Losing Trick Count: the Rule of 18 - Bridge

A recent evening of family bridge was characterized not by misplaying hands nor misdefences but rather by failures to reach game and even slam contracts with fewer than the normally prescribed number of high card points. This raises the topic of evaluating the playing strength of hands in suit contracts, taking into account both distribution and points.

Most readers will be familiar with the "Rule of 20", a method taught in most Israeli bridge clubs, for determining whether a hand with fewer than the standard 12 plus points should, in fact, be opened in first or second seat. The development of the rule is attributed to Grand Life and World International Master, Marty Bergen.

Very simply, add together the number of cards in your two longest suits to the number of points in your hand. If the result is 20 or more, the hand can and should be opened. The standard example given in the literature is the following: ♠ 6; ♥ A Q 9 6 5; ♥ A 10 9 6 5; ♣ 4 2. Adding 5 for each of the red suits to the 10 HCPs gives 20, so the hand is worth an opening bid of 1♥.

Bergen adds a number of qualifications to the rule, specifying, amongst other things, that the points should be in the long suits. Hence a hand such as ♠ A; ♥ 10 9 8 6 5; ♦ K 10 9 6 5; ♣ K 2 should not be opened. By the way, for bridge historians, the first hand satisfies the Culbertson criteria of 2 ½ "quick tricks", the method for evaluating hands prior to the introduction of point-count bidding by Charles Goren. The second hand does not.

What remains a source of frustration to the average player who has mastered the rules of "light" openings like the one above, is that they still do not get to the suit games that the top players do with a partnership holding of sometimes as little as 20 points.

Do experienced bridge players use the rule of 20? Probably not. They have instinctively learnt which hands warrant opening and which not. But many still use a method during the bidding sequence called the "Losing Trick Count" (LTC), which dates back to the 1960s, to evaluate hands in the context of a fit of eight or more cards between their own and partner's hand.

By using this method of counting losers based on distribution and honor cards, we can determine roughly the number of winning tricks we can make on a given hand in a suit contract. Why would such a method be desirable? In excess of 80% of all bridge hands provide an eight-card or greater trump fit with partner. In other words, we normally have a fit with partner, and trump fits allow us to take tricks.

How do we count the losers in our hand? First, look only at the top three cards in each suit and count as a loser any card below the level of Queen. If you have a doubleton in a suit, you should of course only consider those two cards, and a singleton, only one. At most, in the case, of a 4-3-3-3 distribution, the flattest possible, you would consider 12 cards so the maximum LTC is 12.

Next add back one loser for any Queen that is singleton or not "supported" by an Ace or King in the same suit. As responder, or in subsequent bidding, an unsupported Queen with at least 2 smaller cards in a suit bid by partner, can be given back its full covering-card status and you can then reduce your loser count by 1.

Consider the following example: Your hand is ♠ A 10 8 7; ♥ 9; ♦ K 9 5 4 2; ♣ 10 7 2. Partner opens 1♠. You have a good fit in spades - at least 9 cards in that suit together with a minimum of 5 promised by partner. You must raise partner's spade bid directly to show him/her the fit - your hand is too weak in High Card Points (HCP) to bid 2♦ which requires a minimum of 10HCP – but do you bid 2♠ or 3♠ or even 4♠?

You count 2 losers in ♠ (10 and 8), 1 for the ♥ 9, 2 in ♦ (9 and 5) and 3 in ♣ (10, 7 and 2). Your LTC is therefore 8. You do not know partner's LTC but you can assume that an opening suit bid at the one level shows an LTC of at most 7.

Now apply the LTC Formula, which we will call the "Rule of 18":

Your losers + partner's losers = X

24 –X = Number of tricks your side can make
18 – X = Level of the contract you can make

Substituting your own LTC of 8 and the assumed LTC of 7 for partner in the formula gives X=8+7=15. The formula indicates that even if a partner only has the minimum promised for his/her 1♠ opening, your side can make 24-15=9 tricks and you can therefore raise partner's spades directly to the 18-15=3 level. You should bid 3♠. What does this tell partner?

Partner knows that your bid was based on the assumption that his/her LTC was 7, so your 3♠ bid tells partner that you have spade support and an LTC of exactly 8.

In the same way that partner's opening bid of 1♠ promised a minimum of 12 HCP but could be as good as 19 HCP, partner's hand could be better than a 7 loser hand. Partner could be as good as having an LTC of only 4. In any event, partner now re-applies the formula on the basis of his/her actual LCT and your now known LTC of 8. Partner will pass your 3♠ bid with a 7 loser hand, bid 4♠ with an LTC of 6 or 5, and 4NT to check for Aces on the way to the indicated contract of 6♠ with an LTC of 4 or better.

In the above example, because you raise partner's bid suit directly, the situation became immediately clear to partner after your response. This is not always the case, but the position will become clearer as the auction develops.

Suppose partner opens 1♦ and you have: ♠ A 10 8 7 5 4 ♥ 9 ♦ K 9 5 2 ♣ 10 7

You respond 1♠. Even though you have a four-card fit in partner's minor suit, you should clearly bid your major suit first. Your partner now bids 4♠. What is partner telling you?

Your bid of 1♠ promises partner a minimum of a 4 card suit, a minimum of 6 HCP and an LTC of at worst 9. Partner's bid 4♠ shows 4-card spade support (with 5 cards, partner would have opened 1♠) and since the bid was based on the worst-case assumption that you have an LTC of 9, partner must have LTC of 5. (X=5+9=14; 18-14=4)

In fact, however, you only have seven losers. So, taking into account partner's now known LTC of 5, the formula indicates you can probably make 12 tricks with spades as trumps. You could bid 6♠ accordingly, but you should first check that your side is not missing two Aces. You bid 4NT (Blackwood) and your partner responds 5♥, showing 2 Aces. You can now you bid 6♠.

Partner's hand in this example was: ♠ K Q 9 6 ♥ A 10 3 ♦ A Q J 7 4 ♣ 8

You can see that the formula almost magically determines the partnership's available winning tricks and the available level of the contract. There are many more sophisticated methods requiring considerable investment in partnership training but, in terms of simplicity and effectiveness, it's still one of the most useful bridge aids I know. I suggest you start to play the LTC with your favorite partners. I do.

The following question was received in our website

Comment : Is there any way LTC can be applied if you don't have a fit?

In short, the answer is no and it also doesn't apply to evaluating No Trump hands.

Essentially, the LTC gives value to distribution by looking only at the top three cards in each suit. So, if you have a void, the LTC count for that suit is zero and the maximum LTC for the rest of your hand is 9.
But this is meaningless if that's your partners suit or in No Trumps.
Consider the following: Your partner deals and opens 1SP, your right-hand opponent overcalls 2CL, you have ♠ - ♥ Q 7 5 4 3, ♦ 10 6 4, ♣ A 8 5 4 3. On the surface your LTC is 8 – the "naked" ♥ Q does not count as a cover card, but you can't really bid. Obviously, you can't bid spades and you don't have enough points to bid 2 hearts; 1NT is wrong and a negative double is not advisable. So, you pass with the reasonable expectation that the opponents are going to get into hot water.

Now if your RH opponent passes and partner bids 2H, see how everything changes: Your ♥ Q is now a covering card and your LTC drops to 7. Now that you DO have a fit, you can and should bid 4H!