I do quite a bit of coaching on BCL! One could discuss whether my idiosyncrasies should be broadcast, but my coachees do improve, so it can’t all be bad. A number of players wanted to know more about LTC (Losing trick Count) and LOTT (Law of Total Tricks) and I started a number of threads on the Comment board where we discussed them. This article is a rewrite of those threads.
LTC applies to suit contracts where you have an 8 card fit or better. On balance you can have up to 3 losers in a suit, since the 4th card will either be a winner or can get ruffed. This means that your total LTC with partner will be 24, and if you're unlucky enough to hold a 24 loser combination opponents can make a grand. Each time you have an A, K or Q in a suit you have hopes for a trick with this card, so you can subtract 1 loser. If your side has 6 of these cards you can take 6 tricks and your LTC is 18, and if you have 7 then you can make a 1-level contract with a LTC of 17. This leads to the first and fundamental rule:
Subtract your side’s losers from 18 and that is how high you can bid. eg you have 8 spades between you and a LTC of 14 then you subtract 14 from 18 and bid game.
How do we use the theory? A minimum opener has 7 losers (weak NT usually has 8 though). We count our losers by looking at the first 3 cards of each suit in turn subtracting one loser for each A, K or Q held.
xx AQJxx Kxx Kxx has 2 1 2 2 =7 losers and is a minimum opener for example. We've opened on point count since LTC doesn't kick in until we have a fit. Now suppose partner bids 2H in response. A single raise shows 9 losers and partner will have used LTC not points to make this call. eg. x Kxxx Jxxx xxxx is an obvious 9 loser raise of a 1H opener (1 2 3 3).
You as opener now know partner has 9 losers, you have 7; so you have 9+7=16 losers. 18-16 is 2 and that's the limit of your hand.
Bid this: x KQxxxx Axx Qxx. It goes 1H 3H, what should you do? Partner has shown 8 losers by jumping to 3H and you have 6 (1 1 2 2). 8+6 is 14; 14 from 18 is 4, so you bid game. "But I only had 11 points!". Well, you can stay a diamond ranked player all your life if you want, but this is a totally clear-cut 4H bid in my mind.
It's not failsafe, but it's way better than miltons for bidding "fit" contracts
Adjustments can be made to your LTC by up to one loser.
Good things; 2 Aces, no Queens; AJTx(x); a 9th trump
Bad things: 4333; 5422 where your fit is in the 5-card suit; 2 unsupported Q's; Qx
It’s not an exhaustive list. Nett the good and bad things off and adjust your LTC.
1H from partner; xxxx Axxx xx Axx 3 2 2 2 =9, subtract one for 2 Aces (treat the trump K as an Ace for this purpose). 3H is clear. Now look at the opener just above. You've just bid a 19 point game on a finesse for the CK. Opponents are close to 4S too. "What can we do if they bid a 19 point game?" opponents say; shrug politely and suggest you just got lucky; you don't want to tell them that it's completely routine do you?
Klinger earns millions writing 120 pages on what you can read here for free in a page.
In 1960 a Frenchman, Verne, wrote a monograph pointing out that the total number of tricks (TNT) is directly related to and equal to the length of the best fit for each side. To explain further: If we have 9 diamonds and they have 9 spades then the TNT is 18. If we can make 10 tricks in diamonds, then they can make 18-10 = 8 tricks in spades, but if we can make 7 tricks in diamonds then they can make 18-7=11 in spades etc.
Once it's pointed out it is sort of obvious; since if both sides have 4333 hands and a 20 count one would expect each side to be able to make a 1-level contract in their 7 card fit. For each card more in the best fit we will subtract a loser, as will they, and each time we transfer a loser from one side to the other the tricks make-able will go up by one for one side and down by one for the other.
As ever, it's not failsafe, but it helps in your judgement.
In this case Larry Cohen (as opposed to Klinger for LTC) made millions of bucks writing a 120 page book about it when you can read it all here for free, in one page.
How do we use TNT ?
Start at the beginning: If both sides have an 8 card fit and a 20 count both sides can make 8 tricks, but we don't care about that. If LTC tells us we can make 9 tricks and we know both sides have an 8 card fit then opponents can make 7. If they bid at the 3-level, you double. it's simple; they're 2 down and this beats any partscore. What you have to do is to draw up a matrix of the TNT's and use your own LTC to tell you how many opps will make. Your strategy is simply to pass, double or bid one for the road depending what the Matrix says. This is tedious to do, and so we came up with a rule of thumb, which is a distillation of this maths. "At equal vulnerability, bid the level of your fit". So, if we have a 9 card fit, at equal vulnerability, we should bid at the 3-level in competition. Obviously we bid game if LTC=14) but LTC is irrelevant in the sense that either we’re profitably sacrificing or it’s make. We get payback by doing this.
This is why experts, at equal vulnerability, routinely raise partner's overcalls with 3 and jump raise with 4 with no reference to their playing strength. Partner shows 5 for a 1-level overcall and 6 for a 2-level overcall (ok, keep overcalling at the 2 level with your Qxxxx suits, I'll kneecap you whenever it's right) and so a 3 card fit tells you to make a raise with 3 and you're protected by LOTT, since you have competed to the level of your fit. Partner should re-raise holding a card more than promised, and again this is done with no reference to playing strength.
We need to adjust when vulnerability is not equal. At favourable overstate your raise by a trick; at unfavourable understate the raise by a trick; and this caters for being doubled when opponents have game.
In summary, LTC tells you how high to bid for a making contract; LOTT then tells you what opponents can make (assuming you can guess each side’s degree of fit), and tells you how high it's safe to go to save.
In a separate thread on negative double I advocated rebidding 1S on a 3 card suit (and 2S with 4) when I've opened and the auction proceeds 1C (1H) X (P), it's a LOTT competitive auction, we are LOTT protected at the 1 level with a 7 card fit and at the 2-level with an 8 card fit. So I've bid the level of our fit in competition, and I do it immediately, to stop any further nonsense from opponentss.
I wrote the following dissertation for a semi-regular BCL! Partner and it logically slots in here. It’s a bit more advanced than the stuff above.
There are 4 names for the players round the table:
Opener & responder; overcaller and advancer;
There's also balancer (and probably advancer
to the balance, but don't advance my balancing)
When partner overcalls he shows 5 at the 1-level and 6 at the 2 level. He may not have it, but that's his funeral.
LOTT therefore says that at equal vul advancer should raise with 3 and jump raise with 4, almost regardless of his hand. You should adjust up or down 1 at unequal vulnerability, but it takes practice, as partner will have done so too given the vulnerability. This means advancer's raise is pre-emptive; what does he do holding a sound raise?
Bid 2N (which is inconceivable to be natural) holding 4
Cue LHO's suit (again can't be natural) holding 3.
It doesn't matter whether the overcall is at the 1 or 2 level, or whether a major or minor, it always holds true. Just look at what LOTT says/does and it's totally logical.
Wabbits just don't understand the need for these raises as a PRE measure, and back in on the next round. Now your side knows exactly what the LOTT is, and your side's expectation. The double when right becomes obvious.
You can use the methods facing balancer, but remember you must transfer a king and a card as partner will protect 1 card short and 1 King light. My partners have learnt that when I balance, I've bid all the points and cards in their hand, so the only excuse for bidding on facing balancer is extreme distribution balancer didn't expect. (I'll protect with 2S on 3 cards sometimes to give an idea, since a double would show 4)
At this point I also looked at how to respond to an opener. If one is playing 5cM then responder should also use the same methods facing a major opener, and many 5cM players do this: J2NT, UCB, PRE raise etc, but tend to use it badly. In competition or by a passed hand JS should be played as fit-jump (5 of mine, 4 of yours), and 2N as a sound raise of any opener. There are almost NO hands where you should EVER play in 2N, and even fewer where opponents have bid.
It's more interesting playing 4cM, as the LOTT is less clear. You should assume partner has 5 in a major in competition and 4 in a minor though. Acol players play J2N as a 3+ raise, rather than a GF for this reason.
Finally LOTT explains why one should play the transfer break over 1NT. You are LOTT protected, and don’t mind whether the transfer was weak, in which case it’s an advance sacrifice, or invitational in which case the contract makes.
Chienfou March 2007