Cold Game in Spades

Posted on December 1, 2013 by Mike

One hand at the Saturday pairs game at the Hartford Bridge club stuck in my craw. We would have done a little better if I had analyzed hand #25 correctly. I was in the West chair, and we were vulnerable. The bidding was fairly predictable up to my second bid:

North	Pard	South	Me
Pass	1♠	2♥	Double
3♥	3♠	Pass	?

Should I raise to four, or should I pass? I was actually hoping that South would bid 4♥, in which case I would certainly have bid the spade game. When she did not, my mental process was something like the following:

Partner might be showing extra values, or he might just be competing with seven or so spades.
We probably had a fit, so I counted losers. There were surprisingly only six, but that was assessing both unsupported queens as winners. Since partner had shown no interest in my minor suits, one or both might not be worth much in practice.
The opponents could have as few as eight trump. Only one (or even none if the opponents lead trump) can probably be ruffed one in my hand.

It was hard for me to imagine that partner could find ten tricks. So, I passed. It was a mistake. He was easily able to score the required tricks. In retrospect, I surmise that I was guilty of using 1960’s thinking; I paid too much attention to the quality of my holding and not enough to my distribution. The key fact might have been the unfavorable vulnerability. Someone at the table was probably stretching his/her values, but it was unlikely to be my partner. If I placed him with the expected seven or fewer losers (he actually had six), then I should have bid 4♠ in a shot. Even if I depreciated one of my queens, we still would have only fourteen losers. Losing Trick Count says that we should be in game.

I have found that LTC is pretty accurate through four-level bids. Marty Bergen’s method of adjusting point count is another good method. In this case, I have eight high-card points. The singleton brings it up to eleven (although with only two trumps, I might only add two for it), and my two long suits makes this hand easily strong enough for game. I definitely should have bid 4♠.

Maybe someday I will be good enough to use “judgment” to make these decisions, but for the next decade or so, I plan to rely on the conclusions of others with more experience than I have. After all, partner’s hand was far from ideal. We had duplicated values in clubs, and his ♦J only contributes if South leads her singleton trump. He had no wasted values in hearts, but that was indicated by the opponents’ bidding.

I was pleased to discover from the results sheet that we actually got a good score on this board. No one played in 4♠; although one North-South pair played in 5♥. They probably were pushed. In fact, some declarers only managed nine tricks. Perhaps South led a trump. In that case declarer must immediately abandon the idea of ruffing a heart and take advantage of the surprisingly favorable diamond layout to establish that suit before squandering the ♠A as an entry.

LTC v. Bergen (Real World, Part 2)

Posted on March 31, 2013 by Mike

A horrible slam. Continue reading →

The opponents were vulnerable when my partner dealt me this unimpressive collection on one of the last rounds of an equally unimpressive session at the Hartford Bridge Club:

♠A 9 7 4 2 ♥10 6 ♦Q 10 8 6 3 ♣7My partner opened 1♥, and I quickly responded 1♠. After his jump to 4♠ I paused to assess the situation. His rebid generally showed a hand with twenty or so points and five losers. My hand had only six HCP, but there were only seven losers. Losing Trick Count (LTC) analysis said that we could make six. I was most worried about diamonds, so I lied and bid 5♣. My plan was to try 6♠ if he bid 5♦ and to stop at five if he did anything else. Sure enough; he bid his diamond control, and I went straight to 6♠.

LHO made the very passive lead of a diamond. This is what my partner set down on the table:

♠K J 8 5 2 ♥K 8 7 4 ♦A K ♣K Q 6 Could I complain? Well, yes, his opening bid was a bit strange, but he does have nineteen points and five losers. Nevertheless, against best defense this slam was down one off the top, and it would require a bit of luck not to be down two or even more. However, I realized that with a diamond lead it was still theoretically possible to make the contract if both spades and diamonds split, and the A♥ was on side. The fact that LHO did not lead the A♥ even gave me a little encouragement. However, RHO pitched a diamond on the second round of trump. I ended up down two, but it could actually have been worse. Every card was wrong. The opponents could have taken two hearts and a club off the top. If they did, and I made the percentage play of the drop in spades (as I did), I would have only managed nine tricks.

So, what went wrong with LTC? Well, the basic problem was clubs. Partner’s King and Queen were so worthless to me that I ended up pitching them on the diamonds. Add a little bad luck to that, and you end up with an LTC calculation that is off by three tricks!

I later (the game ended shortly before 11 p.m.) remembered that Bergen’s method was better on contracts above the four level. My research had revealed that Bergen’s superiority was usually derived from the fact that LTC’s assessment was too conservative. I decided to reassess my hand using Bergen count. For the starting count Bergen would have added to my six HCP one point for my fifth spade, and one for my fifth diamond to a total of eight starting points. Once partner supported my spades I could claim two for my singleton, one for my doubleton, and one for my long second suit. To him my hand would therefore be worth twelve points if I was declaring spades. Even if partner had had his twenty, we would still have been a little short of the thirty-three that he recommends for a slam bid. I deduced that Bergen would say to pass. At least his method says to pass; my understanding is that Marty himself held the green card in great disdain.

But wait. Partner actually could claim twenty-two dummy points! He has two quality suits and a doubleton in diamonds. In fact, if the suit that my partner actually opened, hearts, had been one of the quality suits, and if the suit without quality had been the one suit that he never mentioned, clubs, I would have had a pretty good play at making the hand. Maybe my bid was not as stupid as I thought when I saw the dummy.

It may be worth noting that we do better if my partner declares the hand. It would have been theoretically possible for him to garner eleven tricks.

LTC v. Bergen (Real World)

Posted on May 14, 2012 by Mike

Diagnosing some slam hands. Continue reading →

In last Saturday’s club game my partner and I missed a slam at each of the first three tables. We later missed still another slam, but we salvaged one on the very next hand. This may sound like a recipe for a disastrous session, but in fact we enjoyed a 65+% game.

Hand #16: My hand (16 HCP; 6 losers):

♠AKJ864 ♥JT ♦AK2 ♣T5Partner’s hand (12 HCP; 8 losers):

♠T75 ♥A832 ♦65 ♣AKJ3I opened a spade; partner put in the game force with 2♣. I rebid my six-card suit. Partner bid four spades.

The opponents held a motley collection of four queens, the K♥, and the J♦. The finesse of the Q♠ works, but so does the drop. You can ruff the diamond at any time. The club finesse works, and there is no reason not to take it. Three of the seven pairs only took twelve tricks, but it is hard to see a strategy that fails to produce thirteen.

Two popular methods for assessing the viability of slams are Losing Trick Count and Bergen Points. These two approaches were described here.

Losing Trick Count predicts that we would only take ten tricks with these cards. It is easy to understand how the spade loser disappeared, but only one finesse was even available. Even if it had lost, twelve tricks would be easy if the opening lead were anything but a heart. This hand seems to be a good example of the type that LTC systematically undervalues.

How about Bergen Points? My hand upticks to 18 using Bergen’s starting points. I can add two points for the long spades and one for the quality of the spade suit. I have to discount the JT doubleton, at least for the time being. Partner earns an extra point for the quality club suit, and he gets to add a point for his doubleton. That gives him 14 dummy points. We are getting close.

The final adjustment goes to my hand. When he shows support for my suit, I get to add another point for the sixth spade and one point for the doubleton. Together we have 34 Bergen Points, and we should definitely have bid 6♠!

How could we have done it using our bidding methods? I think that my partner’s bidding was fine. Even with the two extra points that Bergen allots him he does not have much to brag about. If anyone is going to go on past game, it would have to be me.

What if I had cue-bid the A♦ after he signed off with 4♠? If I think of my hand as a 20-point powerhouse with two flawed suits rather than as a level-two hand with too many losers, it seems a natural bid. If partner then bids five hearts, I know that he has the ace of hearts, but I can never learn about his club holding. Some play that bidding the heart ace implies that he also has the club ace (because I skipped clubs), but we had never discussed his. Maybe we should.

If I had bid Blackwood instead, however, I would have learned about three cards — the two aces that he had and the trump queen that he was missing. That would tell me that at worst the slam was probably hinging on a finesse. If I had an optimistic view of the hand from the point count, I probably would have gone.

The other alternative would have been for partner to bid 3♠ rather than four. That would have made it easier for me, but it would have overstated his values.

Hand #22: My hand (9 HCP; 8 losers):

♠T54 ♥AQ72 ♦K753 ♣32Partner’s hand (21 HCP; 3 losers):

♠AKQJ3 ♥4 ♦A4 ♣AK976Partner, the dealer, faced a very difficult decision. His hand met the 4×4 criterion for opening 2♣, but there were two pretty good reasons to open 1♠ instead. Many experts never use 2♣ for two-suiters. Moreover, one of partner’s suits is clubs, and it is hard to show clubs after a 2♣ opener. At any rate he opened 1♠. I bid 1NT. He jump-shifted in clubs. I vacillated between 3♠ and 4♠. Which would be stronger in this situation? I was not sure. I picked the former, and partner signed off in 4♠. I thought about going on, but I figured that my partner had no fewer than five losers.

This auction was not one of our finest moments, but we beat the two pairs that went to seven, and the two pairs that somehow found a way to lose two or three tricks.

Bergen values partner’s rock-crusher at 24 starting points. I have ten dummy points. Even before partner starts adding in distribution after he discovers our spade fit, we are in slam territory. In fact, Bergen would probably have joined the two pairs who bid the unmakeable grand. For all I know, he would have made it, too.

Hand #31: My hand (17 HCP; 5 losers):

♠Q6 ♥AKQJ852 ♦KT8 ♣QPartner’s hand (12 HCP; 8 losers):

♠A743 ♥9743 ♦A2 ♣KJ8I opened a heart. LHO liked her seven-count well enough to overcall a five-card spade suit headed by the jack. They were even vulnerable! I will try to keep this information in mind for future reference.

Partner bid 2♠. I did not think that I had enough to do anything besides sign off in 4♥.

Three pairs out of seven bid and made 6♠, which can be set with a spade lead. Two defenses found the killing lead.

LTC says that we should stop at four or five. In theory that is correct, but getting the twelfth trick only required the LHO to set down the unprotected A♣ (or any other non-spade) at trick one.

Bergen values my hand as worth 22 points as declarer. Partner has 13 points in support of hearts. From the perspective of Bergen points this one is a no-brainer. The best possible result is 6NT played by partner. I doubt, however, that too many people are going to ignore an eleven-card fit.

At this point I gave our partnership the Wienie Award. We had only played eleven hands, and three times we had been able to claim unbid slams after the first few tricks.

Hand #27: My hand (10 HCP; 7 losers):

♠AQ842 ♥A94 ♦9652 ♣7Partner’s hand (17 HCP; 6 losers):

♠K93 ♥Q8 ♦KQJ ♣AQT93No one found this slam either. After two passes LHO opened 1♦. Partner overcalled 1NT (15-18). I transferred to spades, and we settled for the game in spades. My hand’s only exceptional feature was the singleton in clubs.

Partner had to bring in the club suit in order to score twelve tricks.

I had only 11 starter points; I was not thinking about slam. Partner gets a point for his long club suit and one each for the quality of his minor suits. All told, he has 19 dummy points. When I learn of his spade support, I can add three more points (two for the singleton plus one for the four diamonds). That gives us 33 Bergen Points, and we should have bid slam again!

Maybe this pair of hands would look like a slam to Marty Bergen, who might have consider partner’s hand as too strong for a 1NT overcall. However, my four-card suit is the one that LHO bid, and my singleton is in my partner’s long suit. Adding points for these features seems dubious. The only positive intangible is the fact that the points are all sitting between us. We needed both of those long club tricks to make twelve tricks, and that required RHO to have no clubs higher than the 10. The transportation was tricky, too.

In fact, only three out of seven pairs found all twelve tricks. One played in no trump (making four), two made only four spades, and one five.

Hand #28: My hand (10 HCP; 5 losers):

♠74 ♥KQ6543 ♦__ ♣AJT87Partner’s hand (17 HCP; 7 losers):

♠KQT9 ♥AJ8 ♦AT ♣K954I had no scruples about opening my shapely ten-count. Partner forced to game with 2♣. I rebid my hearts, and he supported. At this point I was not stopping short of slam, and we made it easily.

I was shocked when I discovered that we were the only pair that had bid the slam. LTC says that this one is in the bag as soon as partner shows support for hearts. Bergen would value my hand at 18 declarer points! The challenge for him would have been to avoid bidding the grand without the A♠.

This was a really interesting set of hands. We only bid and made one of them, but our total score was still above average. Someone who used LTC exclusively would have done better than we did, provided that they did not get carried away on hand #22. If Marty Bergen could have controlled his tendency to see thirteen tricks where there are only twelve, he would have been the overall winner.

Here is the final scorecard. The edge for Bergen Points in slam-oriented hands seems even greater in practice than in theory.

161012101012221313101×10,3×12,2×1312311112101×10,2×11,3×1211271112101012281212121012

Hand #

LTC

Bergen

Field

Possible

LTC v. Bergen (Part 2)

Posted on April 9, 2012 by Mike

To evaluate the viability of Losing Trick Count and the Bergen method of counting points, I selected hands in which there was at least an eight-card fit and a makeable (according to Deep Finesse) suit contract. I then determined the … Continue reading → Continue reading →

Bergen
PointsOptimal
Level

Less than 20	1
20-22.5	2
23-25.5	3
26-28.5	4
29-32.5	5
33-36.5	6
37+	7

The table below shows what I found. The Level column shows the level of the most lucrative contract for the team as calculated by Deep Finesse. The numbers in columns two through seven are percentages. The second through fourth columns use Bergen points. The fourth through seventh columns use Losing Trick Count.

———-Bergen—————–Losing Trick Count——-LevelExact1-1.52+Exact1-1.52+


# of Hands
1	25.42	40.50	34.08	45.13	37.27	17.60	2,136
2	26.11	44.63	29.26	44.19	39.07	16.74	2,917
3	30.96	45.74	23.30	42.32	41.50	16.18	2,429
4	33.15	53.86	13.00	39.18	42.03	18.79	2,139
5	49.38	42.22	8.40	35.05	40.83	24.11	1,298
6	47.59	48.64	3.77	29.82	46.08	24.10	664
7	61.07	34.23	4.70	41.61	33.56	24.83	149

1-1.5 means that the specified level by Bergen or TLC was at least one level higher or lower than the best Deep Finesse level but not as much as two levels. 2+ means that the specified level was at least two levels higher or lower than the best Deep Finesse level.

So, the last line of the table (Level 7) indicates that in the 149 hands in which Deep Finesse determined that a grand slam was possible, the Bergen method recommended bidding it 61% of the time, but it was off by one or one and one-half tricks 34% and by two or more tricks almost 5%. LTC was right almost 42%, missed by one 33+% and by two or more 25%. By the way, if the LTC produced a result of more than 13 tricks, I treated that as “Exact.”

In general, Bergen Points appears to be far superior for contracts of level five and above. Maybe this should not be considered surprising for a system that was introduced in a book about bidding slams.

LTC produced more consistent results and had the edge on lower-level hands. In most of those cases Bergen points yielded too high of a bid. Underbidding was rare. Incidentally, the number of hands with low-level contracts is deceptive. In a considerable number of cases the opponents would have dominated the bidding. For example, in many Level 1 boards the opponents would be able to bid game or even slam. Therefore, the fact that Bergen points indicated a higher contract than could possibly be made would be irrelevant. I ran a test on Level 1 hands, however, with those hands excluded, and the results did not change much.

The optimal level calculated by Deep Finesse assumes that both sides play the hand “double dummy.” So, the opening lead is assumed to be the best one possible, and neither the declarer nor the defense make any mistakes. In the real world, of course, people do not play the hands perfectly. Even so, I can think of no better objective way to evaluate the bidding systems.

The other caveat is that some bidding mistakes are much worse than others. A conservative system that recommends bidding at too low of a level will at least produce a positive score. On the other hand, the rewards for accurate bidding at the game level or higher are substantial, especially in total points or IMPs scoring.

In the lecture cited in the first post, Ron Klinger claimed that LTC was “estimated to be at least 80% effective.” The data in this study do not seem to support that claim unless the meaning of the term “effective” is much different from the results of the “Exact” column. It is certainly true that a bid of two spades would be “effective” if nine tricks are available, in the sense that the amount of points won with a two-level bid are the same as with a three-level bid. On the other hand, most bidders would certainly like to know if that ninth trick is likely when the opponents bid three clubs.

I am no expert, but it seems to me that people who depend on LTC — and there are a lot of them — should also consider the adjustments that Bergen recommends, at least on hands with slam potential.

LTC v. Bergen (Part 1)

Posted on April 7, 2012 by Mike

No issue has received greater scrutiny in bridge theory than the quantification of the trick-taking value of a hand, or, since bridge is a team game, a pair of hands. Since Charles Goren’s books began dominating the bridge world after World War II, the primary method has been to rely on point count, where an ace is worth four points, a king three, a queen two, and a jack one. A hand with twelve or thirteen points was considered good enough to open.

A hand with some long suits and some short suits can usually take more tricks. Originally this was accommodated by adding points for short suits. At some point in the last few decades it was found that it was more accurate to add points for length rather than shortness.

The crucial numbers for evaluating the worth of a pair of hands are these:

Game in no-trump: 25.
Game in a major suit: 26.
Game in a minor suit: 29.
Small slam: 32 or 33.
Grand slam: 35-37.

Everyone with any experience at all knew that this method had its shortcomings. For example, a queen-jack doubleton was evaluated as three points, but it might not take any tricks at all. Some people systematically adjusted for various things. For example, some subtracted one for no aces or for 4-3-3-3 distribution. Others simply advocated the use of “judgment.”

Ron Klinger and others have championed an entirely different way of determining the trick-taking ability of a pair of hands. This method is called “Losing Trick Count” or LTC for short. If two hands were found to have an eight-card fit, or if one of the hands had a self-sufficient trump suit, LTC claimed that the number of tricks that could be taken by the two hands together could be closely approximated by subtracting the number of “losers” from the magic number of 24.

Counting losers is not difficult: In each hand each suit can have up to the lesser of three and the number of cards in the suit. Aces and kings are never losers (unless the king is a singleton).

Three or more pieces: Aces and kings are not losers. Queens are not losers if accompanied by another honor: Qxx is 2.5 losers. Jxx or worse: three losers.
Doubletons: AQ is .5 losers.
Singleton Ace is no losers; all others are one.
Void: no losers.

You can estimate your partner’s LTC based on the bidding.

An opening hand generally has no more than seven losers.
A level two hand (15-17 points) has around six.
A jump-shift hand has about five.
A strong two-club opener has four or fewer.
A simple raise (6-9) requires nine or so.
An invitational hand (10-12) has around eight.

A much more detailed explanation is available here.

Note that LTC is, according to Klinger, only applicable when a fit has been found. He recommends using point count when looking for a no-trump contract. Although some people use LTC in determining the value of a hand for purposes of opening, Klinger himself concentrates on using it for determining the optimal level of bidding.

Marty Bergen, on the other hand, has recommended a large number of adjustments to the point count method. He supplied three different algorithms:

“Starting points” are used until a fit is established.
“Dummy points” are used when you can support partner’s suit.
“Bergen points” (I much prefer the term “Declarer points,” and I think that he should have saved his eponymous term for the sum of the two hands) are used when partner has supported your suit.

Bergen uses the same scale for determining the value of the two hands that Goren recommended. In a no-trump contract, both players are expected to use starting points. In suit contracts in which a fit has been established, the declarer uses declarer points and the dummy uses dummy points.

Bergen has published his adjustments in the book Slam Bidding Made Easier and in a series of columns in The Bridge Bulletin. Calculation of starting points begins with high card points, and then makes the following four adjustments:

Quacks: QJ=the number of queens and jacks (bad); AT=the number of aces and tens (good). Calculate (AT – QJ) / 3 and round down. Add that number to your count. If QJ is three or more greater than AT, you will end up subtracting (adding a negative number).
Quality: Add one for each suit in which you have two of the top three honors or three of the top five.
Long: In each suit add one for each card after the fourth one.
Dubious: Subtract one for each unprotected honor.

The total is your starting points. Dummy points are starting points with three adjustments for shortness:

Doubleton: Add one if you have two or more trump.
Singleton: Add two if you have two or more trump; add another one if you have at least four trump.
Void: Add the lesser of five and the number of trump that you hold.

Declarer points also start with starting points, but the adjustments are different:

Length: Add one for each trump after the fifth one. So, a seven card trump suit is worth five extra points (three in the starting Length adjustment and another two here).
Short: Add one for one or more doubletons, two for each singleton, and four for a void.
Side suit: Add one if your second-longest suit has at least four cards.

Bergen’s method is designed to be used both for the purposes of determining whether to bid and for collectively finding the optimal level. Since the latter objective is, for suit contracts in which a fit was established, exactly the same as the objective of LTC, comparison of the two approaches made for an interesting application of the Hand Analysis project. The results will be in the next post.

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Tag Archives: Bergen, Marty

Cold Game in Spades

LTC v. Bergen (Real World, Part 2)

LTC v. Bergen (Real World)

LTC v. Bergen (Part 2)

LTC v. Bergen (Part 1)