Questions and Answers

We can't respond personally to all e-mails, but if we find your question interesting we will post it here for everybody to read. If you don't want your name published, just include a signature.

If you want to submit a deal for us to analyze, use the link "Deals" in the left frame instead. There, too, you may use a signature instead of your name.

I am curious to know what probability distributions were used in the computer programs that generated the sample hands used in your analysis. Computers typically use pseudo-random sequences designed to generate random numbers that conform to a uniform probability distribution, and my assumption is that the hand generation programs use these generators to create sample deals. Does this mimic the real-world setting where cards are shuffled by people, especially in matchpoint events where the decks of cards are assembled from boards where the hands are typically not organized in a truly random fashion? It occurs to me that this could skew the statistics, although I have no idea whether this has any chance of being significant.

In our analysis we have used mostly deals generated by computer programs. The mathematicians say you have to shuffle a deck six or seven times; otherwise, you will get more balanced distributions than the probabilities say you should. Most people don't. So if you shuffle manually, the resulting deals will often differ from deals generated by computer programs. We haven't taken that into account in our work, simply because it is difficult to add that factor to the equation.

I'm not extremely experienced but I can see how your book affects some current popular bidding methods.

One of the most widely adopted uses of The Law is bidding systems designed entirely around The Law. Countless players play Bergen Raises, and it's the best example to critique here.

I can't help but wonder what kind of bidding conventions could arise as a result of the SST and WP method. WP may be guess work at the table (one challenge is estimating how many WP one has when there isn't interference – do you subtract an average of a trick knowing that chances are one finesse will fail or one A is behind a K? I can see people plowing on to 4S with 21 points and an SST of 3 and getting mad because a finesse fails, reducing the WP value and wondering what went wrong). If nothing else you two have created more reason for ad nauseum post mortems. However, SST and WP makes Bergen Raises essentially worthless. Distribution means more than knowing the difference between an 8 and 9 card fit. Now you and your partner are concerned with singletons and doubletons and how many points more than your suit. The reason they seemingly work is a 9-card fit will introduce more distribution than an 8-card fit, I'm guessing.

The ultimate question I would have is, "Have you introduced or changed any bidding conventions as a result of this book, and what are they?" This is obviously a question a lot of people will have and a crutch too many people will rely on instead of their own judgment at the table. However, it has worth, and I'm interested in to see some insight on the website.

It may not surprise you that none of us is a fan of Bergen Raises, and that we would very much prefer to use 3C and 3D in their natural sense (invitational or strong with a good suit).

There are lots of situations where SST thinking can be applied. We will name one. Say that the auction starts 1C - (pass) - 1S - (2D); ?

Instead of using double and 2S to distinguish between your number of spades, might it not be better to show whether you have a good raise or a weak one? One idea is to use double to show either a minimum raise, with a SST of 6, or a strong hand with a SST of at most 4 (responder expects the weaker variety, so if opener has the strong type he takes another bid), while a raise to 2S shows a STT of 5. Since you have the option of jump raising partner with four-card support, if you double and have the strong type, you have precisely three trumps. For hands with an SST of 5 or 6, you can have three- or four-card support.

West	North	East	South
	pass	1	2
?

What call should West make, and why? Do you think this is a close decision or clearcut? If you invite and the opponents then bid 4H what do you do then?

This is my personal analysis. "The law" (in simple-minded form) says "10 trumps = 10 tricks", but 5332 plays crummy if pard also has 5332 (you can ruff a lot except there's nothing to ruff) and you have 3 losers in the opponents' suit. So personally I'd invite rather than jump to game. (Most people probably play 3S = weak these days so the invitation would probably be a cue bid rather than a jump to 3S, but I'm sure every pair has some way to invite.) Also, I suppose if the opponents bid 4H I'd bid 4S (too chicken to let them play a vul game) even if pard passed by invitation or passed over LHO's hypothetical 4H.

We agree with your valuation. This hand is worth an invitation only. Assuming your 8 HCP are 8 WP, we will reason like this.

We know that our SST will be at worst 5. But that only happens if North has 5-3-3-2 with the same doubleton as you. Since expecting that is overly pessimistic, we assume that our SST will be 4 or less (partner is twice as likely to have a doubleton diamond or heart than a doubleton club). To make a game then, partner needs 15 WP or more. Alternatively, he may have a red suit singleton, so that our SST will be 3. Then, a minimum opening will be enough for game. In both cases, partner will know that he should bid 4S. No need for us to bid his cards.

If you should bid 4S over a potential 4H is not so clear. True, 4S won't be very expensive, but going -100 (or rarely -300) instead of +100 (or +200 if you dare to double), is costly at any form of scoring. Heart bids by the opponents increase the chance that East has a singleton there, but then why didn't he bid 4S all by himself? Suppose his reason for passing over 4H was that he had wasted values in their suit. Then, your jack of hearts may play a big role on defense against 4H.

The first part of the book is all about how THE LAW does not work. If the reader accepts that premise, then there is no need to have it proven over and over.

I would have organized the book with the new law in front and the discussions of the old law in the back.

Not everybody who buys the book knows what the Law of Total Tricks states and how it is supposed to work at the table. And even fewer people know the correct figures for how often total trumps really equal total tricks. Therefore, we decided to present the material in the order we did.

I very much enjoyed the book. And I also agree with the concept. I think it was important to first systematically demolish the LAW, so the reader could accept a new concept. I think it was necessary to show the strengths and weaknesses of both systems, so no one comes away thinking it's a hatchet job on the LAW. I have begun using your system, and its quite easy. (I posted a brief over view on Bridge Base on line, and have already dueled with an advocate of the LAW.)

The one part of the book that might have been made a little clearer, is the part where extra WP are awarded for a long side suit (3 per extra card), and 2 for the Jack. While the concept is not difficult to understand, there are some contradictory examples (I think) in your book. On the one hand the QJ may be wasted if our side has 10 cards, headed by the AK. But having a long side suit (perhaps AKxxxx opposite xxxx) should be valued at 13? 4+3+6 (3 points per extra card beyond 4). I think on one page you mention the QJ as being wasted, but on another award extra points.

What I've already been thinking about is bidding conventions that would replace Bergen raises and instead show shape or some other useful attribute. I'd very much like to see articles on new conventions.

To be fair and objective is important. That is also why we started this site, where we hope we can explain some of the finer points, present new ideas, correct errors, expand the discussion, etc.

In our answer to Question 2 (see above), we gave one example of replacing a trump-counting convention with one stressing the SST instead. There we suggested that in a sequence like 1C - (pass) - 1S - (2D), opener's double and 2S could be used not to distinguish between three and four trumps but to show whether opener is strong or weak. According to this New Law Double, opener's double shows either a weak minimum hand (an SST of 6) or a hand with an SST of at most 4 (responder assumes the weaker type, so opener will take another bid with the strong hand type), while 2S shows a good minimum (an SST of 5).

We are sure we will see more ideas eventually, and we might even write a follow-up book with conventions that can be used together with WP and SST.

We're sorry if we haven't been clear enough on the concept of Working Points. We will explain it more carefully on this site, so hopefully everything will be clear in the end. In the example where you had ten trumps headed by ace-king, the queen and the jack aren't needed most of the time. That is true. But you still have 10 WP in the suit. What we meant to say whas that if you have ten or more trumps, the queen and the jack aren't needed to bring in the suit – it would have been better for your side if they had been in a side-suit instead. But we didn't mean you should downgrade those honors to 0 WP.

When you have a side-suit of ace-king sixth opposite four small, which breaks 2-1, and the suit gives you two useful discards, the suit is worth 16 WP. First, the 2-1 break means you have the equivalent of 10 HCP in the suit, and then each discard is worth 3 WP.

If you count HCP, you might wonder why these 21 HCP produce twelve tricks in a spade (or club) contract. But with our concept, everything is easy to explain. To begin with, EW's SST is 4, no matter if they play in spades or clubs. If clubs break 2-1, EW have 24 WP without discards, but since they can win the opening diamond lead with the ace, draw trumps and discard two losers on dummy's long suit, we add 6 WP for those two discards. The resulting 30 WP in combination with an SST of 4 says "12 tricks", and that is precisely what it is.

So the correct description of the deal is that with 30 WP and an SST of 4, East-West took the expected twelve tricks. Since it didn't matter if they used their eight spades or their ten clubs as trumps, the deal is also another illustration to the fact that the number of trumps and the number of tricks are not connected.

Now assume clubs are 3-0 and spades still are trumps. On the same diamond lead you win the ace, draw trumps and play on clubs. The bad split means that when you give up a club, the defenders cash out. This time you only take nine tricks. And once again that can be explained in terms of WP. Now you don't "own" the queen-jack, so you only have 7 WP in clubs; and since you can't use the two long cards for discards either, the fifth and sixth clubs aren't worth anything. In that scenario you are back to 21 WP and an SST of 4, which is the same as nine tricks.

I just finished reading I Fought the Law of Total Tricks and loved it. I believe it will improve my competetive bidding.

I have found it easier to work with Odd Tricks as opposed to tricks we can take, where OT = WP/3 - SST. This gives exactly the same answer provided that you remember to always round up after dividing by 3. OT = Odd tricks or Tricks - 6.

So in fact I calculate OT = (WP + Adj) / 3 - SST. First adding either 0, 1, or 2 so that the adjusted WP is exactly divisible by 3. I find this easier and faster than trying to remember the plus or minus adjustment tables. Anyway it seems to work better for me.

Example: with 16 WP and 3 SST. (16+2) / 3 = (6-3) = 3 OT, or we should be able to make a 3-bid. Or if you prefer: 16/3 = 5 1/3 rounded up to 6. Less 3 SST = 3 OT.

Once you realize that how many tricks one side can take is a function of their distribution and working honors, you are on the right track. All roads lead to Rome, and it is possible to come to the right conclusion in many ways. Your suggested method sounds excellent to us, and if you prefer it to ours, by all means go ahead and use it.

The base for our method is "If we have half the deck in working points, we will lose as many tricks as our SST. For every full 3 WP more than average, we deduct one loser; for every full 3 WP less than average, we add one loser". In your example (16 WP and an SST of 3) we would think "16 WP is a king below average, so we will lose one more trick than our SST. Four losers = nine tricks". We find this simple.

If you take a look at our next question, you will find another proposed method of counting your tricks. That one is excellent too.

In your book you have a few examples where you add three or more WP for long cards in a suit (see Pages 140 and 143 for examples). Are you recommending that this be done as part of hand evaluation whenever you can anticipate that a suit will be a source of tricks? If so, would the rule be something like "count a jack as three points, and add three additional points for each card beyond four in a running side suit"?

I believe I have a simpler method of counting tricks that in each case I tried came out to the same number as with your method:

Assuming that works, I find it an easier calculation although others might prefer the approach in the book.

Now turn to East. He's heard his partner come in with 3H and he's looking at 16 HCP. Should he go on to 4H? He has 13-15 WP (the club jack is worthless, the diamond queen may be), and he can be fairly sure his partner has no more than 5 or 6 WP. The partnership might have 19 WP, but it might not. If he assumes West has a doubleton spade but no other useful doubleton, East's calculation would be 13 - 4 SST = 9 (or my way, 7+2 for the doubletons = 9) with perhaps - 1 for fewer than 19 WP. Clearly, 3H is high enough.

Even though some of both East's and West's assumptions were slightly wrong, the errors pretty much cancelled out. As the cards lie, the diamond king was onside so 3H just makes while 4H has no play

When you have a long suit and know you can use it for discarding losers from the other hand, you should of course take that into account in valuing your cards. If these long cards take tricks, they should be valued as tricks, i.e. 3 points each. Therefore, we agree with what you say about long side-suits.

Regarding your proposed method for counting your tricks, we refer to our answer to question 6 (see immediately above). Your method is excellent. It is just as good as ours or the one suggested by Ben Hooyer. But we still prefer our own "If we have half the deck in working points, we will lose as many tricks as our SST. For every full 3 WP more than average, we deduct one loser; for every full 3 WP less than average, we add one loser".

In your example, we might not have doubled 1NT for take-out with the East hand (we hate doubling with wrong shape unless lots of extra values, especially when both opponents are bidding and haven't found a fit), but once we have, going on to 4H is too much. East has no reason to expect more than their share in working points and an SST of 4. It might even be worse. Pass is indicated. As it was, East had 15 WP but West only had 1 WP. The black queens and jacks were all useless, the diamond queen might have been also. That they still took nine tricks with an SST of 4 is because of their third (useful) doubleton, which adjusts their SST to 3.

[The following questions come from the same person, sent to us in one mail. We have split it up into five smaller parts, to make it easier to see which answer refers to which question, and we have called the parts Question 8a, Question 8b, etc.]

Let me say up front that I am a user of The Law but have had healthy skepticism of it and I am not an apologist for it.

My criticsm of the book is not so much with the analysis – but on presentation. As another person wrote and you posted on your site, you'll forgive me if I say that the first 125 pages of your book is a waste – of my (and I suspect 95% of any reader's) time – and damn frustrating. That could have been summarized in three short lines:

Also, you seemed to go out of your way to attack Larry Cohen (outwardly in the first part of the book and coyly regarding 4-card overcalls near the back). Doesn't make you guys look good at all. Not classy. Attack the idea, not the person, especially in public.

We are sorry if you think we have attacked Larry Cohen. I can assure you that we definitely didn't mean to. We have tried to discuss principles and theories, notpersons, but since Larry has made a lot of claims in print, which can be shown to be false, we simply had to say so. Is that an attack?

I see no clear, simple, definition of Working Points. Where does it say: Working Points are such and such? This is how you figure them. Instead, I get (forgive me) rambling notions of Building Up AQxxxx vs Kxx to 10 working points for no other reason than you say so (yea, the J). The PRESENTATION is poor.

HOW WOULD YOUR ANALYSIS BE AFFECTED IF YOU ADJUSTED DOWNWARD FOR WASTED POINTS TO ARRIVE AT WORKING POINTS INSTEAD OF ADJUSTING UPWARD (AS YOU DO).

Wouldn't that be more in tune with our intuitive feeling that we want to eliminate wasted points from our calculation such as when we have Qx in an opponent's suit that has been bid and raised? But if you keep your upward adjustment approach, at the very least, may humbly suggest that you rename Working Points, INVISIBLE POINTS, cause that's what you're really talking about, both in terms of high cards that aren't there and length tricks, when absolute winning high cards are not there as in a AQJxx vs. Kx in a side suit. It would give the reader a much better feel for things.

Since nowhere in the book do I find a definition of Working Points, let me try one: WORKING POINTS = actual high card points + Invisible Points - Wasted Points

Invisible Points = High card points in your long suits that you don't actually have but your suit will play like you have them or small cards in (semi)solid long side suits. Wasted Points = High card points you do not expect to help you win tricks.

We have written more on working points here on our site. Sorry if we haven't made ourselves clear enough on the subject in the book. Working points isthe sum of the honors, or spot cards substituting for honors, whichtake tricks on offense. If we have, say ace doubleton opposite five smallin a side-suit and have the time to ruff out the suit (it is 3-3) and get two useful discards, those two extra winners are worth 3 WP each.

The way we count will most of the time lead to the correct result (When it doesn't, it has to do with the relation between working aces and working queens. We will discuss this topic more in detail on this site. It's not up yet, but it comes).

Your definition of Working Points sounds good to us. If you read our book carefully, you'll find that this is exactly what we say – so how could we disagree!

Suppose we use the best judgement we can using WP and SST + experience + knowing that xxx in RHO's suit is bad + devine guidance, etc. What is the highest "batting average" we can expect to attain in competitive situations? Suppose we got 3 out of every 4 or 4 out of every 5 correct? That wouldn't be too bad, would it? But that is what YOUR DATA suggest would occur if we simply followed The Law!

You say that 16 and 17 trump hands occur a combined total of 49.78% of the time (page 22). You make a big deal that on 16 trump hands, the Law is only right 44.1% of the time (p.32). But that is not the point. Your table on p. 32 also tells us that with 16 trump (a mandatory 8 and 8 situation you say) that the total number of tricks is 16 or greater 77.8% of the time. Doesn't that strongly imply that it would be winning bridge to bid "3 over 2" even with only 8 trump and virtually never let them play at the 2-level. Even if they can make 9 and we make 7, they have to double before it becomes painful (assuming NV - you don't have to be suicidal when vul).

When there are 17 trump, your table on p. 33 tell us it would be OK to bid "3 over 3" 72.3% of the time, since someone could make at least 9 tricks that often. Even with 18 trump which occur 15.65% of the time, your table on p. 34 says that following the law by bidding would be right 68.8% of the time. Still not bad.

If we take all three where there are 16, 17, and 18 trump (which occur a combined total 65.4% of the time), bidding-on based only on trump length would get you a good result an average of 73% of the time! My bidding decisions should only be this good! So, unless I have missed something terribly, it seems to me that the Law may not so terrible a guideline to follow after all.

Can SST+WP do better than 73%. If it can, you haven't proven it. You've used anecdotal examples. Why not go back and do the same simulations that you did for The Law and see if your way works more than 3/4 of the time. Shouldn't you have done this from the beginning? Why do we have "Actual Data" to denounce the Law but only anecdotal examples to support SST and WP?

With the Law seemingly correct 73% of the time when it tells you to bid, you might say, OK, when the law tells us to bid, maybe we should listen to it, but what about when it tells us not to bid. In those cases, we'll be wrong way too often. You could say that, but in fact on page 102, you conclude exactly the opposite:

"In my observation, if The Law tells you to bid, you can find a valid reason to pass fairly often. If the Law tells you to pass, it is usually right to do so." Isn't that in direct contradiction of the data about the Law you present? So, as I say, I'm confused. I know you guys have been looking at this stuff for a long time and I haven't. I respect that. But: What am I missing?

We're glad you brought this up, because it gives us the chance to kill another of those Law myths. You say you get "a good result 73% of the time by following the Law". But is that so?

Just because there are, say, 18 trumps and 18 tricks, both sides having nine trumps, it doesn't automatically follow that you will achieve "a good result" by following the Law and contracting for nine tricks. Some of the time your side can take 8 tricks in hearts and they ten in spades. If they bid their cold 4S, what good did your competing to 3H do? How can such a deal possibly be labelled "a good result"? When the truth is that it's indifferent, or even bad: if your bidding 3H helped them in bidding a game they wouldn't have had you been passive, it instead produced a terrible result.

And if your side is the one taking 10 tricks, what good is it infollowing the Law and contracting for nine tricks? We much prefer+420/620 (or +300/500 if they save) to +170. Don't you?

In his study in The Bridge World (we mention it in our Statistics section), Matt Ginsberg came to the same, false, conclusion.

Suppose both sides are vulnerable and the opponents bid 4H. Expecting 18 trumps, you follow the advice of "always bidding 4S over 4H". You get doubled, run into two unexpected ruffs and concede 1100. Yes, the opponents could make 6H for 1430, but if it's pairs and nobody else has bid the slam, or if it's IMPs and your team mates only play game, does the fact that the opponents can make a small slam make your result any better? How can such a deal be called "a good result" just because tricks and trumps were equal?

And if we take a more mundane example, where the opponents could have made their contract, for +110, is your going -100 such a hot result? At pairs it might be, but at IMPs the result is a wash. Yet another indifferent result – but the Law pats its back and says "a good result for me!".

And how about the case where you have ten spades and they eight cards in both minors? Even if there are 18 total tricks, what's "good" is it in playing 4S down one, when you actually owned the hand in 3S? Or go two down in 4S doubled when all the opponents could make was +130? In both cases, the deal was according to the Law, and still it was BAD to follow the Law.

Finally, there are the cases when you will make your contract but you would have been better off defending – either because there were fewer tricks than trumps (the remaining 27%) or that you will make an overtrick in your contract. Suppose the opponents bid 3C. Your side has nine diamonds and competes to 3D, making ten tricks. Then, if there were 17 total tricks, it would have been better for you to double them (+300 or +500) or even pass if they were vulnerable (+200). Once more the deal is included in the "good cases", even though doing the opposite would have been better.

The most important thing in competitive auctions is to avoid going minus when you could have gone plus. Results like -100 instead of -110 aren't worth much. But +110 instead of -110 is, just like +100 instead of -100, or if the contract is doubled +200 instead of -500 or +300 instead of -300, etc, etc. Our method concentrates on what one side can do. Therefore, we are in a better situation to judge than the Law who looks at the total, then tries to guess how the tricks are divided.

Our rule of thumb for part-score battles is: "If your estimation says your contract will make, go ahead and bid it – to avoid defending when both contracts make. But if your estimation says your side will not make your contract, don't bid it – to avoid declaring when neither side makes their contract."

Your analysis of SST looks like an extension of Loser Count (with a dose of judgement thrown in) – but you don't say so or give credit to Losing Trick Count Analysis. Just as you say on page 130 and elsewhere, balanced hands with nothing constructive to ruff require extra high cards. So does Loser Count.

Example: As you know, a 4333 hand with 0 HCP has 12 losers; opposite another 4333 zero-count that would mean 24 losers. Replace one of the 4333 hands with a 5521 hand with 0 HCP – it has 9 losers for a total of 21 losers – a difference of 3. Opposite another 4333 hand, 4333 has an SST of 6 and a 5521 has an SST of 3 – a difference of 3. See what I mean? So maybe without meaning to or realizing it, your SST analysis is a rehash of Loser Count. That doesn't make your analysis bad, it just makes it not new.

The Losing Trick Count (LTC) is one of the best ways of valuing your cards, but it suffers from one serious flaw. It looks at one hand at a time, instead of both together. That is the BIG difference between our method and LTC. Suppose you have 5-3-3-2 distribution with all the spade honors. That is 8 losers. Your partner has 3-4-3-3 distribution with all heart honors. That is 9 losers. 24-(8+9)=7, but these two hands take 8 tricks. If we change the second hand to 3-5-3-2 we cut one loser and get to a correct result (8 tricks), but if we change it to 3-5-2-3, the LTC formula says 8 tricks, but now it is 9.

In these three cases, LTC predicts right only once, while our formula gets the correct result each time, since SST will be 5, 5 and 4, respectively – giving a prediction of 8, 8 and 9 tricks.

Even if our method discusses losers, just like LTC, it is not a copy. The concept is original, and it is new. Some of our (wellknown) readers have even called it revolutionary...

On page 101 you warn that if you have wasted points in the opponent's suit, (the example you give is Qx) you state very emphatically that this STRONGLY (your emphasis) indicates that partner will be minimum for his bid. You state this but don't explain why you believe this is so. Could you help? Is it so obvious that it needed no explanation and Mel just doesn't see the obvious?

where you open 1S and they overcall 2C and raise to 3C. You say there's nothing to guide you but judgement as to bidding 3H or not. For many years I have beentelling my students about Mel's Compete Count for exactly these situations. It is a rudementary rule but it gets them in the right ballpark. It utilizes Loser Count. MCC says you figure out Losers by Loser Count and Subtract 1 – that tells you how many tricks you can contract for while going it alone. In this example, we have 5 losers by LC-1 so we have 4 estimated losers and therefore 9 estimated winners, so we bid 3H. And as you say on page 147 it is based on the sensible wish that partner fits one of your suits. It also wishes that partner has a little something – 1 Cover Card, to use LC parlance.

Forgive us for not being more explicit. If our opponents compete for the contract, we can expect them to have some values. If we have wasted honors in their suit, it follows that their share of the points consists of other honors. Had we had two small in their suit instead of Qx, for instance, they could have had that queen. Now they have some other honor(s) to make up for their missing queen, which tells us that the chance that our partner has an unexpected useful honor is smaller than when we have nothing in their suit. It's not a paradox, even if it sounds like one. Better to have 11 HCP with two small cards in theirsuit, than 13 HCP with queen doubleton in their suit.

Mel's Compete Count is surely a good rule, both to teach and practice. Stick to it.

February 2005 Master Solver's Club Problem C:
Matchpoints, N-S vul
You, South, hold

West	North	East	South
	1	pass	?

None of the 28 panelists bid beyond 4S (the plurality bid chosen by 12). Why does nobody cite a "Law of Total Trumps" conclusion that it is safe to bid 6S?

They sure do. We once saw a famous author give roughly this example (East-West vulnerable):

West	North	East	South
			1
pass	1	1	2
?

He recommended 4S: "With ten trumps, just bid at the ten-tricks level!"

We approve of the bid, but not the reason. We bid 4S because of our great distribution. If the number of trumps was our only concern, then the following hand would also be OK for 4S vulnerable against not:

[The four following questions are a follow-up to our answers to questions 8, all from the same person. We have once more split it in parts: 10a, 10b, etc.]

You didn't answer perhaps my most important question. Why do you use statistical analysis to dubunk the Law and then use annecdotal evidence only to trumpet WP+SST? Where is the data that proves that your way of predicting how many tricks your side can take is accurate? I need to know what % of the time it is dead-on, what % of the time it is off by one trick, two tricks etc and in which direciton. And in the same way you did it to debunk the Law, i.e, [say] 250 deals when you are predicting 8 tricks, 250 more when you are predicting 9 tricks, etc. Why isn't such data presented? How can it not be there? Without presenting it, (A) we just don't know if your approach is accurate and (B) you give an analyst like me the impression that your real goal is just to debunk The Law and not to uncover Truth. In my heart I don't believe that's your purpose but...

To see how often the Law is right is (relatively) easy, since all we have to do is check whether total trumps equal total tricks. As shown, it happens roughly 40% of the time, given that both sides play in their best trump suit, and from the right side (if not, the hit rate falls a few percentages).

With all 52 cards on view, our WP+SST formula will be right on target almost always. There are a few exceptions, which we will tell you about on this site, but they are few, so if we say that our formula will be correct more than 90% of the time we are on the conservative side.

It's no secret that we either take tricks by power (honors) or with aid of our distribution (ruffs or long cards in side-suits). Therefore, it can't be surprising that a formula based on those concepts will predict more accurately than a formula which stresses a factor (the number of trumps) which sometimes is useful, sometimes not.

You say: If 18 trump and 18 tricks, 9 and 9, it doesn't follow that bidding on automatically give you a good result. You say if my side can make 8 tricks in H and they 10 in S what did your competing to 3H do? The answer to that is: If they can make 10 tricks in S, presumably they will bid 4S on their own whether or not you bid 3H. Your bid of 3H is irrelevent. You have defended your position by presenting an irrelevent case! So, when I said that following the Law would seem to get you good results 73% of the time, I meant that by doing so, we would achieve par or better on the board. In this case you cite, we would achieve par, because they were on their way to 4S anyway.

Mel says: The only time the Law is wrong is when it produces a bad result. It is not wrong when it produces an indifferent result.

Mel says: Every bridge hand has a Par. In competitive auctions, the objective is to equal Par or beat Par. On any hand, any mechanism or system that leads us to achieve either of those goals is to be considered a successful outcome.

If you don't like our example of a Lawful 3H pushing them up in 4S (which probably isn't as rare as you think it is), say that you have spades and they hearts. If you pass over their 3H, they may be satisfied with that, but if you compete to 3S they may take the push hoping that either side makes its contract.

When we say the Law is wrong on a given deal, we mean that total trumps and total tricks are not equal. But when you write "the Law is wrong", we assume you mean "following the Law is wrong". But if you contract for as many tricks as your side has trumps, you are not assured of "beating or achieving Par" even if total trumps equal total tricks. Part of the time your result will be good, part of the time it will be indifferent, and part of the time it will be bad.

A priori our goal on any bridge hand is the one you state: to equal or beat Par. We agree with you there. But when the bidding becomes competitive, objectives change, and sometimes Par is the worst result you can achieve, for instance when you can double the opponents for +500 or pass and collect +200. If you follow the Law with your nine trumps and score +140, why do you consider that to be a "good" result?

Regarding going for 1100 on ruffs after bidding 4S over 4H in a Lawful manner, when they're on for 1430 but slam isn't bid: Are you saying that bidding 4S was wrong because we ran into unexpected ruffs? What happened to the luck factor you speak of in your book? It certainly isn't a great Law result; but it isn't a bad one as you've implied; it's just an unlucky one. You go on to cite a more "mundane" example of going -100 vs their +110. You say Law people call this a good result. Mel calls it a Par result (imps), therefore a good one.[you conveniently ignore, of course, the real world possibility that when we bid over their 110 contract, they may go one higher and go minus].

Nobody can deny that luck has a role to play. And we would never dream of saying stupid things like "just follow our recommendations and nothing bad will happen to you". Bad things do happen; and even if your decision was excellent, it may turn out badly due to unforseen good or bad luck.

When the opponents bid on and go minus instead of plus, you obviously have a good result. But you mustn't forget that such things happen both when you follow the Law and when you break it. If we have eight hearts and bid 3H over their 3D, which pushes them to 4D down one, when 3H also would have been one down, our 3-over-3 with eight trumps has beaten Par. Following the Law by passing over 3D wouldn't have.

There is another real world possibility which you didn't mention, namely that if you bid over their +110 contract, they may double you for +200 or more.

Your final case is where you say bidding on is OK – you'll make your contract but it would have been better off to defend – either because there are fewer tricks than trumps or that you will make an overtrick. If there are fewer tricks than trump ("27% of the time" you quote me), it is conceded by me that following the Law is the losing option. Using your example, letting them play 3C for down 2 would be better for us.

But you have missed the obvious! If we can in fact make 10 tricks and we follow your advice, we should be using SST and WP and figuring we can go plus in 3D, you say we should bid 3D! You say there is an opportunity cost in using the Law in this case, but the same opportunity cost exists following your methods! Rememer you said in response to my last e-mail:

Our rule of thumb for part-score battles is: "If your estimation says your contract will make, go ahead and bid it..."

Yes, we would also bid 3D and miss the opportunity ... unless we did a similar analysis for the opponents and it showed that they were almost sure to go down. Then, we might rethink.

You point out in your website that such fits help the opponents in the sense that they are assured of an SST of at most 4. On the other hand isn't there something very positive about double fits?: honors in the two suits in question are very likely to be working.

Then I wonder about the three hands on page 244. You showed that Hand #3 produces about 2 tricks more than the others. To be consistent with your methods the North-South SST in this hand should therefore be 2 less than that of the others. However if East-West have a 9-card heart fit, it seem to me that the SST in Hand #3 is actually 3 less. Could you please enlighten me about this?

When you have honor(s) in partner's suit, those honors are very often working, giving your side more WP than if your honors are in the other suits (where they may be useless). And length in partner's suit may also be positive, like when you need five tricks in his ace-king-queen fifth suit: you are more likely to get those tricks if you have three small than if you have two small. So having length in partner's side-suit can also be positive for offense.

But quite often a doubleton in partner's suit is better than a tripleton, because now you can avoid a third-round loser, may ruff out the suit, and are less likely to run into a ruff. We think the negative and positive effects of our double fit even out each other, but if we look at the other side's double fit, it has only positive effects for us.

Your second question is important. Yes, hand #3 has an expected SST of 2, while the other hands have an expected SST of 5. The reason the difference is only 2 tricks, not 3 as you may think, has to do with two things. Firstly, when your distribution improves, the risk of partner's having wasted values in that suit increases. If he has, say, KJxx of diamonds, they represent 4 WP opposite Hand #2, but 0 WP opposite Hand #3. On average, you can expect more WP from partner when you have a balanced hand than when you have an unbalanced. Secondly, partner is more likely to have extra distribution opposite the two first hands. A singleton heart, or a singleton or doubleton in either minor, reduces your SST to 4; and if partner has even better distribution than that, you can come down to 3 (heart void, or minor suit singleton). But to better your SST is harder when you have hand #3 (partner needs a heart void or at most two clubs).

I very much enjoyed reading I Fought The Law. The Law definitely has its shortcomings, as you show here.

The only problem I find with your method is estimating your WP, but it may be nice that judgment is still needed. I myself have for many years counted losers, which has worked well for me. I use a simplified version of the Losing Trick Count. I make no corrections for a suit like Qxx, but I remember it as a minus (like when you estimate the WP count).

I have made a comparison between your method and mine with the aid of some examples from the book:

Page	WP/SST	LTC	Best method
160	9	9	none
161	11	11	none
163	11	10	WP/SST ?
164	12	13	none
165	10	10	none
166+168	11	10	none
169	9	9	none
171	9	10	WP/SST ?
172	9	9	LTC ?
178-1	7	7	LTC ?
178-2	9	8	none
183	9	7	WP/SST
190	8	8	none
191	9	8	WP/SST ?
192	7	7	none

164: Blackwood solves the problem.
166+168: Difficult with so many finesses.
171: 4H is sometimes good against their 3S.
172: Difficult to realize during the bidding that WP is more than 18 (i.e. 10 tricks).
178-1: Most likely you would estimate WP higher, i.e. 8 tricks
183: Here LTC is bad. Singleton versus a bad suit is good.
191: WP could be 16, i.e. 8 tricks

After having read your book, I often think of your method when I play bidge. But I still think counting losers is quicker and simpler, so I will continue doing so. Maybe you need to write a new book to question (kill) my way of reasoning.

As we said in our reply to question 8d, we think The Losing Trick Count is an excellent method, but it has its downsides. Take, for instance, the deal on page 164. Yes, Blackwood allows you to stop in a small slam, but the LTC estimation is too high. Move one of North's clubs to hearts, and it is spot on. Move another club to hearts and it predicts too low. So blindly trusting the LTC equation can be dangerous.

If you analyze these deals with all cards on view, WP+SST will predict accurately 100% of the time, which LTC does not. Therefore, it seems like you try to compare how the two methods would have fared at the table. That is more difficult to judge, of course. And we are not sure we accept all your conclusions. For instance: if we were South on 178-1, we would expect 8 tricks, but as North we would expect 7 tricks. Somebody using LTC would come to the same conclusion. And on 178-2 you say "none", when WP+SST predicts correctly, which LTC does not. Using our method, on 178-1 neither player would bid 3S, while on 178-2 North would bid 3S. What will LTC do? That is not clear to us.

If you feel more comfortable with LTC, we suggest you continue using it – as long as you remember that it isn't perfect.

I am a mathematician, which impels me to express your method of trick estimation as compactly as possible. Two contributors to your website have already independently discovered the pieces of what I'm about to say. You replied that their methods were fine, but explained why you still preferred the original formulation. I hope you find some merit in the "complete compactification" of your method, your preferences notwithstanding. Perhaps you will even present it somewhere in your future writings as a worthwhile alternative. Here it is:

THE WIRGREN ESTIMATE of the number of tricks declarer will take (given an adequate trump fit) is the sum of two numbers. The first number is WP/3, which must be "rounded up" if it is not a whole number. The second number is the number of "shortness tricks." For this second number, count 3 tricks for each nonduplicated void, 2 for singletons, 1 for doubletons.

Explanation: The square brackets are a reminder to "round up" after dividing WP by 3, and ST is the number of shortness tricks.

Notice how short this is, once WP is understood. Tables like those on pages 139, 146, and 149-152 are not needed. Also, there is no place in this description for subtracting from 13, or for any arithmetic except dividing WP by 3. Next, let's mention SST. I believe that the concept of SST is more complicated (especially with 3 short suits) and less intuitive than the concept of shortness tricks. Although I am happy to eliminate the SST concept, I guess that you justifiably have the opposite feeling. First of all, SST led you to your exciting breakthrough. Secondly, SST has already started to enter the world's bridge lexicon.

A short comment: the word 'nonduplicated' refers to doubletons and singletons also. Then, a doubleton opposite a singleton or void counts for nothing, just like a singleton opposite a void.

A question re Singleton Aces. When it comes to SST, should I count the stiff Ace as One or as Zero (as good as a void) since I have no losers in that suit?If I do count it as Zero, then can I still count it as (at least) 3 WP?

PS
I have been puzzling over coming up with a 'snappy' name for your new evaluation method. For the moment pard and I call it the AW-LAW(Anders Wirgren – LAWrence).

You have one card in the suit and 4 HCP, so we suggest you count 4 WP for the ace singleton and the length as one card. That is what you have, after all. You could count the suit length as 0, but then you shouldn't assign the ace any WP at all (if you do, you will count it twice). In the end, your estimation will be the same.

The first portion of the book seems to be method justification. Percentages and charts ad nauseam. Your book is anything but user friendly. "I Fought the Law" has a lot to say. Pity that one has to endure endless data before getting to the bottom line. It smacks of author insecurity... An Adlerian approach where one chips away at the other's pedestal and shoves the chips under ones own. Nothing has to be lost. Restructuring is definitely needed. The quick fix would be to relocate at least most of the first 64 pages toward the back of the book.

You have some great concepts here. Suggest the 2nd edition be a rewrite WITH THE READER IN MIND. Currently the feeling is that it smacks of bitterness, for whatever reason. It seems like a personal vendetta.

This book says a lot, but I doubt that many would recognize a Mike Lawrence writing style.

So far, most readers seem to agree with how the book was written, but if amajority express views like yours we will consider restructuring thematerial. Most writers agree with our approach, which was to show theintent of the Law as well as our views on it. It is hard to critiquesomething if few readers know exactly what it is.

We disagree with your feelings that we were bitter or that we have apersonal vendetta. Our aim has been (a) to show that the base for the Lawof Total Tricks is wrong, and (b) to present a new way of estimating howmany tricks one side can take. Nothing else. You may perceive this but itwas not our goal. Perhaps the fact that the Law has become a part of ourlanguage has stirred up some feelings. Frankly, there is no way to debateimportant issues without causing some fervor.

I have read with interest your book, I Fought the Law of Total Tricks. I have found your approach quite interesting, stimulating and a good addition to bridge bidding theory.

In your book you do not rigorously define what comprises a short suit. In your 2 short suit case it is implied that the third shortest suit, which is usually a 3 card suit, takes on a value of zero while a value of 3 if the shortest or next shortest suit. In the 3 short suit case you rigorously define what a short suit is (void, singleton or doubleton) and you describe this as a special case.

To clarify this in my and my wife's mind I have generalized your approach where a short suit is now rigorously defined and where there is now no distinction between the methodology in handling the two and three short suit case. Also my approach emphasizes that each of the three non-trump suits have a distinct short suit value and that your SST is the sum of those three distinct values.

I still have difficulty with quantifying WP in hand evaluation. I hope that in due course you will provide more guidance in this area. Good luck in this work and I look forward to seeing any advances in this technique.

If you find it easier to view SST as the sum of all three side-suits, we suggest you do so. Other readers have suggested similar solutions (see questions 6, 7 and 13). Most of the time, though, you will have one side-suit with three or more cards in both hands, so looking at only the two shortest suits will be enough. Another reason why we prefer our approach is that even if we have, say, three side-suit doubletons, it is possible that one of them does not reduce our losers. If we have, say, KJx opposite Qx in diamonds, the doubleton doesn't reduce our losers, and we could just as well view our diamonds as KJx opposite Qxx.

To estimate how many WP a hand has can be tricky, but the auction gives you many clues. A good guide is that stray jacks and queens, sometimes even kings, opposite suits where your partner has not advertised length often isn't working, so such honors should be downgraded. The same goes for honors, which are wrongly placed for your side (like when you have king third in a suit your LHO has bid strongly). And strong suits opposite partner's known shortness is also bad, unless you have the time to use your honors for discards. On the plus side, we have chunky suits like AJ109, which opposite three small may produce two tricks by power and give you one discard. If the discard is useful, these 5 HCP are as much as 9 WP (6 WP for two tricks with both hands following, an extra 3 WP for the discard).

I have just read I Fought the Law of Total Tricks with great pleasure and I translate it in French to discuss with my wife and some friends. This seems to me a good tool for evaluating the combined hands potential in competitive situations when a critical decision is to be taken. I use it in the form NT=13-SST-((W-20)/3).

When you compare the result given by that formula and the real number of tricks at the table, the precision is almost 100% because the SST and WP are evaluated on a double dummy basis. The real problems for evaluating its real prevision potential is the accuracy obtained at the table for the estimation of SST and WP. This requires a lot of experience and judgment, probably more than required by the Law or by LTC.

My question is: what is the precision of your own evaluations of SST and WP at the table when the informations obtained are both not complete nor always reliable?

You are right. Both the Law of Total Tricks and the Losing Trick Count are simper to use, since they require less judgment – but that is also why they aren't as accurate as our method.

Our own experience with the method is good. Most of the time our estimation will be either spot on or close to. Some of the time we will estimate too high, because partner's values were in places you didn't expect them to be or that his distribution was worse than expected; and some of the time we will estimate too low, either because an honor we thought was worthless was valuable or because our partner had an unexpected distributional plus value. But as long as we estimate realistically, we'll do fine.

you should just simply bid the game (after 1

-2

), not invite. In a IMP pairs game, W/W , would this also apply to the identically shaped and counted

If not, and playing 2-way game tries, is the short suit try (3

) preferable to the long suit try (3

Jeff Meckstroth have said "I always bid game when I have 6-4 distribution and get a raise in my long suit." And indeed, with an SST of 3 and an adequate trump fit, you're in contention for ten tricks if your side has half the deck in working points. Jeff's advice shows that he knows how important distribution is.

The hand from our book is slightly stronger than the one you had, but we wouldn't object to a game bid with that one too. After all, you might make game opposite as little as 3-3-3-4 with the king of diamonds and nothing else. So at IMPs, we vote for 4S. A good thing about your hand is that you don't have too much in trumps. Six solid spades and four small diamonds would have been worse.

If you prefer to make a game try, we suggest you show your shortness. Your four-card suit is chunky, so even if partner has no fit there, it may do very well on its own.

As a reader, my only criticism of the SST+WP theory is its complexity. My question is, at the table when you have only a few short seconds to hitthe table with your bid, have you any suggestions as to reaching your finalanalysis is as short a time as possible.

The best way of reaching your decisions quickly is thinking in advance, using the clues you get from the bidding and your own cards. Suppose partner opens with 1S (five-card majors), where you have a fit. You immediately know that your SST will be 5 or lower, since your partner's shortest suit will be at most a doubleton. If your hand includes a doubleton, assume it is not matching your partner's, and expect your SST to be at most 4. But if the opponents bid and raise your doubleton suit, you may expect duplication and go back to 5. Quite often, you will be spot on, and even if you are wrong, you're rarely off by more than one.

Estimating your side's WP is more difficult, but a good guide is to assume partner has a minimum in working points and proceed from that. Say that he has shown support for your opening suit and 6-9 HCP. Hoping for 6 WP opposite is a realistic estimate. It takes into account the possibility that if partner is maximum in high-card points some of his values are useless.

There is one aspect of the Law that was comforting and that is not presentin the AW-LAW system. That is, knowing when to sacrifice.

The knowledge that the Law was protecting me (notwithstanding the fact that it probably wasn't) by giving me a minus score that was better than theopponents positive score was a good feeling. In your answer to Mel'squestion (8c) you advise that if "your estimation says your side will notmake your contract, don't bid it – to avoid declaring when neither sidemakes their contract." I am doing that but it seems that the opponents arebuying a lot of contracts at the 2 or 3 level and outscoring us.

Isn't there some feature of the system that would give me guidance onsacrifice bidding?

Our recommendation of trying for plus scores is a good strategy at IMPs, at least at the part-score level, since the difference between plus and minus (e.g. +110 instead of -110) is bigger than between two plus results (e.g. +140 instead of +100) or two minus results (e.g. -50 instead of -110). At other forms of scoring, things are more difficult, since conceding -100 is a good result if the opponents could have taken eight tricks in a major or nine in a minor. At pairs, it may be worth lots of matchpoints; at rubber it may stop the opponents from converting a part-score; and at board-a-match it may win the board. Still, being able to estimate how many trick your side is likely to take is valuable even here.

In sacrifice situations the first thing you should do is estimate your tricks. If it says you are not going to make your contract, sacrifice only if the opponents would have scored more in their contract AND you think it is likely that they would have made it.

Since you don't know anything about the opponents' distribution, you have to make an educated guess, but you often have clues pointing in the right direction. Suppose you know your side has roughly 17 HCP and the opponents bid 4H. How likely are they to make it? If all their HCP are working, they need an SST of 4 to succeed. If some of their HCP are not working, so that they have, say, 20 WP, they need an SST of 3. Sometimes, they will have more than 23 WP (e.g. when their trumps are AQxx opposite xxxxx and the king is doubleton onside), when even an SST of 5 may be enough for ten tricks. If you think that one of these situations is likely to be present, go ahead and save; if not, defend!

Don't forget the clues from the bidding. If one of your opponents shows a singleton, you know their SST is at most 4, and it may easily be lower. The same when one of them shows at least 5-4 distribution, or a six-card suit. If one of them has shown 5-5, or a seven-card suit, their SST will never be more than 3, etc. And don't forget that if there is a bad split in one of their key-suits, it's a good chance that they will take less tricks than the formula says.

Some time ago when trying to improve on The Law, I came up with the idea of "Total Losers (TL)". Total Losers is the number of losers for NS plus the number of losers for EW. Provided the suits are "pure" with no duplication, TL is (usually) equal to the sum of the shortest holdings in each of the four suits.

I find Total Losers to be helpful during the post-mortem but more difficult at the table.

If neither side has wastage opposite shortness, and there are no defensive ruffs, TL will usually be the same as SST for North-South plus SST for East-West. So your idea is close to ours. And since it deals with the most important thing – distribution – we consider the concept more important than the concept of total tricks.

I hurried to begin reading your book but, up to my knowledge, I'm wondering how do your guidances apply when you can see only your own hand and only have an idea of that of your partner.
Rule of counting SST doesn't appear to me very clearly stated : having no certainty if the short suites of our partnership are those where I've myself shortness (he may have length facing my shortnesses), how have I to count SST looking to my sole hand ?
As to WP, it's not either easy to know precisely how will honors' concordance between the two hands work ?

If you look a deal with all four hands on view, it's easy to figure out each side's WP and SST. But, as you correctly say, it's more difficult at the table. You can't always know which honors are working nor your exact SST.
  What the WP + SST formula can do is help you looking at the important items, so that you are in a better position to judge what your side can make.
  Here is one example: You open with 1S, West overcalls 3C, and your partner raises to 3S. If you consider raising to 4S with 5-3-3-2 distribution including ace-king in both majors, you can expect your WP to be 14 (it doesn't have to; if partner has a singleton heart, and the heart king doesn't provide a useful discard, you only have 11 WP). Thus, you know that if your partner has no distributional feature for you (i.e. three or more cards in both red suits and at least two clubs), he needs 11 WP for your side to have the potential for ten tricks. But if he has a useful doubleton, 8 WP will be enough.
  Sometimes you know a bit about partner's distribution, sometimes you don't. In the latter case we recommend a slightly optimistic estimation. Suppose you know that your partner has a balanced hand with five hearts, and you have the distribution 4-4-2-3, you know that it is possible that your SST is 5 only if partner has a doubleton diamond. If his doubleton is in any of the other suits, your SST will be 4. Unless the auction has made it likely that you have matching doubletons (e.g. when the opponents bid and jump raise diamonds), we suggest you expect an SST of 4 and proceed on that basis.

Love your book: I Fought the Law of Total Tricks. Don't like the Titlethough!
  My quick mnemonic for your system is MLAW or the Law according to "St Lawrence and Anders" (MikeLawrenceAndersWirgren)
  I am an engineer and Bridge Life Master, and have formulated exact equations/functions for the LAW.
  These equations (and/or algorithms) have been extended to cover MLAW, and will be published soon as the LOR (Law-Of-Roy).
  I have however one issue that I would appreciate your comment. How do you apply MLAW to the special situation where each hand contains all 13 cards in one suit?
  Each side has 20 HCP or 20 WP. Each Side has 3 voids and SST= -3. Then each side can make 16 Tricks, clearly not possible.So do you place a limit of 13 tricks on the MLAW function? Or do you take the view that as 10 HCP in each suit is opposite a void, then all HCP are worthless, making WP=0. Or do you take the view that for each hand, a void is opposite a void, then SST= 0 (i.e. only count each suit once)
  As an aside, the LAW would predict the total number of tricks at: 26 Tricks for this hand, based on each side having 13 trumps.Also the LTC would predict 13 tricks per Side, (always providing eachside plays the contract in one of its suits).

If each player has one suit only, both sides have 20 HCP, but only 10 WP (dummy's honors won't produce useful discards, so we don't assign any value to them). And with an SST of -3, the formula says 13 tricks, which obviously is right.

I am an engineer, with a statistic background. I have always been a law-follower, but with the feeling, that something was wrong. Thank you for the statistic work, you have shared with us in your book. The law is about right, the average trick count equals the trump count, but your work shows, that the variance is too big. I am looking forward to the coming bridge season where I am going to analyse a lot of deals with SST/WP.
  Have you read the book "Saknade point" (Missing Points) by Bertil Johnson, from "Jannerstens BridgeBibliotek"? I think your method, with SST/WP and his with the missing points/cover poins are much the same. Agree? Your method are far more simple; easy to learn and use.
  You seem to avoid an important point in your analysis. 3-points does not mean a trick, it is the average change to take a trick. Points are used to give an estimate of tricks, it's an evalution method. Instead of counting tricks, we use the more refined method of counting 1/3 "chance to get a trick" (and we hope that average/variance in long term are right)
  It feels wrong, when you count points after you know the position of other cards than your own. For one you can only count 3 point at a time. Of course you can see where the tricks come from, given a good guideline for points to trick evaluation, but they are tricks, not points. If you use the bidding to place cards, the definition of 1/3 point looses its statistic meaning. I don't know what to use instead of. As a good friend of mine says: "how many points to count for that ten of trump" when a slam depended of him having it.
  I hope you will collect a lot of input and gather them in a new book, where your methods will be refined. I will hope for a tighter definition and a systematic scheme/review for the method.
  If you want, say 20 players to evaluate 100 randoms hands with the SST/WP method, to get a statistic material, I will be glad to help.

Yes, points and tricks are not the same. The idea of "3 points equal 1 trick" is derived from the fact that if you have a suit of, say, A-K-x opposite Q-x-x, you take three tricks with your honors: one with 4 HCP, one with 3 HCP and one with 2 HCP. The average trick taken is with 3 WP. So, we could instead say that 3 WP is what we use on average in order to take a trick with an honor.
Yes, we have read Bertil Johnson's book, which is based on a method developed by Swedish internationalist Alvar Stenberg roughly 50 years ago. Stenberg introduced the method of Missing Points (mp) for strong unbalanced hands (Acol two-bids or even stronger), but it is possible to use it in other areas as well. Since that method also considers the two prime factors: distribution and working honors, I wouldn't be surprised if it comes to similar results as WP + SST.

The book you have written, Fighting the Law, is both well researched and well written, thoroughly enjoyable.
  I would however say that when Vernes wrote the famous article on the Law of Total Tricks he was not laying out a gospel. Vernes was a mathematician, if I am not wrong, and he outlined a trend resulting from his researches. When the Law was popularised in the 1980s, it was almost imperative to present is as a true gospel, to simplify the issue, and make it digestible to the public. There is no doubt that putting it on a tall pedestal can be annoying at times (recent converts are the worst, as usual); on the other hand it is not such a bad advice for the average bridge player. In a way,it is in the same class with the old rules for defence (second low, cover ahonor and so on), or with Blackwood.
  Just a couple of points I am interested into:
  I have not done a statistical research, but I have the strong impression that the Law is much more effective with balanced or semi-balanced hands. It would have been interesting to find in your book a disaggregation of the relation trumps-to-total tricks in terms of SST. The WP concept is interesting (although not completely new). I would suggest you to flesh it up with a discussion on the value of intermediate cards (and small honor combinations) in fit suits. The 10 was rightly praised and valued (a 10 in combination with higher honor(s) is certainly more valuable than a Quack); however the 9 is also quite valuable, as are small fourchettes (10-8) or combination like Q98x.
  I would treasure your opinion on these two questions.
  Best regards

In his Bridge World article, Vernes mentioned initially that he was talking about an average, but in the end of his article he forgot and started reasoning as if his law was true most of the time. As our research has shown, that was wrong.
  In all fairness, we have to agree that Vernes' law isn't that bad – if it were, people would have stopped using it long ago – but it is much overvalued. It's not "the solution to all your competitive problems", as the fans usually claim.
  We think, just like you, that Vernes wanted to show a trend, and nothing more. But the revival of the law have led to stupid and false statements. And it has also led to too many people thinking that counting trumps is more important than valuing their hands.
  For not so many total trumps (up to 17), deals with balanced hands will often be OK for the law. But for deals with 18 or more trumps, the balanced deals will often produce fewer tricks. Here is one example from Larry Cohen's To Bid Or Not To Bid (page 31):

Congratulations to a fine book, but something is missing. Look at the following deal, from Bergen: "Declarer Play etc.", p 144.

North-South have a fit in spades, a SST of zero (three singletons) and WP 19. So they should win 13 tricks. But it is impossible to win more than 10 tricks.

What is wrong in the calculation? Are there adjustments that are not shown in your book?

If you click on the link "Errors" (under "What's important?") in the left frame, you can read about some factors which may cause our formula to come up with a false result.

The first thing is that even though North-South have 19 HCP, they have less than 19 WP, because they have too many aces. That may surprise you, since we have all been taught that aces and kings are undervalued in suit play.

Working points (WP) is the sum of our trick-taking honors, so in this example North-South have five trick-taking honors: the four aces and the trump king. Usually, 19-21 WP will be the same as six trick-taking honors, but it might be seven or five. When you have seven trick-taking honors, you will get one extra trick, but if you only have five, you will take one too few. That is the case here.

The second missing trick comes from the very low SST. When one of the sides has an SST of 0 or 1, they will sometimes take less tricks than estimated if they (a) don't have enough tricks to ruff all their losers (like here), and (b) no strong side-suit taking tricks (they don't have that either).

Another thing is that there is no way for estimating a lucky split. If West gets one of East's hearts in exchange for a club, North-South take 12 tricks by ruffing out clubs. But when clubs are 4-2 (with two trumps in the short hand), there are only 10 tricks.

The Losing Trick Count is saying 15 losers between the two hands, no game. With the adjustment for controls there are 14.5 losers.

That the Losing Trick Count (LTC) comes up with the wrong answer on such a simple hand suggests there is a flaw with the method. Still, LTC is one of the best method of evaluating there is.

Our method gets to the correct result. If the major suits are distributed 3-2, East-West have "half the deck in working points" and will lose as many tricks as their SST. Since SST is 3, our estimation is ten tricks, which obviously is correct.

If one of the majors is 4-1 (or 5-0), we might take less than ten tricks. Then, the formula fails, since the estimation doesn't cater to "bad luck".

I'm now on my second reading of I Fought The Law and I ask your comments on the following hand from the Master Solvers' Club in The Bridge World (May 2004, problem A):

How can one go about using the SST + WP formula here? I have a void in clubs and partner probably has a singleton diamond, so my SST = 1. I have no idea whether my partner's points are in spades, hearts, or clubs but I do know that if they are in clubs they don't help me on offense.

I suppose that one could argue that if partner's points are in hearts they are valuable for offense or defense while if they are in clubs they are valuable for defense only. But give parter a yarborough like

and as long as spades are 2-1 and the heart honors are split, it looks like I can take 5 spades, 2 hearts, and 2 ruffs = 9 tricks, whereas the opponents will lose only 2 hearts = 11 tricks. Give partner

and assuming that the QH can be located then I'll take 5 spades, 3 hearts, and 2 ruffs = 10 tricks whereas the opps may lose 3 hearts = 10 tricks.

Since partner did, apparently, have something along the lines of that hand, it would have worked better for partner to make a non-fit bid of 4C, but that would also have given away the show to the opponents.

Bottom line is that while I can easily see how to estimate SST during the auction, the estimation of WP seems far more nebulous (except as it relates to holding like Qx in their suit or AQJ when partner has denied length in the suit) and would function best as a post-mortem analytical tool.

The hand you present is difficult because it is possible both that neither side can make a 5-level contract or that both sides can. It is further complicated by the fact that 5S may be a good save against 5D, or that 5D is a save against 4S. As you write, it largely depends on where partner has his values (if any).

You ask "How can we use the WP + SST formula to decide what to do?". The answer is that we can use it to estimate what partner needs for us to take nine, ten or 11 tricks. Assuming our SST to be 1, we need roughly 16 WP for 11 tricks, 13 WP for ten tricks and 10 WP for nine tricks. If we assume South has 10 WP, it suggests nine tricks opposite a yarborough, which is a correct estimation if partner has your first example hand.

It is also possible that North has a diamond void. If so, our SST is 0, which gives us the potential for another trick (but no guarantees: on a trump lead, North's 4-3-0-6 yarborough won't take more tricks than when he is 4-3-1-5). In the Errors section, you can see that a very low SST often overvalues your tricks if you have no strong side suit.

Therefore, we can conclude that bidding 5S is likely to lead to a minus result.

If we do the same estimation for the opponents, we know that their SST is likely 4 (3-3-4-3 opposite 1-3-4-5, e.g.) or 3 (3-2-5-3 opposite 1-3-4-5, e.g.). In the first case they need 26 WP, in the second they need 23 WP – and all this assumes that the breaks are normal. Here, we can see that both minors are breaking badly and that we have a good defensive holding in hearts behind the stronger opponent (if partner has the heart queen, declarer's king of hearts isn't the 3 WP he thought it was). Therefore, it is likely that they will lose (at least) one extra trick due to the bad breaks, so that they will need 29 or 26 WP, respectively, to make their game. Can we expect them to have that much?

We think this "bad breaks argument" is so strong that we vote for double. After all, it is possible that South can defeat 5D without help from North. And with a little luck (like North's having the ten or the jack singleton in diamonds plus one stopper in clubs), we might defeat them two or more tricks.

I've been to the "errors" section at newbridgelaw.com, and make the following observation. The discussion of 'not enough trumps' shows that short trumps can render short suits inutile. The two examples were 3 card trump support with a doubleton (repeated trump leads means no ruffs in dummy) and 3 card trump support with a singleton (repeated trump leads means one ruff only).

This could be made explicit under the following principle: trumps that are 3+ cards longer than your short suit is a plus factor (i.e., 3 with a void, 4 with a singleton). Trumps that are 2 cards longer than your short suit (i.e., 3 with a singleton and 4 with a doubleton) are expected. Trumps that are 1 card longer than your short suit (i.e., 3 with a doubleton) is a minus factor.

Obviously, I don't have access to the kind of database you have, but intuitively this seems right. The problem is that I always hated counting half-losers when using adjusted forms of the Losing Trick Count, and that's the direction this points to.

Sometimes you need to take lots of ruffs in dummy. Then the number of trumps is important. Other times dummy has a strong side suit, which will provide enough tricks, and your short suits are only stoppers (you intend to draw trumps, then establish and run the long side suit). Then, the number of trumps is not important.

Most of the time, you don't have that strong suit in dummy, which suggests that this will be an excellent rule of thumb. If you don't want to count fractions, why not add or deduct from you WP. After all, the difference between an SST of, say, 3 and 4, is the same as the difference between, say, 20 and 23 WP, i.e. one trick. So if you feel like adjusting half a trick, you can add or deduct 1 or 2 WP. That will be close to the truth.

I just read your book last week and I thought it contained some really good ideas, but when I tried to apply them last evening at the our club, I came across the following hand:

East opened 1NT. I bid 4 Hearts, thinking that my SST was 2 and I had 10 WP. If my partner contributed some hearts and a few WP, I had a good takeout or possibly even could make it. West doubled and that was it.

West led the King of Clubs and I admired the dummy: We actually had a SST of -1 and 14 WP, so your rule suggests 12 tricks. I made only nine. After a club trumped, the Ace of spades, a spade trumped andanother club trumped, I was in dummy and since West held only a doubleton spade and 10xx in hearts his trump ten was promoted after a spade continuation (fortunately for me, he also discarded his fifth club, so I ended up with 9 tricks).

So even without a trump lead, which would be disasterous (I would make only 7 tricks), I can be held at 8 tricks, so your estimate is off 4, which I consider a lot. Do you have an explanation?

I really thought you were on to something, but now I am in doubt again whether your estimate is better than the law.

We have a section called "What's important? -> Errors" on our site. There we show some factors which may causethe formula to come up with the wrong answer. The second entry "Not enough potential" starts like this:

Had West led a trump, NS's SST will be the same as South's SST (i.e. 2), but since the club suit can't produce any tricks, your SST is in fact no better than if your distribution had been, say, 1-6-3-3 (when you have anSST of 4). So, NS's "effective" SST was 4 (after the trump lead). Add to that their 14 WP and the formula suggests 7 tricks.

All this means that when your side is clearly outgunned in high-card points, but has a very low SST, you often take fewer tricks than suggested, if the defense can lead trumpsand destroy some of that distributional value. The stronger your side is, the better the formula will function.

A K Q 3 2		J 9 4
9		7
A 3 2		8 7 5
10 5 3 2		A K 9 8 5 4

Q J		x x x
J x x x x x		A K Q x
x x		A Q 10 x
Q x x		J x

	A 7 6
	9 5 2
	J 10 7 5
	Q 8 7
K Q 9 4 2		J 8 5 3
A K 7		Q J 10 3
9 2		8
A 6 3		10 9 4 2
	10
	8 6 4
	A K Q 6 4 3
	K J 5

	Q 10 5 4
	Q 9 8 7 5
	J 3 2
	7
8 7 6 2		A 9
10 4		6 3
A 10 8 7		K 6 5
A 9 3		K Q 10 6 4 2
	K J 3
	A K J 2
	Q 9 4
	J 8 5

	A 10 8
	A 6 4
	A 9 7 5 4 3
	6
J 9 6		Q 7
K Q J 9		10 8 7 3 2
Q 10		K J 8 2
Q 10 9 4		K J
	K 5 4 3 2
	5
	6
	A 8 7 5 3 2

	A 10 9 x x x
	x x
	J 10 x x x
	–
x x		K J x x
10 x x		A x
Q x x		A K x x
K Q J 9 x		10 x x
	Q
	K Q J 9 x x
	x
	A 8 x x x

RHO	You	LHO	Part
1NT	2	3	4
5	?