Losing-Trick Count

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In the card game contract bridge, the Losing-Trick Count (LTC) is a supplement to the high card point (HCP) method of hand evaluation used in situations where shape and fit are more significant than HCP in determining the optimum level of a suit contract. Based on a set of empirical rules, the number of "losing tricks" held by a partnership is estimated and deducted from 24; the result is the number of tricks the partnership can expect to take[citation needed] when playing in their established suit, assuming normal breaks and assuming required finesses work about half the time.

Origins[edit]

The origins of the Losing Trick Count—without that name—can be traced back at least to 1910 in Joseph Bowne Elwell's book Elwell on Auction Bridge. In the preface (page v), Elwell mentions chapters on "Estimating the Values of Hands". The sections later in the book (pages 80–89) are mostly tables with differing titles beginning with the word "Estimating" but ending differently. Elwell sets out a scheme for counting losers in trump contracts that looks very much like the simple 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 18 printings). On page two 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.' From this we may speculate that Elwell's ideas filtered through Fraser-Campbell to Courtenay.

The Englishman George Gordon Joseph Walshe contacted Courtenay about issuing a British edition. Together they edited the American edition and retitled it The Losing Trick Count for the British market. This title went through dozens of printings and remained in print for two decades. (Subsequently it has been republished by print-on-demand re-publishers.)

LTC was 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.

Basic counting method[edit]

The estimated number of losing tricks (losers) 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; 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.

(Some authorities treat Qxx as 3 losers unless the Q is "balanced" by an A in another suit.) LTC also assumes that no suit can have more than 3 losing tricks and so suits longer than three cards are judged according to their three highest cards. 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.  J x x x  J x x  J x x  J x x has 12 losers (3 in each suit), whereas  x x x x x  —  x x x x  x x x x has only 9 losers (3 in all suits except the void which counts no losers).

Until further information is derived from the bidding, assume that a typical opening hand by partner contains 7 losers, e.g.  A K x x x  A x x x  Q x  x x, has 7 losers (1 + 2 + 2 + 2 = 7).

Example[edit]

To determine how high to bid, responder adds the number of losers in his hand to the assumed number in opener's hand (7); the total number of losers arrived at by this sum is subtracted from 24 and the result is estimated to be the total number of tricks available to the partnership.

Thus following an opening bid of 1:

  • partner jumps to game in 4 with no more than 7 losers in his own hand and a fit with partner's heart suit (7 + 7 = 14 subtract from 24 = 10 tricks).
  • With 8 losers in hand and a fit, responder bids 3 (8 + 7 = 15 subtract from 24 = 9 tricks).
  • With 9 losers and a fit, responder bids 2 (9 + 7 = 16 subtract from 24 = 8 tricks).
  • With only 5 losers and a fit (5 + 7 = 12 subtract from 24 = 12 tricks), a slam is possible so responder may bid straight to 6 if preemptive bidding seems appropriate or take a slower forcing approach.

Refinements[edit]

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.
  • 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)[edit]

Astute players realize that basic LTC undervalues Aces and overvalues Queens. Insights to this concern led to the "New" Losing-Trick Count, or NLTC (The Bridge World, May 2003). For more precision, this method of hand evaluation utilizes the concept of "half-losers" and it distinguishes between 'Ace-losers', 'King-losers' and '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 basic LTC make adjustments to compensate for the imbalance of Aces and Queens held. The author of The Bridge World article (Johannes 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 tend to outnumber missing Queens that add losers.

When counting losers in a hand, consider only the three highest ranking cards in each suit:

  • missing Ace = three half-losers (1½ losers)
  • missing King = two half-losers (1 loser)
  • missing Queen = one half-loser (½ loser)


Void 0 losers

AKQ 0 losers

AKJ ½ loser

AQJ ½ loser

KQJ 1 losers

KJT 1½ losers

Axx 1½ losers

Kxx 2 losers

Qxx 2½ losers

QJT 2½ losers

Ax 1 loser

Kx 1½ losers

Qx 2 losers

KQ 1 losers

KQx 1½ losers

A 0 losers

K 1 losers

x 1 losers

xx 2 losers

xxx 3 losers

JT9 3 losers



Adopters of NLTC must recognize that all singletons, except singleton A, are initially counted as three half-losers (1.5 losers), and all doubletons that are missing both the A and K are initially counted as five half-losers (2.5 losers). As with basic LTC, with NLTC no suit contains more than three losers, so a suit with 3+ length and missing A and K and Q is counted as six half-losers (3.0 losers).

Consider the effect of NLTC with these three basic hands:
Axxx Axx Axx Axx - 8 losers w/LTC, 6 losers w/NLTC
Kxxx Kxx Kxx Kxx - 8 losers w/LTC, 8 losers w/NLTC
Qxxx Qxx Qxx Qxx - 8 losers w/LTC, 10 losers w/NLTC


With NLTC an opening bid of 1C/1D/1H/1S is assumed to have 15 or fewer half-losers, or 7.5 losers, which is half a loser more compared to a hand of minimum strength using basic LTC. NLTC also differs from LTC in that it utilizes a value of 25 (instead of 24 with basic LTC) as part of the formula that is used to determine the trick-taking potential for the two hands, assuming normal breaks and finesses working about half the time. Hence, in NLTC the expected number of tricks equates to 25 minus the sum of the losers in the two hands (i.e. half the sum of the half-losers in both hands). So, 15 half-losers opposite 15 half-losers leads to 25-(15+15)/2 = 10 possible tricks.

Similar to basic LTC, users may employ an alternate formula to determine the appropriate contract level. The NLTC alternate formula is: 19 (instead of 18 with basic LTC) minus the sum of the losers in the two hands (i.e. half the sum of the half-losers in both hands) = the contract level to which the partnership should consider bidding. So, 15 half-losers opposite 15 half-losers leads to 19-(15+15)/2 = 4-level contract. Players who already use the basic LTC variation of this formula will recognize the difference between 25 (total projected tricks) and 19 (projected contract level) as the number of tricks required by declarer to secure a "book", which is 6.

The NLTC solves the problem that the basic 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

W             E

A543
KQ2 A43
KQ2 A43
KQ2 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%. As a result, NLTC still produces the preferred result.

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

AQ432

W             E

K8765
KQ 32
KQ52 43
32 KQ54

will yield 10 tricks only, provided defenders cash their three aces. 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[edit]

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[edit]

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

W             E

AK874
743 A5
KJ2 AQ54
632 54
QJ53

W             E

AK874
743 A5
632 AQ54
KJ2 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 helpsuit trials and short suit trials are available for this purpose.

Notes[edit]

Further reading[edit]

  • Courtenay, Dudley; Walshe, George (1935). The Losing Trick Count, as used by the leading contract bridge tournament players, with examples of expert bidding and expert play. London: Methuen. p. 176.  Nine editions published between 1935 and 1947. Republished in 2006 as Losing Trick Count - A Book of Bridge Technique by F. Dudley Courtenay, ISBN 978-1-4067-9716-9. Reference: Tim, Bourke; Sugden, John (2010). Bridge Books in English from 1886-2010: an annotated bibliography. Bridge Book Buffs (Cheltenham, England), 711 pages plus supplement. ISBN 978-0-9566576-0-2.  Page 93.
  • Maurice Harrison-Gray articles in Country Life magazine in the 1950s and 1960s.
  • Klinger, Ron (1986). Bidding to Win at Bridge, Book One, The Modern Losing Trick Count. Modern Bridge Series. Northbridge, Australia: Modern Bridge Publications. p. 122. ISBN 0-575-05650-9.  Republished in 1987 (Gollancz, London), 1989 (Modern Bridge Publications), 1993 (Gollancz, London) and 2001 (Cassell, London), under The Modern Losing Trick Count.
  • Koelman, Johannes M.V.A. A New Losing-Trick Count. The Bridge World, May 2003, Vol 74, Issue 8, p. 26. 
  • Jones, Jennifer (2011). Losing Trick Count. Jennbridge. 
  • Jones, Jennifer (2012). Losing Trick Count Vol. II. Jennbridge.