Source: Wikipedia

A “New” Losing-Trick Count (NLTC) was introduced in The Bridge World, May 2003, by Johannes Koelman. Designed to be more precise than LTC, the NLTC method of hand evaluation utilizes the concept of “half-losers”, and it distinguishes between ‘missing-Ace losers’, ‘missing-King losers’ and ‘missing-Queen losers.’ NLTC intrinsically assigns greater value to Aces than it assigns to Kings, and it assigns greater value to Kings than it assigns to Queens. Some users of LTC make adjustments to the loser count to compensate for the imbalance of Aces and Queens held. Koelman argues that adjusting a hand’s value for the imbalance between Aces and Queens held isn’t the same as correcting for the imbalance between Aces and Queens missing. Because of singletons and doubletons [and because losing-trick counts assign losers for the first three rounds of a suit], the number of losers from missing Aces tends to be greater than the number of losers from missing Queens.[5]

NLTC differs from LTC in two significant ways. First, NLTC uses a different method to count losers (explanation and loser-count lists below). Consequently, with NLTC, the number of losers in a singleton or doubleton suit can exceed the number of cards in the suit. Second, with NLTC the number of combined losers between two hands is subtracted from 25, not from 24 (explanation below), to predict the number of tricks the two hands will produce when declarer plays the hand in the agreed trump suit. As with LTC, the NLTC formula assumes normal suit breaks, it assumes that required finesses work about half the time, and it must only be applied after an 8-card trump fit or better is discovered. When counting NLTC losers in a hand, consider only the three highest ranking cards in each suit:

  • Count 1.5 losers for a missing Ace in a suit of at least 1 card in length
  • Count 1.0 losers for a missing King in a suit of at least 2 cards in length
  • Count 0.5 losers for a missing Queen in a suit of at least 3 cards in length
  • Count 0 losers for a void suit

The following hands highlight the differences between the LTC and NLTC methods:

 Axxx  Axx  Axx  Axx – 8 LTC losers, but only 6 NLTC losers
 Kxxx  Kxx  Kxx  Kxx – 8 LTC losers, and also 8 NLTC losers
 Qxxx  Qxx  Qxx  Qxx – only 8 LTC losers, but 10 NLTC losers

Here is the basic NLTC list. For simplicity, cards below the rank of Queen are represented by “x”:

Suit Length
3 Cards (or More) Doubletons Singletons Void
Holding NLTC Holding NLTC Holding NLTC NLTC
AKQ(x)
AKx(x)
AQx(x)
Axx(x)
0
0.5
1.0
1.5
AK
AQ
Ax
0
1.0
1.0
A 0 0
KQx(x)
Kxx(x)
1.5
2.0
KQ
Kx
1.5
1.5
K 1.5 0
Qxx(x) 2.5 Qx 2.5 Q 1.5 0
xxx(x) 3.0 xx 2.5 x 1.5 0

All singletons, except singleton A, are initially counted as 1.5 losers, and all doubletons that are missing both the A and K are initially counted as 2.5 losers. Professional bridge player, Kevin Wilson, explains this concept of a suit that contains more losers than it contains cards: “Think about how much of declarer play is about timing. When you’re missing an Ace, you’re losing more than just a trick; you’re losing timing because the King, Queen and Jack that you might hold can’t score immediate tricks. First you must force out the Ace [and when the opponents win their Ace, they might immediately score more tricks, or they might establish winning tricks for later in the play]. The idea of 1.5 losers for a singleton [and 2.5 losers for a doubleton] should be within your grasp.” In Kevin’s article, he coins the term “modified” losing-trick count, or MLTC.

As with LTC, players seeking greater accuracy can also make adjustments to the NLTC. While the LTC normally uses only whole numbers and players who adjust with LTC commonly adjust in ½-loser increments, because NLTC uses fractions already, adjustments are usually made in ¼-loser increments or smaller. Players might prefer to adjust for the presence of Jacks and Tens, as these honor cards are assigned no value in the NLTC, but they’re valuable holdings, particularly when they’re together in the same suit, and especially when they’re together and they support higher honors in the suit. Similarly, players might prefer to consider a singleton King as being more valuable than a singleton 2. As with other methods of evaluation, players can upgrade or downgrade the value of a given holding based on the ensuing auction.

As previously stated, NLTC uses a value of 25 (instead of 24 with LTC) in the formula for determining the trick-taking potential for two hands. Here’s a basic pair of hands that helps illustrate why:

xxxx xxx xxx xxx
xxxx xxx xxx xxx

With both LTC and NLTC, the combined loser count with these two very weak and flat-shaped hands is 24 (12 losers in each hand). According to the LTC formula, there is no trick-taking potential with these hands (24-24 combined losers = 0 winning tricks). We must remember, however, that both forms of the losing-trick count are used only after the partnership knows it has an 8-card fit or better. In addition, losing-trick count predictions assume that all suits will break normally. In this example, given we possess an 8-card spade fit, and assuming the outstanding spades (trumps) split 3-2, the defenders can’t prevent the (hypothetical) declarer from scoring one trump trick with these otherwise worthless hands. A losing-trick count formula that doesn’t predict one winning trick with these two hands poses a theoretical concern. With NLTC we deduct the total combined losers from 25, not from 24, so the NLTC formula accurately predicts the trick-taking potential of these two hands (25-24 losers = 1 winner).

It’s worth noting that these two example hands are flat shaped and are therefore poorly suited to considering losing trick counts, as losing-trick counts are not designed for notrump hand evaluation. Instead, losing-trick counts are intended primarily for suit contract evaluations, particularly when one or both hands are unbalanced. Indeed, when one partner has 12 losers – which can only occur with 4333 shape – basic LTC can’t predict 13 tricks. NLTC however can predict a grand slam with balanced hands (examples below). For more information about NLTC, including new losing-trick counts in balanced hands, refer to Lawrence Diamond’s Mastering Hand Evaluation.

Also similar to basic LTC, NLTC users may employ an alternate formula to determine the appropriate contract level for two fitting hands. The NLTC alternate formula is: 19 (instead of 18 with LTC) minus the sum of the losers in the two hands = the projected safe contract level when declarer plays the hand in the agreed trump suit. So, 7.5 losers opposite 7.5 losers leads to: 19-(7.5+7.5) = 19-15 = 4 (4-level contract). Players who use the basic LTC variation of this formula (i.e. 18 – total combined losers = suggested safe contract level) will recognize the difference between 25 and 19 as the number of tricks required by declarer to secure a “book”, which is 6.

So, with 6.5 losers opposite 9.5 losers, we would calculate (19-16) = 3-level contract, or (25-16) = 9 tricks. With 4.5 losers opposite 7.5 losers: (19-12) = 7-level contract, or (25-12) = 13 tricks. This can help guide the bidding, as a standard opening hand typically has no more than 7.5 losers, and a typical hand with enough strength to respond typically has no more than 9.5 losers. So, when an 8-card or longer major-suit fit has been established, if the opening bidder holds a hand that has one less loser than a minimum opening hand, then opener can safely invite to game and bid to the three-level. If opener holds a hand that has two fewer losers than a minimum opening hand, then opener can force to game.

If an uncontested auction has proceeded as 1-1, then opener with four-card heart support would act according to the following guidelines:

  • 7.5 losers: minimum values (simple raise)
  • 6.5 losers: game-invitational values (a jump to three, for example)
  • 5.5 losers: game-forcing values
  • 4.5 losers: consider investigating slam
  • 3.5 losers: investigate slam

Next consider responder’s hand. Opposite partner’s 1H or 1S opening, with 3-card support, responder knows an 8+ fit exists and can bid according to the following table:

  • 9.5 losers: minimum values (simple raise)
  • 8.5 losers: game-invitational values
  • 7.5 losers: game-forcing values
  • 6.5 losers: consider investigating slam
  • 5.5 losers: investigate slam

N.B. since this response system focuses on major-fits, it can be seen that to reach a minor-suit game at the 5-level, the hand must have one less loser for each of the above-listed actions.

The NLTC solves the problem that the LTC method underestimates the trick taking potential by one on hands with a balance between ‘ace-losers’ and ‘queen-losers’. For instance, the LTC can never predict a grand slam when both hands are 4333 distribution:

KQJ2
KQ2
KQ2
KQ2
W             E A543
A43
A43
A43

will yield 13 tricks when played in spades on around 95% of occasions (failing only on a 5:0 trump break or on a ruff of the lead from a 7-card suit). However this combination is valued as only 12 tricks using the basic method (24 minus 4 and 8 losers = 12 tricks); whereas using the NLTC it is valued at 13 tricks (25 minus 12/2 and 12/2 losers = 13 tricks). Note, if the west hand happens to hold a small spade instead of the jack, both the LTC as well as the NLTC count would remain unchanged, whilst the chance of making 13 tricks falls to 67%.

The NLTC also helps to prevent overstatement on hands which are missing aces. For example:

AQ432
KQ
KQ52
32
W             E K8765
32
43
KQ54

will yield 10 tricks. The NLTC predicts this accurately (13/2 + 17/2 = 15 losers, subtracted from 25 = 10 tricks); whereas the basic LTC predicts 12 tricks (5 + 7 = 12 losers, subtracted from 24 = 12).

Second round bids

Whichever method is being used, the bidding need not stop after the opening bid and the response. Assuming opener bids 1 and partner responds 2; opener will know from this bid that partner has 9 losers (using basic LTC), if opener has 5 losers rather than the systemically assumed 7, then the calculation changes to (5 + 9 = 14 deducted from 24 = 10) and game becomes apparent!

Limitations of the method

All LTC methods are only valid if trump fit (4-4, 5-3 or better) is evident and, even then, care is required to avoid counting double values in the same suit e.g. KQxx (1 loser in LTC) opposite a singleton x (also 1 loser in LTC).

Regardless which hand evaluation is used (HCP, LTC, NLTC, etc.) without the partners exchanging information about specific suit strengths and suit lengths, a suboptimal evaluation of the trick taking potential of the combined hands will often result. Consider the examples:

QJ53
743
KJ2
632
W             E AK874
A5
AQ54
54
QJ53
743
632
KJ2
W             E AK874
A5
AQ54
54

Both layouts are the same, except for the swapping of West’s minor suits. So in both cases East and West have exactly the same strength in terms of HCP, LTC, NLTC etc. Yet, the layout on the left may be expected to produce 10 tricks in spades, whilst on a bad day the layout to the right would even fail to produce 9 tricks.

The difference between the two layouts is that on the left the high cards in the minor suits of both hands work in combination, whilst on the right hand side the minor suit honours fail to do so. Obviously on hands like these, it does not suffice to evaluate each hand individually. When inviting for game, both partners need to communicate in which suit they can provide assistance in the form of high cards, and adjust their hand evaluations accordingly. Conventional agreements like help suit trials and short suit trials are available for this purpose.