Losing-Trick Count

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. ♠ 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, it is assumed that a typical opening hand by partner contains 7 losers, eg. ♠ A K x x x ♥ A x x x ♦ Q x ♣ x x, has 7 losers (1 + 2 + 2 + 2 = 7).

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 Klinger.
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 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.

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

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!
[edit] 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.