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 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
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 have others:
AQ doubleton = ½ loser according to Ron Klinger.
Kx doubleton = 1½ losers according to others.
AJ10 = 1 loser according to Bernard Magee.
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 honour 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:
♠
KQJ2 ♠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 ♠
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
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:
♠
♥
♦
♣
QJ53
743
KJ2
632
♠
♥
♦
♣
AK874
A5
AQ54
54
♠
♥
♦
♣
QJ53
743
632
KJ2
♠
♥
♦
♣
AK874
A5
AQ54
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.