid as an overcall at the two level?

    The result was somewhat predictable.  The spade bidder doubled with ♠ AKT962 J75 AK8 ♣ 5 and the 1NT bidder passed with Axx.  The result was down 3 for -500.  This score wasn't even mentioned among the instant matchpoints so was scored as 0/100.  Maybe it would have been OK if the opponents were vulnerable.  They do have a game, after all, either 3NT or 4♠.  They can even make 6 from RHO's side (but only 4 from the other side).  The point is that with no fit and only 24hcp, only one pair bid and made a game, so -500 was still going to be almost a bottom.

    All the experts tell us that, if we're going to make an overcall or other tactical bid, get in and get out early.  Preferably, before the opponents have had a chance to exchange useful information.

    Is it the fault of the intermediate players when they make these bad overcalls?  No, I strongly suspect the bridge teachers.  I often hear beginning players use the expression "... only an overcall" as if the requirements for an overcall are so much less stringent than for an opening bid.  They must be getting this notion from somewhere, and I'm sure it's not in any books.  Of course many hands qualify for both and many qualify as neither.  The difference is not just a question of strength: it's a question of suit quality, offensive orientation, preemption and several other factors.  In many respects, the requirements to qualify as an overcall are a lot more exacting than they are for an opening bid!

    Thursday, September 16, 2010

    When to bid a slam

    I often hear players saying something like "if it were IMPs, I'd bid the slam" or "if it were matchpoints, I'd bid it".  In fact, Marty Bergen's September column in the Bridge Bulletin quotes people saying the former sentiment.  This reasoning doesn't directly follow from the scoring table, but I think I can understand the logic behind it.  Let's do the math.

    In theory at matchpoints, that's to say when you are playing against your peers, making any bid will be right if it gains 51% or more of the time and wrong if it gains in 49% or fewer cases.  If you make the bid and the resulting contract is on a pure finesse, then you'll break even in the long run.  Therefore, you want your slam to be better than 50% to be right.

    At IMPs, again assuming you are playing against your peers, a slam is theoretically also a 50-50 proposition.  If you're right (bidding/not bidding as appropriate), you gain 11 imps not vulnerable and 13 imps vulnerable.  If you're wrong, you lose 11 or 13 imps respectively.

    So there's no difference in the form of scoring as far as bidding slams, right?

    Well, not quite.  If you're not playing against your peers (let's say you're a good player at a daytime bridge game), you may get a good board just by making 12 tricks when the others only gather 10 or 11 tricks.  You don't need to risk going down in slam under such circumstances.  Let's say you're contemplating bidding 6NT (no good fit having been found).  Weaker players are notoriously bad at taking all their tricks in notrump contracts, so just making 12 tricks is likely to get you 8 (or 9) out of 11 points.  That's a decent result.  Thus bidding the slam risks 8 to gain only 3.  The argument is weaker when there is a good major suit fit and lots of points because many pairs are likely to bid slam and if it's there, most will make 12 tricks.

    What about at IMPs?  Going back to our hypothetical 6NT.  You will likely gain only 1 or, at most, 2 imps by your superior declarer play.  Not nearly so compelling.  Thus there's a little more incentive to actually bid the slam.  Even so, against weaker declarers, you are risking 11 (13) to gain only 10 (12).

    And what about grand slams?  At matchpoints, we theoretically need the same 50% when playing against our peers.  But again, just taking 13 tricks may be good enough against weaker players.  Especially since some of those players won't even be in a small slam and so bidding and making 6 with an overtrick is likely to be a very good score, perhaps 10 out of 11.  In other words, you will be risking 10 mps to gain 1.  Not good odds!

    The gain for bidding and making a grand at IMPs is essentially the same as for a small slam: 13 or 11 imps, depending on vulnerability.  However, the risks are greater.  If you're wrong (and the small slam is making), you are losing 17 or 14 imps depending on vulnerability.  Thus the probability you need is either 56.7% (vul) or 56% (n-v).  These are the figures when you are playing your peers.  The odds are even less in favor of bidding when you are playing a weaker team.  They might not even get to the small slam at the other table!

    In this case, by stopping in six, you were already gaining 11 or 13 imps.  The extra grand slam bonus would amount to only a net gain of 3 or 4.  The risk is admittedly slightly less now: 11 or 13, as in the case where you were deciding on slam versus game.  So, playing the weaker team, you risk 11 (or 13) to gain 3 (or 4).  Now you need cards that give you a probability of at least 78.6% (n-v) or 76.5% (vul).  That's why you shouldn't bid a grand unless you can count 13 tricks.  And why the late great Barry Crane expressly forbade his teammates to bid grand slams. 

    So, in conclusion, I suppose there are hands where, at the club, you'd bid a slam at IMPs where you wouldn't at MPs.  But at the Life Master Pairs (or equivalent), the small slam odds really are 50-50 at either form of scoring.

    Wednesday, September 15, 2010

    The Principle of Least Commitment

    Do you know all 656 of the suit combinations in the Bridge Encyclopedia?  Neither do I. Can you always visualize exactly what's out against you and evaluate every line in terms of its percentage success rate?  Neither can I.

    So begins the article that I've been working on for several years which might eventually make it into some bridge magazine if I can ever perfect it.  This is the current state of the article. It seems to me to be a valuable principle, as much so as the principle of restricted choice, to which it is related, for example.  But I've never heard anyone mention anything like it.  Am I missing something?  Is it so blindingly obvious that I'm the only person to think it worth writing down?

    I was reminded of it last night at the bridge club because there were two PLC transgressions at our table, at least that I noticed.  Here's one: you are in a 3NT contract with 24 hcp and you have the following suit to play: AQT94 in dummy opposite 65 in the closed hand.  You have the tempo and sufficient entries to both hands.  How do you play the suit to maximum advantage?  Well, you finesse the 9/T.  If the K and J are split then you are simply guessing.  If they're both guarded offside you're doomed to lose two tricks in the suit regardless.  But here's the case where it matters: KJx on your left and xxx on your right.  By finessing the T first, you pick up the entire suit.  If you finesse the Q first, you must give up a trick.  Least commitment.  As it happened, KJxx was on the left so it didn't matter but the declarer didn't give himself quite the best chance.

    Here was the second case: You're in 3S and your trump suit is 632 in the dummy and AQT874 in the closed hand.  At first sight you might say, aha, just like last time, let's finesse the T first (as the actual declarer did, losing to Jx).  But here there are only four cards out, as opposed to the six in the last example.  You should expect to be finessing once only (not twice as before).  This despite the fact that you have an extra card in the short hand with which to finesse.  In "normal" layouts of the suit (2-2 or 3-1 splits), the cards T and below are essentially irrelevant here.  Correct play is to take the obvious finesse of the Q which has a 27% chance of picking up the entire suit (essentially, you need the K onside and a 2-2 split or some other fortuitous event like singleton J offside).

    In this case, there were three losers outside the trump suit.  Our opponents had stopped in 3S where some might have been in game.  Thus, there might be something to be said for taking the safety play for five tricks.  However, as is often the case when we have no sequences of our own (here, they have none either), the "least commitment" strategy is to bang down the Ace (that takes no guesswork at all!).  Now, you increase your chance of taking 5 tricks to 83%.

    If you can offer any suggestions for my description of the PLC, I'd appreciate it.

    Wednesday, September 8, 2010

    How likely is it that NT bid has three cards in my major?

    Dave, a bridge friend of mine who lives in Colorado and works for the Rockies (I imagine him, like George on Seinfeld, discussing business strategy with the Rocky equivalent of the late Mr. Steinbrenner), recently posed me a bridge probabilities problem.  Dave was interested in the likelihood of an opening notrump bidder having 2, 3, 4 or 5 cards in responder's major

    In principle, it's a simple problem.  Let's assume that we have five hearts and therefore, after counting partner's guaranteed doubleton, there are six hearts to be distributed among the three unseen hands.  Naturally, I used a method based on the principle of Vacant Places and with the starting assumption that opener has only 5 vacant places (remember, he has two cards guaranteed in each suit) and that the unseen hands have 13 vacant places each.  Still, because there are six hearts to "deal out", it quickly led to quite a bit of complexity (if you were to examine every case, there are 3^5 = 243 different ways to deal those cards).  Since there were eight probabilities in total he was seeking (he was also interested in the situation where we have a six-card major), I decided that a little Java programming was in order.

    The results are a little surprising perhaps: the most likely holding opposite is three, with a probability of 44% or so (almost 50%!), regardless of our own length.  Another way of looking at it is that only roughly one third of the time will I be disappointed and find a doubleton in his hand opposite my own longish suit.  I also added the figures for a four-card suit in responder's hand.

    The following table shows the specific probabilities, always assuming of course that opener is "allowed" to open 1NT with a five card suit (but no longer), but is not allowed to open with any suit shorter than a doubleton:

    Partner's length:2345
    My length:

    So, now I'm well set up for doing any vacant-places calculations of any complexity.  Comments welcome.

    Are there style points for going down in a hand slowly?

    The answer to the question posed in the title is surely no.  An exception might be made for running a squeeze or throw-in because these normally need to be performed late in the hand.  If the throw-in or squeeze doesn't operate, you've usually lost nothing but at least gained some style points.

    So why do I continue to try to delay a bad result simply by playing off winners?  Here's a case in point.  I held ♠3 AK93 AKT873 ♣A9 in an IMP pairs.  A very nice hand by any yardstick.  With opponents silent, the auction proceeded: 1, 1♠, 2, 3NT.  Clearly 3NT showed enough values for game opposite a minimum reverse but otherwise a balanced hand with nothing more to say.  I tried 4, partner bid 4 and I closed the proceedings with an ambitious 6.  A club was led and dummy was reasonable, though not quite what I was hoping for: ♠AJ84 J86 Q6 ♣Q832.  Still, he had the other Ace (not perhaps as useful as a King somewhere else) and the Q of trumps.

    I tried the ♣Q without much confidence and it was covered by the K which I won with the A.  Now what?  The lead was very damaging.  I might avoid a heart loser by leading low to the J and finding the Q on my left, but a club will be cashed immediately.  What about trying for the QT on my right?  This is only a 24% shot and, needless to say, if one of the cards is wrong, my contract will go down in flames at trick 4 (after I've crossed to the Q and run the J).

    Something in the back of my mind nagged at me that it was extremely ignominious to go down as early as trick 4 so guess what I did?  I abandoned even my 24% shot and played for a miracle.  I'm not exactly sure which miracle I was hoping for (QT doubleton or somebody pitching the J and T of clubs perhaps?).  But suffice to say I went down with no style points whatsoever several tricks later.

    As it happens of course, my execrable bidding was about to be rewarded with a very fortuitous lie of the cards, except that I didn't take the finesse at trick 3 and thereafter had only one entry to dummy (the ♠A). 

    So, why am I telling you this?  Because just maybe I can get it into my thick skull that there's really no difference whether you go down at trick 4 or trick 13.  Down is down!  And a small chance is better than no chance.