Losing-Trick Count
Encyclopedia
The Losing-Trick Count is an alternative, or supplement, in the card game
contract bridge
, to the high card point (HCP) method of hand evaluation
to be used in situations where shape and fit are of more significance than HCP in determining the optimum level of a suit contract - it should only be used after a fit has been found. Based upon a set of empirical rules for counting, the number of "losing tricks" held by a partnership is first estimated and deducted from 24; the result is the number of tricks the partnership can expect to take when playing in their established suit.
in a book whose spine simply has Auction Bridge but the cover says Elwell on Auction Bridge and the title page proclaims The Principles, Rules and Laws of Auction Bridge Stated, Explained, and Illustrated. 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.
It is also assumed 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, eg. has 12 losers (3 in each suit), whereas has only 9 losers (3 in all suits except the void which counts no losers).
Until further information is derived from the bidding, it is assumed that a typical opening hand by partner contains 7 losers, eg. , has 7 losers (1 + 2 + 2 + 2 = 7).
Thus following an opening bid of 1:
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.
A typical opening bid is assumed to have 15 or fewer half losers (i.e. half a loser more than in the basic LTC method). NLTC differs from LTC also in the fact that it utilises a value of 25 (instead of 24) in determining the trick taking potential of two partnering hands. 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 of both hands). So, 15 half-losers opposite 15 half-losers leads to 25-(15+15)/2 = 10 tricks.
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:
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:
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).
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:
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.
Card game
A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games...
contract bridge
Contract bridge
Contract bridge, usually known simply as bridge, is a trick-taking card game using a standard deck of 52 playing cards played by four players in two competing partnerships with partners sitting opposite each other around a small table...
, to the high card point (HCP) method of hand evaluation
Hand evaluation
In contract bridge, various bidding systems have been devised to enable partners to describe their hands to each other so that they may reach the optimum contract. Key to this process is that players evaluate and re-evaluate the trick-taking potential of their hands as the auction proceeds and...
to be used in situations where shape and fit are of more significance than HCP in determining the optimum level of a suit contract - it should only be used after a fit has been found. Based upon a set of empirical rules for counting, the number of "losing tricks" held by a partnership is first estimated and deducted from 24; the result is the number of tricks the partnership can expect to take when playing in their established suit.
Origins
The origins of the Losing Trick Count -- without that name -- can be traced back at least to 1910 when Joseph Bowne Elwell wrote on auction bridgeAuction bridge
The card game auction bridge, the third step in the evolution of the general game of bridge, was developed from straight bridge in 1904. The precursor to contract bridge, its predecessors were whist and bridge whist....
in a book whose spine simply has Auction Bridge but the cover says Elwell on Auction Bridge and the title page proclaims The Principles, Rules and Laws of Auction Bridge Stated, Explained, and Illustrated. 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
Maurice Harrison-Gray
Maurice Harrison-Gray , known always as 'Gray', was an English professional contract bridge player. For about thirty years from the mid-thirties to the mid sixties he was one of the top players, and won the European Championship four times - in 1948, 1949, 1950 and 1963.- Life :Gray was the child...
in Country Life magazine in the 1950s and 1960s. In recent decades, others have suggested refinements to the basic counting method.
Basic counting method
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, Kx or KQ = 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.
It is also assumed 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, eg. has 12 losers (3 in each suit), whereas has only 9 losers (3 in all suits except the void which counts no losers).
Until further information is derived from the bidding, it is assumed that a typical opening hand by partner contains 7 losers, eg. , has 7 losers (1 + 2 + 2 + 2 = 7).
Example
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
Thinking that the method tended to overvalue unsupported queens and undervalue supported jacks, Eric Crowhurst and Andrew Kambites refined the scale as follows:- AQ doubleton = ½ loser according to Ron KlingerRon KlingerRon Klinger is a leading bridge author, writing more than 50 books on the game. He is an Australian Grand Master and a World Bridge Federation International Master.-Biography:...
. - Kx doubleton = 1½ losers according to others.
- AJ10 = 1 loser.
- 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
Ron Klinger
Ron Klinger is a leading bridge author, writing more than 50 books on the game. He is an Australian Grand Master and a World Bridge Federation International Master.-Biography:...
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)
Recent insights on these issues have led to the New Losing Trick Count (Bridge World, 2003). For more precision this count utilises the concept of half-losers and, more importantly, distinguishes between 'ace-losers', 'king-losers' and 'queen-losers':- a missing Ace = three half losers.
- a missing King = two half losers.
- a missing queen = one half loser.
A typical opening bid is assumed to have 15 or fewer half losers (i.e. half a loser more than in the basic LTC method). NLTC differs from LTC also in the fact that it utilises a value of 25 (instead of 24) in determining the trick taking potential of two partnering hands. 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 of both hands). So, 15 half-losers opposite 15 half-losers leads to 25-(15+15)/2 = 10 tricks.
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:
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:
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
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:
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
Game try
A game try in the card game of bridge is a bid that shows interest in bidding a game and asks partner to help in making the decision....
are available for this purpose.
Further reading
Nine editions published between 1935 and 1947. Republished in 2006 as Losing Trick Count - A Book of Bridge Technique by F. Dudley Courtenay, ISBN 9781406797169.- Maurice Harrison-GrayMaurice Harrison-GrayMaurice Harrison-Gray , known always as 'Gray', was an English professional contract bridge player. For about thirty years from the mid-thirties to the mid sixties he was one of the top players, and won the European Championship four times - in 1948, 1949, 1950 and 1963.- Life :Gray was the child...
articles in Country Life magazine in the 1950s and 1960s. Republished in 1987 (Gollancz, London), 1989 (Modern Bridge Publications), 1993 (Gollancz, London) and 2001 (Cassell, London), under The Modern Losing Trick Count. - Koelman, Johannes. The Bridge WorldThe Bridge WorldThe Bridge World , the oldest continuously published magazine about contract bridge, was founded in 1929 by Ely Culbertson. It has since been regarded as the game's principal journal, publicizing technical advances in bidding and the play of the cards, discussions of ethical issues, bridge politics...
, Vol 74, Issue 8, p. 26, May 2003.