[jdiana]

So, I finished reading To Bid or Not to Bid (Larry Cohen's book on the Law of Total Tricks) and I think it's useful even just in terms of general hand evaluation. But I have to say that I'm still not really confident that I could apply it at the table.

I assume most of you are familiar with it but, basically, it argues that the total number of tricks available to both sides in any bridge deal is equal to the total number of trumps (i.e., the number of cards held by each side in their longest suit, added together).

To really apply the Law, you would mentally construct a table of scores. For example, if there are 16 total tricks and we take 8, then the opponents would take 8. Non-vulnerable, the scores would be +140, -140, assuming both sides were playing in a major. If we take 7, they take 9, etc. (See the Timm article below for an example.) The numbers would vary based on vulnerability and majors vs minors. I couldn't possibly do that at the table.

To short-cut the need to construct these tables in our heads, LC derived some general rules, some of which are familiar to people who have never read his book, or even heard of "the Law of Total Tricks", such as: "We should compete to the level of the total number of trumps we hold." and "We should strive not to let the opponents play in a fit at the two level."

Anyway, the point of this post is to ask whether anyone has ever tried to construct a table along these lines (I have to describe it because I don't know how to create a table in this forum): The first column would be "Expected Number of Total Tricks (Adjusted)"; then the column headings would be 2-over-2; 3-over-2; 3-over-3; 4-over-3; 4-over-4. The cells in the table would just be a "Yes" or "No" for whether to compete to that level. We would (I think) need separate charts for vulnerability, and maybe for majors vs minors. Oh, and doubled vs undoubled.

Neil Timm took a step in this direction here - https://bridge-tips....Tricks-Nill.pdf

I'm sure I could learn a lot by building these tables myself, but I'm lazy. Does anyone know if such a thing exits already?

[P_Marlowe]

I dont understand, what you are looking for, but

#1 If you have a 8 card fit, you should not let them play at the 2 level, i.e. you should compete to the 3 level
#2 If you only have a 8 card fit, you should not bid 3 over 3, i.e. if you bid over their 3 level contract you
compensation, in the form of add. trump length, aka the 9th trump.

Vulnerability has not much to do with it.

Obv. if you are playing MP, and you are red, if you outbid them you riks going for 200 if they find the MP double.
Playing IMPs you are some what protected, they fear 3?X=.

The Law still holds for higher trump fit / total tricks, but starts to become unstable.

[jdiana]

P_Marlowe, on 2025-March-03, 14:15, said:

I dont understand, what you are looking for, but

#1 If you have a 8 card fit, you should not let them play at the 2 level, i.e. you should compete to the 3 level
#2 If you only have a 8 card fit, you should not bid 3 over 3, i.e. if you bid over their 3 level contract you
compensation, in the form of add. trump length, aka the 9th trump.

Vulnerability has not much to do with it.

Obv. if you are playing MP, and you are red, if you outbid them you riks going for 200 if they find the MP double.
Playing IMPs you are some what protected, they fear 3?X=.

Thanks.

I might be over-complicating it - I'll give it some more thought.

[Chas_P]

jdiana, on 2025-March-03, 09:54, said:

So, I finished reading To Bid or Not to Bid (Larry Cohen's book on the Law of Total Tricks) and I think it's useful even just in terms of general hand evaluation. But I have to say that I'm still not really confident that I could apply it at the table.

Mike Lawrence also wrote a book entitled "I Fought the Law....of Total Tricks" in which he argues that "The Law" is wrong more often than it's right. And then there's Larry Who?

[blackshoe]

Marty Bergen has a series of 40 pamphlets on various useful subjects, one of them being the LOTT. I haven't read it in years, but it may have what you're looking for, or a good substitute.

Last I checked the pamphlets are 10 or 11 bucks from the usual sources, but you can buy a set of 39 (apparently he's run out of one, or he's randomly deciding which one you don't get) for I think 180 bucks or so direct from Marty.

[jillybean]

Burn's Law of Total Trumps:
"When you are declarer, the total number of trumps held by your side should be greater than the total number of trumps held by your opponents."


https://blakjak.org/burn_law.htm

[jdiana]

Chas_P, on 2025-March-04, 15:32, said:

Mike Lawrence also wrote a book entitled "I Fought the Law....of Total Tricks" in which he argues that "The Law" is wrong more often than it's right. And then there's Larry Who?

Thanks. LC also wrote a sequel, but I'm not buying either of those books. I know the LoTT isn't perfect, but I think it may help answer the question "Should I bid one more or maybe double?" in certain situations.

It's kind of like Losing Trick Count. Some people swear by it; others think it's nonsense. I'm looking for ways to improve my bidding judgment, especially in competition. I think experts are able to look at a hand and make a lot of quick mental evaluations of how high to bid (not to mention visualizing all the hands their partner and opponents might have, based on their bidding). While I'm waiting (probably forever) to develop that kind of subjective judgment, I find "crutches" like LoTT and LTC to be helpful shortcuts, if applied judiciously and without expecting perfection. YMMV.

[jdiana]

jillybean, on 2025-March-05, 10:08, said:

Burn's Law of Total Trumps:
"When you are declarer, the total number of trumps held by your side should be greater than the total number of trumps held by your opponents."


https://blakjak.org/burn_law.htm

That's a popular link.

So, we should never bid 3-over-2 when each side has 8 trumps?

[jillybean]

I think any research, reading and discussions us mere bridge mortals can do to improve our game is worthwhile. I did not intend to belittle your question, it is a good question. I do believe there are few bridge questions that can be answered by a Law, and I just love David Burn's humour.

As a real newbie, I had been badly stung in 5X contracts, I just kept bidding in competitive auctions and when I didn't have the nerve to bid more, I passed. I never doubled my opponents.
When I played in my first Regional where there was an 'Ask An Expert' forum, I put my hand up and asked "In a competitive auction, how do you know when to bid one more or double?". I think I was hoping for rule I could understand, such as "you are not allowed to open 1nt with 2 doubletons". The room chuckled at my question and the Expert, with a nice smile on his face said that my question was too complex for this forum but as I progressed in my bridge, I would develop the tools.

I'm still trying to develop those skills.

[jdiana]

jillybean, on 2025-March-05, 11:28, said:

I think any research, reading and discussions us mere bridge mortals can do to improve our game is worthwhile. I did not intend to belittle your question, it is a good question. I do believe there are few bridge questions that can be answered by a Law, and I just love David Burn's humour.

As a real newbie, I had been badly stung in 5X contracts, I just kept bidding in competitive auctions and when I didn't have the nerve to bid more, I passed. I never doubled my opponents.
When I played in my first Regional where there was an 'Ask An Expert' forum, I put my hand up and asked "In a competitive auction, how do you know when to bid one more or double?". I think I was hoping for rule I could understand, such as "you are not allowed to open 1nt with 2 doubletons". The room chuckled at my question and the Expert, with a nice smile on his face said that my question was too complex for this forum but as I progressed in my bridge, I would develop the tools.

I'm still trying to develop those skills.

No worries!

I think it might make more sense to people if I could show what I had in mind. It might still not be worth doing but at least you could see what I was thinking. I did one set of tables in Excel, but I don't know how to share an image here. It looks like it might need to be posted online, with an http: address. If anyone knows how to do that and would be willing to volunteer, I'd be happy to send you the Excel file by email. Just send me a PM with your email address.

[pescetom]

jdiana, on 2025-March-05, 10:17, said:

It's kind of like Losing Trick Count. Some people swear by it; others think it's nonsense. I'm looking for ways to improve my bidding judgment, especially in competition. I think experts are able to look at a hand and make a lot of quick mental evaluations of how high to bid (not to mention visualizing all the hands their partner and opponents might have, based on their bidding). While I'm waiting (probably forever) to develop that kind of subjective judgment, I find "crutches" like LoTT and LTC to be helpful shortcuts, if applied judiciously and without expecting perfection. YMMV.

I swear by neither, but I do take consideraly more account of LoTT.
I confess I never read the book, but I have read plenty of articles and posts and they all seem to match.
FWIW as I employ it, the two biggest danger areas I have found are:
1) raising preemptively to 3-level on a 9-card fit at unfavourable vulnerability (maybe not an overall MP loser, but costly in terms of partnership confidence)
2) 20+ total trumps easily produce even more total tricks

[DavidKok]

I forgot to mention, but it's on topic.

Almost two years ago I was playing around with the dealer scripting language, and one of the programs I wrote generated a table of the Law of Total tricks. In particular, I compared the total trumps (sum of length of longest fit of NS + longest fit of EW) against the total tricks (highest number of tricks by NS in a trump contract + same for EW - not necessarily the same strains as the longest fits!). I only ran the script for just under 4 hours, but that was enough to solve 200,000 hands and compare them.

Of those the Law was:

• Too optimstic by 3 or more tricks: 10,971 deals (5.5%).
  
• Too optimstic by 2 tricks: 22,269 deals (11.1%).
  
• Too optimstic by 1 trick: 50,688 deals (25,3%).
  
• Exactly right: 67,913 deals (34,0%)
  
• Too pessimistic by 1 trick: 38,046 deals (19.0%)
  
• Too pessimistic by 2 tricks: 8,788 deals (4,4%)
  
• Too pessimistic by 3 or more tricks: 1,325 deals (0,7%).

There was also a slight skew depending on the total number of trumps: the LAW seemed a little bit more accurate when the total number of trumps was lower, though it didn't vary all that much and it still held up reasonably well up to 19 total trumps. On average it was 0.37 tricks too optimistic, and especially at high total trumps the mode of the distribution moved to "Too optimistic by 1 trick" rather than "Exactly right". There are many ways to interpret the numbers above - personally I like to cite that the LAW is, on average, within one trick of accurate approximately 78% of the time - but at the very least I think this is a valuable statistical tool in situations with a lot of uncertainty, even without any adjustments or nuances.

The full table of results are available on request. Maybe I should run the code for a couple of days sometime, to increase the sample size a little.

[mike777]

Ty David
Would be interested in how Mike L. Fought the law FTL fairs in comparison

[jdiana]

DavidKok, on 2025-March-05, 17:37, said:

I forgot to mention, but it's on topic.

Almost two years ago I was playing around with the dealer scripting language, and one of the programs I wrote generated a table of the Law of Total tricks. In particular, I compared the total trumps (sum of length of longest fit of NS + longest fit of EW) against the total tricks (highest number of tricks by NS in a trump contract + same for EW - not necessarily the same strains as the longest fits!). I only ran the script for just under 4 hours, but that was enough to solve 200,000 hands and compare them.

Of those the Law was:

• Too optimstic by 3 or more tricks: 10,971 deals (5.5%).
  
• Too optimstic by 2 tricks: 22,269 deals (11.1%).
  
• Too optimstic by 1 trick: 50,688 deals (25,3%).
  
• Exactly right: 67,913 deals (34,0%)
  
• Too pessimistic by 1 trick: 38,046 deals (19.0%)
  
• Too pessimistic by 2 tricks: 8,788 deals (4,4%)
  
• Too pessimistic by 3 or more tricks: 1,325 deals (0,7%).

There was also a slight skew depending on the total number of trumps: the LAW seemed a little bit more accurate when the total number of trumps was lower, though it didn't vary all that much and it still held up reasonably well up to 19 total trumps. On average it was 0.37 tricks too optimistic, and especially at high total trumps the mode of the distribution moved to "Too optimistic by 1 trick" rather than "Exactly right". There are many ways to interpret the numbers above - personally I like to cite that the LAW is, on average, within one trick of accurate approximately 78% of the time - but at the very least I think this is a valuable statistical tool in situations with a lot of uncertainty, even without any adjustments or nuances.

The full table of results are available on request. Maybe I should run the code for a couple of days sometime, to increase the sample size a little.

Interesting - thanks!

This is consistent with what I've read elsewhere, i.e., that the "Law" is generally pretty accurate +/- 1 trick and that it works better at lower level decisions and with relatively fewer total tricks. I think there's a sweet spot at around 14-18 total tricks and with 3-over-2, 3-over-3, and 4-over-3 decisions, but can't back that up statistically. Some of the adjustments LC suggests, like subtracting a trick when we have minor honors (QJ) in the opponent's suit or poor intermediates in our own suit, should be relatively easy to make and are really just part of good hand evaluation.

[akwoo]

There is actually a pretty simple rule.

At MPs, no one vulnerable, you should bid as long as you are confident that total tricks bid <= total trumps + 1 (i.e. at most one contract is going down). If someone is vulnerable, this is still the correct rule if there is no double, but if one side has enough strength to double (or understands correctly that they are in a free double situation based on MP odds), you should be more conservative. (Total tricks bid is the number of tricks for the contract you're contemplating bidding + tricks for the contract currently on the table.)

So you bid 3-over-2 if you're almost sure there are at least 16 total trump, 3-over-3 if you're almost sure there are at least 17.

At IMPs, you should bid as long as there is a reasonable possibility that total tricks bid <= total trumps (i.e. there is a possibility both contracts make). So you need more trumps, but less confidence in the actual number. This difference in certainty is important because frequently you don't know total trumps (especially after the usual adjustments).

Here you bid 3-over-2 if there might be 17, and 3-over-3 if there might be 18.

[smerriman]

akwoo, on 2025-March-05, 19:12, said:

There is actually a pretty simple rule.

At MPs, no one vulnerable, you should bid as long as you are confident that total tricks bid <= total trumps + 1 (i.e. at most one contract is going down). If someone is vulnerable, this is still the correct rule if there is no double

While I'm not saying you're wrong, how do you resolve the contradiction between this and the PDF linked to in the OP for the 3 over 3 case (at least), which states that you should bid 3 over 3 with 16 total trumps when favorable or both non-vulnerable, without doubles being a factor?

[akwoo]

smerriman, on 2025-March-05, 20:18, said:

While I'm not saying you're wrong, how do you resolve the contradiction between this and the PDF linked to in the OP for the 3 over 3 case (at least), which states that you should bid 3 over 3 with 16 total trumps when favorable or both non-vulnerable, without doubles being a factor?

It's easy to do the calculation. Bidding 3-over-3, neither vulnerable, with 16 trumps, assuming Law is correct, the possibilities are:

Us making, them down 2 - bidding gets us +140; doubling gets us +300; passing gets us +100
Us down 1, them down 1 - bidding gets us -50/100; doubling gets us +100; passing gets us +50
Us down 2, them making - bidding gets us -100/300; doubling gets us -alot; passing gets us -140

In the middle case, bidding is definitely wrong. In the other cases, bidding is right only if no one doubles. Of course you have no idea what case you're in, but in a field where people know to double, you shouldn't bid. With an even split of points, generally the middle case is most likely (but not by much). The MP odds for doubling in the last case frequently make it worth it even if you're just hoping to set the contract.

[smerriman]

Yup, agreed, and that now matches the PDF - and doubles definitely impact things - just wanted to clarify your previous post where you said your rule still applied if nobody doubled.

[jdiana]

https://acrobat.adob...ea-4987caf8cf26

I think I found a way to share the table I made in Excel as a PDF document. The format got a little messed up - the third column got put on page 2, if that makes sense.

You can see that you would have to make a boatload of these tables but I might do it just to see what I can learn. Please let me know if this makes any sense to you. (This one assumes no one has doubled.)

Thanks!

[DavidKok]

 mike777, on 2025-March-05, 17:54, said:

Ty David
Would be interested in how Mike L. Fought the law FTL fairs in comparison

I have not read the book (and maybe I should end the story there), but it was my impression that Mike Lawrence challenged the law not as a statistical tool but as an absolute law. I have read his book on overcalls, and in my opinion most of it is outdated and incompatible with modern aggressive shape bidding.