[Laird]

Hello All
This is often used in answering other posts and I'm sure this has been discussed many times and yet, so far, it still is a little bit mysterious to me.
As I understand it you add the assumed n/s trumps to the assumed e/w trumps and this gives the total tricks.....Mmmm Yes ??? :-

Can someone please explain the relevance, using an example, to show its value in coming to a decision regarding the optimum level to bid up to. Taking account of vulnerability and premptive aspects and level at which it ceases to be of value.

Kind regards
John

[Codo]

Hi John,

I guess you will receive longer and better answers, but for a first look:

You look at your longest suit and count the cards (in both hands) and try the same with the trump suit in opps hand.
You add these two numbers. The result is the number of total tricks you may reach.
F.E.
You have a 10 card fit in spades, they have a 10 card fit in Hearts.
The total tricks are 20. So, if they make 4 Heart (10 tricks) you make 10 tricks in spade.

If they make 8, you make 12 tricks
they 9 you 11 tricks

etc.

This does NOT depend on HCPs at all.
It is just a wonderful rule how to act in competetive bidding.

Another example:
They have a 9 Card fit in Hearts, you have an 8 card fit in Spade. They bit 4 Heart. Should you defend?

The number of total tricks is 17.
So if they make 4 Heart, you will just get 7 tricks. So, no good idea at all to bid 4 Spade.
If you think, that you can make 4 Spade, they will be in 4 Heart -3. So again, better don`t bid, double.

But if they just bid 3 Heart, you should think about 3 Spade.
If they get 9 tricks, you will have 8 and 3 Spade-1 is better then to let them play 3 Heart =.

If they were on their way to 3 Heart -1, you will make 3 Spade, again a win.

Of course, this simple rule is not as easy as it looks like.
First: Do you always know the total number of trumps in all hands?
Second: There are some adjunctions to the law.
F.E.Honours in opps. suit. are better for defending and downgrade the number of total tricks avaiable.
A double fit and/or very freakish hands do increase the number of total tricks.

So I am not the one who prays for this LOTT tool. But if in doubt, I like to use it.

Btw: The complete idea behind bergen raises is just the LAW. After pd shows 5 cards in a major, you emmedeately jump to "your" level. With 4 trumps in your hand, you jump to the 3. Level, with 5 you jump to the 4. Level.
Easy doing....

Kind Regards

Roland

[Rado]

Hi John,
LOTT says that the sum of tricks each side has when playing in their longest fit is equal to the sum of both sides best fit

none vulnerable, dealer S
...............AQJxx
...............xxx
...............AK
...............xxx

xx................................xx
AKJxx...........................Qxxx
Jx.................................Qxxxx
AQ10...........................Jx

...............Kxxx
...............x
...............xxxx
...............Kxxx

S - W - N - E
p - 1H - 1S - 3H
?

Here S knows about 9 cards Sp fit and minimum 8+ cards opps fit in He
1.Assume 9Sp + 8 He= 17 total tricks
1.1 if 3He=just (9 trikcs) then 3Sp=17-9=8 one down
1.2 if 3He 1 down (8 tricks) then 3Sp=17-8=9 just

at both cases LOTT shows that bidding 3sp gives better result for N-S
2. Assume 9Sp +9He = 18 total tricks
2.1 if 3He=just (9 trikcs) then 3Sp=18-9=9 just
2.2 if 3He 1 down (8 tricks) then 3Sp=18-8=10 +1

again bidding 3sp is better.

At our example both sides have 9 tricks when playig at their longest fit for 18 total tricks = number of total trumps
Also see that if we change King of Cl from S to N hand
then we will have 8 tricks at He contract and 10 tricks at Sp contract - the total number of tricks does not change from the displacement of the honours

Useful advise: when sure 8 cards fit only never bid 3 over 3, when sure 9 cards fit then always bid 3 over 3.

Larry Cohen wrote 2 very intersting books on the LOTT: "To bid or not to bid" and "Following the law"

I strongly recommend both of them :-))))

Also good link:
http://www.users.qwest.net/~jplanier/bridg...ge/LOTT-MP.html

Best regards, Rado

[csdenmark]

Here you find WEB-info about the Law and other important stuff. I think no need to re-write.


http://www.users.qwest.net/~jplanier/bridg...ge/linksOS.html

Yours Claus - csdenmark

[luis]

Hi all,
I'm posting this very quick and incomplete summary of The LAW, hope you find this helpful to answer your questions.

The LAW fundamental principle:
"The TOTAL number of tricks available in a hand is equal to the number of trumps each side has in its best fit added"

Example: If NS have an 8 card fit and EW have a 9 card fit the TOTAL number of tricks available is 17.

Once you know how many tricks are available you can base your bidding decision on "chart logic" example:

If they are in 3s and we consider whether to bid 4c or not then

If the total tricks is 17 then
If they make 9 tricks we are down 2 in 4c
If they are down 1 in 3s we are down 1 in 4c
If they are down 2 in 3s we make 4c

So at IMPS the winning option is to pass. But what happens if the number of tricks is 19?

Then
If they make 9 tricks we win 4c
If they are down 1 we win 5c
If they are down 2 we win 6c
If they make 4 we are only down 1 in 4c

So now the winning option is to bid 4c.

Some tips that are quickly derived from "The LAW"

* Unless there're very good reasons always bid 4s over 4h is 3/1 better.
* With 8 trumps don't compete to the 3 level. Don't bid 3 over 3
* Don't let them play in 2x with an 8 card fit
* With 9 trumps bid quickly to the 3 level.

Adjustments:

The number of total tricks in a hand should be adjusted using the following rules:

- If you have "minor honors" Qx, Jxx, Jx then substract 1/2 trick
- If you have a double fit then add a trick
- If you have "purity": honors in your suits add 1/2 a trick
- If you have honors in opponents suits then substract 1/2 trick

Example:

You have
Qxx, Kxxx, Jx, Qxxx

LHO opens 1s, pd overcalls 2h and RHO bids 2s.
Assuming they have an 8 card fit you have a 9 card fit so chart-logic suggest bidding 3h over 2s with 17 trumps. If you apply adjustments you will know that the number of total tricks should be adjusted to 16. Then the LAW applies "with 16 total tricks don't bid to the 3 level"
Why?

Because:
If you make 9 tricks they are down 1 in 2s
If you are down 1 they make 2s
If you are down 2 they make 3s

So you are not winning imps for bidding 3h because if 3h makes you are expected to be +50 in 2s.

HTH
Luis

[bglover]

This was discussed in the expert section a while back and you can find the thread there so I won't get long-winded here.

Lost in this discussion is a basic fact of life about bridge hands and the Law: The most important thing to look at before you apply the Law when responding to partner is your hand's distribution. The flatter your hand is (4333 or 4432) the less likely your hand is to be helpful to partner. Why? Because your hand is not going to provide any ruffing tricks if you are flat.

Do not blindly bid 4 of a major if partner opens 1 just because you have 5 trumps.... you are flirting with disaster if the hand is 5332 and you have a paucity of high cards... The fifth trump isn't really helpful (just guarantees that a trump suit that probably didn't have a loser to start still doesn't).

To put it more plainly, don't apply the law based solely on the total number of combined trumps. One needs to understand why the law works before actually applying it and that depends on other factors as well, including distribution, working and non working honors, the potential defensive value the hand has, etc.

The more positive shape (singeltons and voids) for partner, the better the hand for offensive competition. The more working "slow" honors (guarded kings and queens) the better for defense.

[inquiry]

Hi John,

As I understand it you add the assumed n/s trumps to the assumed e/w trumps and this gives the total tricks.....Mmmm Yes?

That's a big YES

Let me begin by saying, originally I was a skeptical of LOTT. Then I became a true believer, to my point now where I use it, but not as ardently as I once did. The problem I found out is that trying to estimate the total number of trumps is not as easy as it seems. Sure with Bergen raises, support doubles, fit jumps (very important IMHO) etc, combined with a partner who you know will apply the LAW from his side, you can usually guess about how well your fit is. But trying to figure out what the random opponent's trump fit looks like is not so easy. Partner can help, as we shall see.

Can someone please explain the relevance, using an example, to show its value in coming to a decision regarding the optimum level to bid up to. Taking account of vulnerability and premptive aspects and level at which it ceases to be of value.

I think everyone has taken a shot at explaining the relevance, and the link Rado and Claus provided contains lots of information (BTW, I am with Rado on highly recommending Larry Cohen's two books, but in my view, the second one is redundant, so if you need really only purchase either one of them). So I will try to deal briefly with your issue of "taking account of vul and preempt, at which level [LOTT] ceases to be of value". I will do this by examing one of your hands where you could have applied LOTT yourself at a high level.

This is a hand you held on June 1nd playing with Joly3. They were vul you are not

Your partner open's 2D (weak) and you held

S-32
H-K5
D-T93
C-QT9842

2D-(2NT)-P-(3H)
4D-(4H)--?

Should you bid 5D's at favorable vul? What does LOTT say?

You have a 9 card Diamond fit (partner has six or would open 3D). How long is their heart fit? If it is 8 card fit. The law says there are 17 tricks. If they can win 10 tricks in hearts, 5Dx will be down 4. If they have a nine card fit, and if they can win 10 tricks, you would be down 3. And of course, in either case, they maybe able to win 11 tricks, or maybe only 9 tricks.

Let's examine a table of the trump fits, number of tricks for each side (in 17 card fit, if they can win 8 tricks, our total is 17-8 or 9).

17 trumps
They win Our "likely imps"
num tricks 4H 5Dx
8 +11 -11 (+200 v -300)
9 +12 -12 (+100 v -500)
10 +5 -5 (+620 v -800)
11 +10 -10 (+650 v -1100)

18 trumps
They win Our "likely imps"
num tricks 4H 5Dx
8 +7 -7 (+200 v -100)
9 +9 -9 (+100 v -300)
10 -3 +3 (+620 v -500)
11 +4 -4 (+650 v -800)

19 trumps
They win Our "likely imps"
num tricks 4H 5Dx
8 -8 +8 (+200 v +550)
9 +5 -5 (+100 v -100)
10 -8 +8 (+620 v -300)
11 -4 +4 (+650 v -500)


As you can see from these tables, if they have a 17 or 18 card heart fit, it is by far best to stay out of the bidding. 5D is a "winner" only when they have a 9 card fit and can win exactly 10 tricks, and even then it wins only 3 imps.

If they have a 10 card fit bidding 5D is ok. But do you really think they can have a ten card fit? If partner he was 6-5-1-1, he would bid his long black suit, and maybe if he was 1-2-6-4 too. If he was 3-1-6-3 and felt a burning need to bid 4D, he could help you by making a double (takeout) with 4D as a potential landing spot (you didn't raise D's after all, so he doesn't really know 4D is at all safe). So with a thoughtful (thinking LOTT) partner, I think it is a safe assumption that partner has at least 2Hearts. Even if partner has only one heart (giving them 10), your heart king might be useful on defense (giving you one extra trick), but not provide any help on offense... making the LOTT be off by one (a negative adjustment). (And if they have 10 card fit, you REALLY aren't ever going to beat them two).

Should you bid 5Ds?
I say no. Obviously when they have 8 card fit, it is NEVER right. When they have 9 card fit, it wins in only one case, and even then only 3 imps. The table does suggest if they have a 10 card fit, it is right to bid on. But the table maybe wrong if the Heart King is working on defense, but not offense.

It would help to know if your partner would pass or bid with good Diamonds and singleton heart? Or would he be more likely to bid with good diamonds and 3 hearts? If you knew your partner had a singleton in hearts, you would know what to do here. I think he can't have a singleton heart, however, as I suspect DBL over 3H should be 3-1-6-3 or something like that on the way to 4D as opposed to simply bidding an uninformative 4D.

What happened at the table?

Pass 4H and you set it one for +2 imps, bid 5Dx and you go down 2 for -7.3 imps. A net swing of 9.2 imps. Just about what the LAW predicted.

Ben

[mishovnbg]

Main problem with LOTT is that is simple not true in 65% of cases. With all corrections and suppouse it was made right, max percentage can reach 41% of sucsess. If somebody interest were to read about very large statistical research: www.e-bridgemaster.com/Canada/csArticleSampleNoWindow.asp?Article=1307 author Anders Wirgren.
Note: i think you must be am e-bridge member, but you can use 1 month try.
Misho

[Cave_Draco]

Quote

Main problem with LOTT is that is simple not true in 65% of cases. With all corrections and suppouse it was made right, max percentage can reach 41% of sucsess. If somebody interest were to read about very large statistical research: www.e-bridgemaster.com/Canada/csArticleSampleNoWindow.asp?Article=1307 author Anders Wirgren.
Note: i think you must be am e-bridge member, but you can use 1 month try.
Misho

Lol, one has to be a member!

LoTT always struck me as akin to "Culbertson's Law of Symmetry"... We have all seen it work but it is specious!

Is there a different set of "adjustments" for MP as opposed to IMPs?

;D

[pbleighton]

"We have all seen it work but it is specious!"

I disagree. However, the name works against it - "The Law" implies a greater degree of precision than it has, or than its proponents claim that it has.

As a practical matter, it should be renamed "The Guideline Of Total Tricks". I have found (from my quite non-expert perspective) that knowing how high it is GENERALLY safe to bid is very useful information. I am not anywhere near as precise in my deliberations as Ben, but I use it to begin my decision process, then use vulnerablity, shape, hcp, scoring, etc. ("judgement").

It's nice for judgement to have a starting point.

[Cave_Draco]

The comment was intended to apply to Culbertson's Law... LoTT is useful, whereas Culbertson's Law is simply misleading, ;D.

They do, however, have similarities. I would be interested in Misho's ref. but cannot get there, .

I do recall an analysis of "Short Club" v "Better Minor" which implied little or no difference!

[inquiry]

Hi good friend Misho,

While I have no belief that the LAW is right anywhere near 100%, my personal experience with it is right more frequently than 41% of the time. The real trick, is how much is it off? When it is off, generally by one trick, high or low. Since these average out, it seems be right +/- a fraction of a trick, let's say a third or half. As Larry Cohen says in his book, [paraphrasing] you can't estimate the number of "trumps" in the four hands that well, so why sweat it?

I would be willing to investigate a randomly selected date of hands you played on the BBO (not less than 10 on that day, and if more than 20, then only the first 20 played) as a test of the law. For such a test, the following law corrections will be in effect:

Plus factors:
Double-Double fit (two 8 card fits for both pairs)
Exceptionally purity in your trump suit
Voids
Extra long suits

Minus Factors
Poor Intermediates in trump suit (either side)
Flat hands
Misfits

I will add 1 trick for two plus factors, and subtract one point for 2 minus factors. 2 plus and 1 minus or 2 minus and 1 plus results in no addition. EXCEPTION: QJx, KJ9 or AJ9 of their trumps I will subtract a full trick. Two plus factors matched with the EXCEPTION subtraction leads to no change.

As a test of this evaluation and to demonstrate what I have in mind I picked your game from June 3, 2003 because it is current, and more importantly, you only played 10 hands. Here is how application LOTT with these corrections worked on these ten hands (anyone wanting to look at the hands can find them at http://bbo.bridgebase.com:81/perl/history....34&p=2003-06-03

Hand one, two 8 card fits. Here both sides have good intermediates in their trumps suits, and there is a void too boot. Three additions raise trick total from 16 to 17. Here you can make 11 tricks in hearts (they get AK) and you can take D-AK, S-AK, C-AKQ against their contract, so they can make 6 tricks. The 17 the law suggest.

Hand two, 8-8 fit, bad intermediates for both sides, two deductions = 15 tricks.
Best defense, you make 2S (you made 3), best defense they make 1C for 15 tricks

Hand three. Both sides have a nine card fit (18 trumps) and a second 8 card fit (double double fit). In addition, your side has Wonderful trump intermediates, so I would add a trick to the total. But, your partner has QJx in their long suit, this is almost always worth a trick on defense that is not useful on this double-double fit, so it is an automatic subtraction from the trick total. You lose one Heart in either of your suits, and you can hold them to 6 tricks in hearts (partner leads a trump in here, and you win 1H, 3S, 2D, 1C). The 18 tricks predicted by LOTT

Hand four. Two 8 card fits, good intermediates both sides, so add 1, for 17 tricks. You can make 7 tricks in diamonds, they can make 10 tricks in spades.

Hand five is a freak. They have 11 card Club fit, you have 10 card heart fit. There is clearly bad intermediates in hearts, so subtract one from the total. They can win only 9 tricks in clubs (7C, 1D, 1H with good defense). You on the other hand can win 11 tricks in hearts (lose 1C, 1H). That is a total of 20 tricks. Once again, with the correction for the bad heart intermediate, right on the money.

Hand Six. Is a double-double fit, with 8 cards in each of the fit. That is 16 plus a small addition for double double fit, but there is no second addition, and no subtraction so it stays at 16. They can make 10 tricks in hearts, you can make only 6 tricks in spades or diamonds. For a total of 16.

Hand Seven. 9 trumps you, 8 trumps then for 17. On this hand, there is a subtraction from their total due to poor trump quality, dropping total from 17 to 16. You can make only 10 tricks in spades on HA lead, they can win only 6 tricks in clubs or diamonds.

Hand Eight another 8 and 8 trump fit for 16. Your holding of a slow trump trick in their suit is a definite subtract one, for 15. They win 8 tricks in Spades, so might be surprised to see that you can win 9 tricks in diamonds. In other words, this is a 17 trick hand. So this one the law fails, and I think it fails by two tricks, because I would have thought this a 15 trick hand.

Hand Nine. is an 8 card and 8 card fit, for a lowly 16 count. On this hand, there are no additions but the club suit has what I considered a big minus with QT7x of your trumps in one opponent hand. Like having QJ9 or AJ9, holding four to QT I count as a full point subtraction (one extra trick on defense against clubs, that is not a winner on offense). So my adjusted LAW says the TT is 16-1 = 15. It is a little surprising then that one side win 9 tricks in hearts, while the other wins 7 tricks in clubs for 16. I would say that the law FAILED on this one, because using corrections I would expect 15, not 16 tricks.

Hand Ten, everybody has seven card fits. We look at two things. How many notrump can then make versus how many of our best fit can we make (LOTT says total tricks = 7 plus our long suit, or 14), versus what is each of the longest suits. They can make 3NT (9 tricks), and if you play in your 7 card fit, they can take 8 tricks (2H, 1H ruff, 3C, 2D), leaving you with 5 tricks. 5+9 =14. How about if they play in your 7 card Diamond fit? They win 9 sure tricks. Again = 14 the law predicted.

So how did the law do on these 10 hands? Right on 8 times (1-7, & 10), a non-typical failure (by being right) on one (9) and clearly wrong one (8).

Now for the fun! LOTT disbelievers are invited to review the hands above and prove my analysis wrong (or right), and Misho is invited to pick another set of hands by himself, me, or anyone else to evaluate, hopefully as random as I picked these. In evaluating the contract, remember the law calls for double dummy play (not what will make, but the maximum with double dummy play both ways. The 80% right rate in this example is slightly higher than my real world experience, but 41% is a huge underestimate I think. (GOSH, who would have thought I would be defending the LOTT, remember I posted in this thread that "to my point now where I use it, but not as ardently as I once did".

Ben

[Cave_Draco]

41% means you are better off tossing a coin!

I can accept that, but I would like to see the figures, ;D.

[mishovnbg]

I like facts and statistics. Here some of it Ben, if you like you can verify it ;D.
World championship finals 1981-1983: 37.22%
for deals with 24+ hcp, any side: 30.61%
for deals with 17- hcp, any side: 41.95%
GIB analyse 600 deals: 37.33%
You can read more about detailed analysis from 8 parts "The law series". author Anders Wirgren. For me is enough clear that LOTT is only next false belief.
Misho

[Laird]

Hello Everyone

I would just like to thank you all very much for responding and taking the time to explain this concept. The e-links and book references are most welcome.
Yet for me, the examples given and tips provided are equally important as I am confident about the quality of the content and the motivation of the writers.
Such examples are easier for my mind to absorb and I thank you for that.
I'm glad that Ben in his personalised example chose one of my hands which had a favourable outcome. There are many he could have chosen which would have had outcomes not nearly so favourable.
I hope that other readers will have found the posts equally enthralling.
Thank you all most sincerely
John

[inquiry]

Quote

I like facts and statistics. Here some of it Ben, if you like you can verify it ;D.
World championship finals 1981-1983: 37.22%
for deals with 24+ hcp, any side: 30.61%
for deals with 17- hcp, any side: 41.95%
GIB analyse 600 deals: 37.33%
You can read more about detailed analysis from 8 parts "The law series". author Anders Wirgren. For me is enough clear that LOTT is only next false belief.
Misho

97.63% of all Bridge statisitcs are wrong (including this one).

As I said in my first post, in the beginning I was a disbeliever in the LOTT. Then I became a true believer, then I backed off to be somewhere in between the two extremes. But I have personnally analyzed a lot of hands one after the other, and since then, look at almost everyhand where I was thinking about using LOTT (or did use it), to see if it would have "worked". My own non-scientific study suggest that the law is right just above 70% of the time if you apply the corrections.

There is little doubt that the LAW goes astray somewhat when HCP are not divided equally. I have seen this issue addressed nicely in two places, once here by Dwayne in a post (not clear if this was his own creation or cut-and-paste from elsewhere, but excellent either way)
http://forums.bridgebase.com/in...ay;threadid=187

and once at http://www.calculato...otalTricks.html A statistical analysis of tested this HCP-corrected LOTT on 300,000 deals – comparing the predicted results with the results of a double-dummy solver with surprisingly good results, reported that the mean error is -0.02 tricks and the standard deviation is 1.22. The data for normal, uncorrected "Law" accuracy which was reported to be 0.126, standard deviation 1.039.

Others doing statistics on LOTT include Matt Ginsberg (author of GIB) "On the law of total tricks" 1996 Bridge World, Larry Cohen (see his books), and of Jean Vernes in the Bridge World (sorry, can't read the french), and Peter Peter Cheung (a mathematician/bridge fan) on his web site http://crystalwebsit...m/a_the_law.htm

It is worth noting, that for large statistical studies, usually no correction factors where used. The 300,000 hands using the correction for hcp seems the first to try such corrections. I couldn't get on to the ebridge site despite the free registration, so maybe some ebridge member will summarize how the study Misho is refering too was performed.

I try to use LOTT in competitive bidding situations a tool for offering me advice as to bid, pass, or double. Again, my experience is it is MUCH better than 41% being right. That is all I am trying to say. I would hate for some one unfamilar with the LAW to read your quoted statistics and assume that using LOTT is worse than blind guess (50-50) and convince them that looking into the law is useless, rather than allwoing them to study the LAW and deciding on their own its merits.

Ben