Losing-Trick Count

In the card game contract bridge, the Losing-Trick Count (LTC) is a method of hand evaluation used in situations where a trump suit has been established and shape and fit are more significant than high card points (HCP) in determining the optimum level of the contract. The method is not suitable for notrump or misfit hands;^[1] also, the trump suit must be at least eight cards in length with no partner holding less than three.^[2]

Based on a set of empirical rules, the number of "losing tricks" held in each of the partnership's hands is estimated and their sum deducted from 24; the result is the number of tricks the partnership can expect to take when playing in their established suit, assuming normal suit distributions and assuming required finesses work about half the time.^[1]

History

The origins of the Losing Trick Count (LTC)—without that name—can be traced back at least to 1910 in Joseph Bowne Elwell's book Elwell on Auction Bridge wherein he sets out, in tabular form,^[3] a scheme for counting losers in trump contracts similar to the basic counting method given below.

The term "Losing Trick Count" was originally put forward by the American F. Dudley Courtenay in his 1934 book The System the Experts Play (which ran to at least 21 printing editions).^[4] Among various acknowledgments, the author writes: 'To Mr. Arnold Fraser-Campbell the author is particularly indebted for permission to use material and quotations from his manuscript in which is described his method of hand valuation by counting losing tricks, and from which the author has developed the Losing Trick Count described herein.'

The Englishman George Walshe and Courtenay edited the American edition and retitled it The Losing Trick Count for the British market; first published in London in 1935, the ninth edition came out in 1947.^[4] Subsequently, it has been republished by print-on-demand re-publishers.

The LTC was also popularised by Maurice Harrison-Gray in Country Life magazine in the 1950s and 1960s.

In its original British edition of years before, it had not been very lucidly presented and it seemed to suffer from a certain wooliness of definition of some of its concepts... With the blessing of Mr. Courtenay, Gray sharpened up the definitions, plugged some holes in the logic and made the whole conception intelligible to the average player.

— Jack Marx, in the Introduction to Country Life Book of Bridge by M. Harrison-Gray (1972)

In recent decades, others have suggested refinements to the basic counting method.

The original LTC

The underlying premise of LTC is that if a suit is evenly distributed, i.e. three players hold three cards in the suit and one player holds four, a maximum of three losers can be assumed in any one suit held by the partnership and, in turn, the maximum number of losers held by the partnership in all four suits is 24 (three in each of the four suits in each of two hands, i.e. 3 x 4 x 2 = 24). The LTC method estimates the total number of losers held by the partnership and deducts that total from 24 to estimate the number of tricks which the partnership may expect to win and provides guidance as to how high to bid in the auction.

Methodology

The basic LTC methodology consists of three steps:

Example

You hold ♠ AQxx ♥ Qxx ♦ Kxxx ♣ Qx and partner opens 1♥.

At this stage in the bidding, one estimates that the partnership can take at least 10 tricks.

Refinements

Thinking that the method tended to overvalue unsupported queens and undervalue supported jacks, Eric Crowhurst and Andrew Kambites refined the scale, as have others:

• AQ doubleton = ½ loser according to Ron Klinger.
• KQ doubleton = 1 loser (obvious).
• Kx doubleton = 1½ losers according to others.
• AJ10 = 1 loser according to Harrison-Gray.
• KJ10 = 1½ losers according to Bernard Magee.
• Qxx = 3 losers (or possibly 2.5) unless trumps.
• Subtract a loser if there is a known 9-card trump fit.

In his book The Modern Losing Trick Count, Ron Klinger advocates adjusting the number of loser based on the control count of the hand believing that the basic method undervalues an ace but overvalues a queen and undervalues short honor combinations such as Qx or a singleton king. Also it places no value on cards jack or lower.

New Losing-Trick Count (NLTC)

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, missing Aces that add losers to a hand tend to outnumber missing Queens that add losers.^[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":

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."^[6] 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 with NLTC. LTC normally uses a one-loser "resolution" (i.e. degree of accuracy), and players who adjust with LTC commonly adjust in ½-loser increments. To compare, NLTC normally uses a ½-loser resolution, and typical NLTC adjustments are made in ¼-loser increments. For even more accuracy, players can also adjust using ⅛-loser increments. Jacks and Tens are initially assigned no value in losing-trick counts, but these lower honors can be valuable (not to mention the value of intermediates like Nines, Eights and Sevens). Jacks and Tens are more valuable when they're together in the same suit, and they're most valuable when they're together and they support higher honors in the suit. Other holdings that possess no initial losing-trick count value, but can be considered for upgrades, include unprotected Kings, Queens and Jacks in short suits. As with other methods of hand evaluation, players can either upgrade or downgrade the value of a given holding based on the ensuing auction. With no additional information available, the following is a list of plausible initial NLTC adjustments:

AKJ - ¼-loser upgrade
AKT - ⅛-loser upgrade
AQJ - ¼-loser upgrade
AQT - ⅛-loser upgrade
AJT - ¼-loser upgrade
AJx - ⅛-loser upgrade
AT9 - ⅛-loser upgrade
KQJ - ¼-loser upgrade
KQT - ⅛-loser upgrade
KJT - ¼-loser upgrade
KJx - ⅛-loser upgrade
KT9 - ⅛-loser upgrade
QJT - ¼-loser upgrade
QJx - ⅛-loser upgrade
QT9 - ⅛-loser upgrade
JT9 - ¼-loser upgrade
JTx - ⅛-loser upgrade
AQ doubleton - ¼-loser upgrade
AJ doubleton - ⅛-loser upgrade
KQ doubleton - ¼-loser upgrade
KJ doubleton - ⅛-loser upgrade
QJ doubleton - ¼-loser upgrade
Qx doubleton - ⅛-loser upgrade
K singleton - ¼-loser upgrade
Q singleton - ⅛-loser upgrade

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 should give a theoretician 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).

(*) These two example hands are flat shaped, and flat-shaped hands often play better in notrump. Losing trick counts are not inherently designed for notrump hand evaluation.^[1] Instead, losing trick counts are intended to be used primarily for suit contract evaluations, particularly when one or both hands are unbalanced. In fact, when one partner has 12 losers - which can occur with 4333 shape, as in the example above - LTC can never predict 13 tricks.^[5] NLTC however can predict a grand slam with balanced hands (see additional example hand below). For more information about NLTC, including new losing-trick counts in balanced hands, refer to Lawrence Diamond's Mastering Hand Evaluation.^[7]