The Losing-Trick Count (LTC)
is an alternative, or supplement, 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. The "losing tricks" in a hand are added to the systemically assumed losing tricks in partners hand (7 for an opening bid of 1 of a suit) and the resultant number is deducted from 24; the net figure is the number of tricks a partnership can expect to take when playing in the established suit.
The basic method assumes 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, thus
- 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.
- suits longer than three cards are judged according to the three highest cards since no suit may have more than 3 losing tricks. Thus hands without an A, K or Q have a maximum of 12 losers but may have fewer depending on shape: Jxxx, Jxx, Jxx, Jxx ... has 12 losers (3 in each suit), whereas xxxxx, -, xxxx, xxxx ... has only 9 losers (3 in all suits except the void which counts no losers).
A typical opening hand, eg AKxxx Axxx Qx xx, has 7 losers (1+2+2+2=7). To calculate how high to bid, responder adds the number of losers in their hand to the assumed number in opener's hand (7). The total number of losers arrived at by this sum is subtracted from 24. The answer is deemed to be the total number of tricks available to the partnership and this should be the next bid by responder, Thus following an opening bid of 1H:
- partner jumps to game with no more than 7 losers in hand and a fit with partner's heart suit (3 if playing 5-card majors) ... 7 + 7 = 14 subtract from 24 = 10 tricks.
- With 8 losers in hand and a fit, responder bids 3H (8+7=15 which deducted from 24 = 9 tricks).
- With 9 losers and a fit, responder bids 2H.
- With only 5 losers and a fit, a slam is likely so responder may bid straight to 6H if preemptive bidding seems appropriate or take a slower forcing approach.
Refining the scale
Thinking that this method tends to overvalue unsupported queens and undervalue supported jacks, this scale can be refined (Crowhurst & Kambites 1992) as follows:
- 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" Klinger advocates adjusting the number of loser based on the control count of the hand.
New Losing Trick Count (NLTC)
Extending these thoughts, Klinger believes 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.
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 (ie 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 rebid. Assuming opener bids 1H and partner responds 2H; 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 suite eg 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 both 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.
The method was originally put forward by the American F. Dudley Courtenay and the Englishman George Gordon Joseph Walshe. They wrote a book in 1935 entitled The Losing Trick Count, as used by the leading contract bridge tournament players, with examples of expert bidding and expert play
. (This was republished in 2006 as Losing Trick Count - A Book Of Bridge Technique
by F. Dudley Courtenay, ISBN 9781406797169.) Courtenay's method was subsequently popularised by Maurice Harrison-Gray
in his articles in Country Life
magazine in the 1950s and 1960s.