A very ordinary hand

It has been said that the way to win at bridge is to make sure you get the ordinary hands right. In other words, squeezes, endplays, deceptions, coups of various sorts, etc. don't come up sufficiently often to give an advantage to the better player. But ordinary hands come up all the time.

Here's a hand from yesterday's STAC game:

I was sitting West and essentially took no part in the proceedings. Our opponents, two experts who are married (to each other) and sometimes--but not usually--play together, had the auction all to themselves. I might have opened 1C in third seat and perhaps I should have but I suspect that would have pushed them into a making 4H).

At my club, every N/S pair was in a heart part-score, mostly 2H by North but sometimes, as at our table, 3H by North and, once, 3H by South. My partner led the C4, clubs being the only safe-looking lead, although either red deuce would also be safe on this layout. Declarer ruffed out the spades, took two diamond finesses and emerged with 10 tricks pointing his way. A flat board, right?

Wrong. This was by no means a flat board. Here were the scores: 1 @ 200 (11), 6 @ 170 (7.5), 3 @ 140 (3) and 2 @110 (.5). I'll dispense with the anomalous scores of 200 and 110 and concentrate on the 170s and 140s.

At first, I couldn't see why our score was below average (3.5). We didn't put a foot wrong. How could declarer not take 10 tricks. And then I saw it: some declarers must have taken the spade finesse.

This hand of course is a perfect illustration of the (general) superiority of a 4-4 trump fit over, say, a 5-3 or 5-2 trump fit. You can usually use long cards in the long suit to discard losers from the other hand while using small trumps to ruff with, possibly ruffing out losers to establish the long suit.

But the main point here is that considering a suit, the spades in this case, in isolation may yield a different plan than considering the suit as part of a whole hand. If you were in a spade (or notrump) contract here, you would consider your play in the spade suit and opt for the 43% likelihood of the bringing in the suit with a finesse against the queen, versus the 18% chance of dropping a doubleton or singleton queen. Not even a close decision.

But here, you are in a suit contract and you have the luxury of being able to ruff a spade (we'll assume that trumps are 3-2, as here, for the sake of simplicity). The probability of dropping the queen after a ruff is: 36% for a 3-3 split, plus the same 18% chance that the queen would have dropped anyway. That's a total probability of 54%. The failure zone (46%) is made up of 32.3% for Qxxx, 12% for Qxxxx, and 1.5% for Qxxxxx.

So, again, it's not really a close decision if you know your probabilities (54% vs. 43%). Incidentally, it's a very common error to regard the finesse as a 50/50 shot. But when we can only finesse twice, as here, there will be holdings on our right that we can't pick up: half of the Qxxxx and Qxxxxx layouts we noted above, that's to say 6.75% of cases.

The conclusion is that the situation where you are missing six cards is a tricky one--and also a common one. It's worth spending some time to learn the probabilities.

Discipline vs. guessing

One thing I've noticed about experts is that they try not to guess. That doesn't mean they never guess. But they do try never to take the last guess. Is this the same thing as "discipline?"

One type of undisciplined bid is when you deliberately fudge your hand to fit a bid that you'd like to make. For example, you pick up a balanced 14 count with no special features and, just because you feel like it, or want to be declarer, you decided to open 1NT showing 15-17. Sometimes, this will work well when partner has 9 hcp and a long minor and 3NT is cold on 23 hcp. But other times, partner will invite game and the limit of the hand will be 1NT. This kind of thing is a partnership issue, and your partner will eventually become unhappy, unless your declarer play is first rate.

But there's a different kind of discipline where you are likely making the last bid for your side. Partner is probably not going to bid again, so can't really be deceived. A lot will depend on the form of scoring and the state of play, so to speak. Matchpoints vs. IMPs? Competitive situation vs. non-competitive? High-level or low-level decision? High entropy or low entropy (entropy is complementary to information)?

Here's a high-level, IMP pairs, competitive, high-entropy situation, i.e. a lot is resting on this decision:

AKJ3 KJT983 T8 9. All vulnerable.

Partner opens 1S in second seat and RHO bids 5C. That's annoying! We have no idea whether partner has a minimum or maybe is just below a 2C opener.  Well, we do have a pretty good idea that RHO has most of the high cards in clubs and we have 12 high card points. Partner can't have much more than 18 then.

Let's do some arithmetic.  What might happen if we pass? Partner will probably be passing too and we might go anywhere from +200 to +400. What about double? Assuming that partner doesn't take it out then we could score 500 to 1100. If he takes it out to 5D, we can always go back to 5S.

Can we make 5S? Assuming that we have no trump losers, we've got three losers. Surely, with his opening bid, partner can cover one of those. So, it looks like 650 is likely available to us. There might be a few pairs defending 5C, possibly doubled. Bidding 5S is probably worth about 4 to 6 IMPs over defending.

What about slam? This is where, the lack of information is really troubling. We can no longer ask for keycards so it's going to be decision time immediately.

If partner has two aces (particularly if one of them is the diamond ace--not an unreasonable expectation), we can very likely make 1430 for 13 IMPs over and above the 650 and about 14 IMPs over and above defending. In other words, just by bidding 5S we are almost locking in 5 (approx) IMPs. Bidding 6S will gain an additional 9 IMPs if it makes.

But, what if it doesn't make? We will be -100. We lose not only the 5 for grabbing the declaration but an additional 7 or 8 for going down.

To put it mathematically, we risk 13 to gain 13. An even money bet. We'd take the same bet at matchpoints.

This is how many bridge players would evaluate this choice: mentally flip a coin, likely favoring the slam decision simply because it's just more fun that way.

But the true expert will say this: "I can't find out if 6S is on, so I'll assume that it isn't and just bid 5S." A popular expression that covers this situation is "when you're fixed, stay fixed."

The Vienna Coup

Looking at the MITDL Bridge Club's web site recently, I was a little embarrassed to note that there's a link there to my blog claiming that it's updated every week. Those were the days! This is my first post for nine months!

Today I had the pleasure of playing with Harrison Luba a.k.a. The Twerp. He's currently a freshman in High School and is an incredible player already. Like most Juniors, he believes that all doubles are for takeout unless it's blindingly obvious that they're for penalties. Those of you who follow (or attempt to follow) my blog know that I have a set of very specific (although quite simple) rules on this. So, we had a couple of bad scores today (-730 and -670) due to differences of opinion about doubles. Well, I will admit that perfect--I would claim double-dummy--defense by me would have turned the second one into +200 (and 8/11 matchpoints).

We mostly make up for these setbacks with many tops of our own. Here are a couple which are entirely due to Harrison's good play.

First board. The unopposed auction is short and sweet: 2C--2D--2NT--7NT.  The lead is a small club, if I recall.

83 Q432 AQT6 AQ2

AKQJ4 AK6 J7 K95

Maybe there was some slight overbidding going on but don't worry. The play's the thing. There are an easy twelve tricks on top. The diamond finesse is a 50% shot. But, and Harrison figured this out in a couple of milliseconds: the spades will furnish three discards from dummy. That makes a Vienna Coup possible (cash DA and then pitch all of dummy's small diamonds).

But you need the same player to have the DK and the heart length. Doesn't that bring the probability down to 25%? No, that's the beauty of an automatic squeeze like the Vienna Coup, i.e. where dummy has an idle card and so doesn't have to commit a threat card before RHO plays. We can victimize either opponent this way, which means that the probability of success is back up to 50%. Indeed, the diamond King was off-side. But that player also had five hearts. Scoring up 1520 for all the matchpoints.

One other pair got to a making 7S but most were in 6NT making 6.

Two boards later. Partner's arithmetic seems to have gone off the rails a little and we end up in 4NT when everyone else will be in 6NT.

AK32 A862 J3 AQ2

QJ4 KQ7 AK85 963

The helpful lead is a small diamond which allows dummy's jack to score a trick. Now, we're up to 11 tricks. This time, the chances of making 12 tricks are basically 36% for a 3-3 heart split plus a few more percentage points for the same player having four hearts and KJT of clubs (or a very small chance of one player having a singleton club honor). Because that would allow for another Vienna Coup, either opponent will do as victim. The probability of success here is going to be something like 36% (hearts split) plus 64% x 12.5% (three specific cards in same hand as the heart length). That gives a total of 44%, not too bad actually. 

And so it proved. Harrison rectified the count at trick 2 by ducking a club to RHO's ten. He could always take the club finesse later if he wanted to. As it turned out, RHO had five hearts and the club ten. Maybe she'd have the K and J too.

This is where the beauty of a squeeze comes in. A finesse risks losing the lead, even to a stiff honor. But squeezes (mostly) don't give up the lead--you just keep playing and either the last trick comes out right or it doesn't. 

Harrison worked out one other thing. Almost everyone will be in 6NT and if the finesse of the king is on (and they receive a helpful diamond lead) they'll have 12 tricks in the bag. We basically cannot outscore those declarers. But, if the CK is indeed offside (knowing that RHO has the heart length), then we will likely outscore any pair that's not in slam and certainly all of the pairs that did bid the slam.

It's always fun and educational when I play with Harrison. I enjoy it to the max while I can!