In the card game contract bridge, the Losing-Trick Count (LTC) is a method of hand evaluation that is generally only considered suitable to be used in situations where a trump suit has been established and when shape and fit are more significant than high card points (HCP) in determining the optimum level of the contract. The method is generally not considered suitable for no trump or misfit hands; also, the trump suit is generally considered to require at least eight cards in length with no partner holding fewer than three.
However, the LTC method of hand evaluation has been used successfully to evaluate unbalanced and balanced opening hands, and overcalls, since 1938 (combined with ‘quick trick’ evaluation and defined biddable suits), and by itself since 2017, before a fit and trump suit have been established based on the premise that a fit could usually be found later.
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 either 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) or 18 (the result is the bidding level the partnership can expect to make their contract when playing in their established suit, assuming normal suit distributions and assuming required finesses work about half the time). F. Dudley Courtenay originally referred to the latter option as the “Rule of 18”.
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, 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). 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. 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 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 either 24 to estimate the number of tricks which the partnership may expect to win or 18 to estimate the bidding level the partnership may expect to make their contract. Using either of the LTC method options thus provides guidance as to how high to bid in the auction.
Methodology The basic LTC methodology consists of three steps: Step 1: Count losers in one's own handThe estimated number of losing tricks (LTC) in one's hand is determined by examining each suit and assuming that an ace will never be a loser, nor will a king in a 2+ card suit, nor a queen in a 3+ card suit; accordingly a void = 0 losing tricks. a singleton other than an A = 1 losing trick. a doubleton AK = 0; Ax or Kx = 1; Qx or xx = 2 losing tricks. a three card suit AKQ = 0; AKx, AQx or KQx = 1 losing trick. a three card suit Axx, Kxx or Qxx = 2; xxx = 3 losing tricks.
It follows that hands without an A, K or Q have a maximum of 12 losers but may have fewer depending on shape, e.g. has 12 losers (3 in each suit), whereas has only 9 losers (3 in all suits except the void which counts no losers). Step 2: Estimate losers in partner's handUntil further information is derived from the bidding, assume that a typical opening hand by partner contains 7 losers, e.g. , has 7 losers (1 + 2 + 2 + 2 = 7). Step 3: Deduct the total from 24 or 18The total number of losers in the partnership is determined by adding the numerical results of the previous two steps. Deducting this result from 24, gives an estimate of the total number of tricks that the partnership should win and therefore how high to bid. Deducting this result from 18, gives a direct estimate of the bidding level the partnership can bid to and expect to make.
Example You hold and partner opens 1. If playing five-card majors, you know you have at least an 8 card heart fit. Step 1: Count losers in one's own hand AQxx counts as 1 loser Qxx counts as 2 losers Kxxx counts as 2 losers Qx counts as 2 losers This is a total of 7 losers. Step 2: Estimate losers in partner's handOpening partner is assumed to have 7 losers. Step 3: Deduct the total from 24 or 18The total number of losers held by the partnership is 7 + 7 = 14. Consequently the total number of tricks expected to be won are 24 - 14 = 10 and the expected bidding level may be subsequently worked out to be 10 - 6 = 4, or alternatively the expected bidding level can be calculated directly 18 - 14 = 4, At this stage in the bidding, one estimates that the partnership can take at least 10 tricks and bid to the 4 level.
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. QJx = 2 losers 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 losers 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 [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.
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:
- 8 LTC losers, but only 6 NLTC losers - 8 LTC losers, and also 8 NLTC losers - 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 Length3 Cards(or More)DoubletonsSingletonsVoidHoldingNLTCHoldingNLTCHoldingNLTCNLTCAKQ(x)AKx(x)AQx(x) Axx(x) 00.51.01.5 AKAQAx 01.01.0 A 0 0KQx(x)Kxx(x) 1.52.0 KQKx 1.51.5 K 1.5 0Qxx(x) 2.5 Qx 2.5 Q 1.5 0xxx(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