# BBO Discussion Forums: How to calculate the distributive strength of the hand? - BBO Discussion Forums

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## How to calculate the distributive strength of the hand? Dstributive strength

### #1gergana85

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Posted 2014-March-04, 07:46

This material aims to identify the factors which influence the distribution strength as well as to clarify the mechanism of their action. The solution of this problem will help us create a new, more accurate method for hand evaluation.
To eliminate the influence of the honors strength on the common strength of the hand we decided to examine only hands which lack honors.
The only indicator that is devoid of subjectivity (e.g. the ability to play well and the position of the honors are subjective) and solely reflects the distribution strength is the maximum number of losers in the hand (Lmax). Here we assume, the same way the LTC method does, that each fourth and next card in a certain suit is a winner.
Based on this assumption we can say that Lmax varies from 0 (distribution 13-0-0-0) to 12 (distribution 4-3-3-3).

DEPENDENCY OF THE MAXIMUM NUMBER OF LOSERS ON THE DISTRIBUTION

The result of the analysis of all possible distributions clearly shows that the main indicator that determines the value of Lmax is the sum S1,2 = S1 + S2, where S1 and S2 are the number of cards in the two longest suits. Furthermore, we determined that in some cases Lmax is influenced not only by the sum of the lengths of the two longest suits but there is an additional dependency on the lengths of the three longest suits. We found that:

Lmax = 19 – S1,2 – ( P1 + P2 + P3 )

P1, P2 and P3 are corrections that depend on the number of cards in the three longest suits.
According to thise formula the sum S1,2 and the corrections P1, P2 and P3 decrease the maximum number of losers in a hand and therefore they increase its distribution strength.
It is worth noting that the probability of getting a hand where (P1 + P2 + P3 ) ˃ 0 is no more than 3.8%. In the rest of the cases Lmax depends only on the sum of the lengths of the two longest suits.
This dependency can be summarized in The Law of the two longest suits which states:

The maximum number of losers in a hand is inversely proportional to the sum of the lengths of the two longest suits.

It also proves the famous hypothesis: "The potential of a hand to win tricks is directly proportional to the sum of the lengths of the two longest suits."

CORRECTIONS P1, P2 AND P3

For some unusual distributions Lmax is influenced by the length of the three longest suits.

The correction P1 represents the presence of at least one of the top three honors in the longest suit, when it has more than 10 cards (S1 > 10). This correction has no real practical application, only in theory. Such distributions are too unbelievable and therefore we ignore them.

P1 = (|10 – S1| - (10 – S1))/2

|10 – S1| is the absolute value of the difference (10 – S1).

The correction P2 is positive only for S2 < 3 and it's a result from the decreased number of losers in the third and fourth longest suits in the hand. Of all distributions that satisfy this condition the only two that needs attention are 7-2-2-2 and 8-2-2-1, where P2 = 1. The other distributions that satisfy this condition (9-2-1-1, 9-2-0-0, 10-2-1-0) and 11-2-0-0 are ignored. It is still necessary to point out that when S2 = 1 (10-1-1-1, 11-1-1-0, 12-1-0-0) then P2 = 2 and when P2 = 0 (13-0-0-0) then P2 = 3.

P2 = (|3 – S2| - (S2 - 3))/2

|3 – S2| is the absolute value of the difference (3 – S2).

The correction P3 refers to the 3-suited distributions (4-4-4-1 and 5-4-4-0) in which the number of cards in the third longest suit is exactly four (S3 = 4). Such distributions are stronger by one trick compared to the other distributions in which the sum of the two longest suits is the same. This is because the longer third suit decreases the number of losers in the fourth suit.

P3 = (|3 – S3| - (3 – S3))/2

|3 – S3| is the absolute value of the difference (3 – S3).

CONCLUSIONS

The research shows that it is necessary to reconsider the factors that determine the distribution strength of the hand. We can make the following conclusions:

• The sum of the two longest suits (S1,2) is the most important factor that changes the distribution strength of a hand. In the 4-3-3-3 distribution (S1,2 = 7) Lmax = 12. With any increase of the sum S1,2 with 1 card we get a decrease in the maximum number of losers (Lmax) by 1 and therefore an increase in the potential of the hand to win by 1 trick;

• For some unusual distributions, in which the second longest suit has two cards, the maximum number of losers is decreased by 1 trick. When the second longest suit has 0 cards (distribution 13-0-0-0) or 1 card (10-1-1-1, 11-1-1-0 and 12-1-0-0) the potential of a hand to win tricks is increased by 3 and respectively 2 tricks. In practice though we have only the cases where the second longest suit has 2 cards (S2 = 2). This is because SS2 may have 1 or 0 cards only in distributions where the longest suit has 10 or more cards. However, such distributions most likely will never happen in a lifetime;

• 3-suited hands have a higher potential to win tricks. Under similar conditions it is a trick higher compared to other hands for which the sum S1,2 is the same. In practice this needs to be taken into consideration;

• It is necessary to reconsider the evaluation of the hand strength. It is the usual practice to first evaluate the honor strength and then correct it for a specific distribution. The analysis that was done shows that it is more proper to first estimate the maximum number of losers in the hand (calculate of the distribution strength) and only then to determine how many (and what) are the honors that would covers those losers. The difference between these two variables gives the potential of the hand to win tricks. The suggested model makes this evaluation quite accurate.

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### #2Cyberyeti

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Posted 2014-March-04, 09:17

gergana85, on 2014-March-04, 07:46, said:

How to calculate the distributive strength of the hand? See that: http://bridge-law.hit.bg

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### #3gszes

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Posted 2014-March-05, 20:55

I also could not load the link so I am going to guess and give you
my general (offensive) upgrade to a hand based solely on suit length

5 card suit + 1
6 card suit + 1.75
7 card suit + 3.25
8 card suit + 5
keep adding +2 for every card above 8.

I have a tendency to downgrade these bonuses by .5 if I do not have
the A or K in the suit unless there are great intermediates. I hope
his is what you were looking for
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### #4Vampyr

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Posted 2014-March-05, 21:24

Honestly, the topics posted in the "Expert" forum have been getting worse and worse. I hope this is the nadir; I think I am fairly confident that it is, though.
I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones -- Albert Einstein
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### #5jogs

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Posted 2014-March-06, 15:06

Vampyr, on 2014-March-05, 21:24, said:

Honestly, the topics posted in the "Expert" forum have been getting worse and worse. I hope this is the nadir; I think I am fairly confident that it is, though.

Guess what you want is users with fewer than 1,000 posts aren't allowed to start threads on the "Expert" forum.
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### #6nige1

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Posted 2014-March-06, 17:57

gergana85, on 2014-March-04, 07:46, said:

How to calculate the distributive strength of the hand? See that: http://bridge-law.hit.bg
The Bridge World published a relevant article called "Benchmarks" by John Matheson, explaining rules of thumb that you can use, especially in competitive auctions.

I use Winners, a method, based on advice from my father Charles Guthrie, roughly equivalent to the losing trick count (but I now accord slightly less weight to shape)
A = 1.5, K = 1, Q = 0.5
(except singleton Ks and doubleton Qs are just plus values)
Doubleton = 1, singleton = 2, Void = 3 (Although this seems to overvalue shortages, in practice)
Adjust for duplication (e.g. shortage opposite strength)
Total winners = Your winners + Partner's winners + Trump control
You count one for trump control, if you have enough trumps, to ruff losers and draw opponent's trumps.

It is beneficial to agree some yardstick with partner, to avoid wasting a lot of time, trying to assign the blame, after "judgement" failures.
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### #7johnu

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Posted 2014-March-06, 18:16

jogs, on 2014-March-06, 15:06, said:

Guess what you want is users with fewer than 1,000 posts aren't allowed to start threads on the "Expert" forum.

Sub-forums are not divided by newbie posters, occasional posters, frequent posts, or prolific posters

The description of the Expert-Class Bridge Forum says "Forum designated for expert bridge players to discuss more advanced topics."

Would you consider the OP's question to be closer to an advanced topic or a Novice and Beginner question?
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### #8mycroft

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Posted 2014-March-07, 11:18

I'd consider it as, and have done something [Edit: reported it] assuming it was, spam. When this user's posting history is <50% the identical ad for a web site (granted, posted in semi-appropriate places), I'll start reading the user. Might even visit that web site.

[Edited: since it's been noted by a yellow, I feel more comfortable being less circumspect.]
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### #9jogs

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Posted 2014-March-07, 17:55

johnu, on 2014-March-06, 18:16, said:

Would you consider the OP's question to be closer to an advanced topic or a Novice and Beginner question?

It really doesn't matter what I think. The OP thought his thread was worthy of the expert forum.
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### #10johnu

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Posted 2014-March-07, 18:33

jogs, on 2014-March-07, 17:55, said:

It really doesn't matter what I think. The OP thought his thread was worthy of the expert forum.

Posters with hundreds or even thousands of posts routinely post novice and beginning level problems here because they want expert advice, based on the mistaken belief that only novices and beginners answer posts in the Novice and Beginners forum. The original poster can clarify, but I would be willing to bet that's what happened in this case. The other possibility is that the OP posted in the wrong forum by mistake, which also happens a lot.
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### #11Vampyr

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Posted 2014-March-07, 19:19

jogs, on 2014-March-07, 17:55, said:

It really doesn't matter what I think. The OP thought his thread was worthy of the expert forum.

Why does this matter? The poster is wasting the time of experts and others looking here for advanced topics, not his or her own.

Do you not think that there is a role for the expert forum?
I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones -- Albert Einstein
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### #12gszes

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Posted 2014-March-09, 09:41

When do I get to start downgrading those posters that rag on the poster??
They think of the poster as spamming them and I view their jaundiced opinion
as spam to me. IE adding absolutely nothing of worth to the conversation at
hand and wasting my time with irrelevancies over how they feel disrespected
at having to even view such simplistic questions.

Remember wayyyyyyyyyyyyyyyyy back when you were looking at the hand
analysis and you saw 2 or 3 of the top players in the room all made 4n while
the rest of the field made 3n despite getting the same lead???? You could have
probably stared at the hand for hours and not figured out why they scored better
than average. If you took the time to ask you commited the same "spam" you are
accusing others of now---if you do not like a question please just ignore it
and move on so I don't waste my time reading your drivel and writing this
diatribe over and over and over ad nauseum.
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### #13mikeh

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Posted 2014-March-10, 08:57

gszes, on 2014-March-09, 09:41, said:

When do I get to start downgrading those posters that rag on the poster??
They think of the poster as spamming them and I view their jaundiced opinion
as spam to me. IE adding absolutely nothing of worth to the conversation at
hand and wasting my time with irrelevancies over how they feel disrespected
at having to even view such simplistic questions.

Remember wayyyyyyyyyyyyyyyyy back when you were looking at the hand
analysis and you saw 2 or 3 of the top players in the room all made 4n while
the rest of the field made 3n despite getting the same lead???? You could have
probably stared at the hand for hours and not figured out why they scored better
than average. If you took the time to ask you commited the same "spam" you are
accusing others of now---if you do not like a question please just ignore it
and move on so I don't waste my time reading your drivel and writing this
diatribe over and over and over ad nauseum.

Your advice about ignoring a post doesn't work until one has read the post. One cannot (usually) tell that a post in the expert forum is a non-expert issue until one has read it.

The very notion that one uses an arithmetical approach to hand evaluation, adding or subtracting points or half points, as you say you do, is inappropriate for the expert forum, if we are talking about real experts rather than self-proclaimed BBO experts.

I'd be interested in hearing from the real experts here as to how many of them use an arithmetical formula for distributional points at the table. I haven't done so in so many years that I can't recall when I stopped.

Hand evaluation can be discussed at the expert level, but it is far too subtle a concept, at that level, to be reduced to a number. That approach, useful tho it will be for the advancing player, is far too simplistic, no matter how one fine-tunes the formula, for expert usage.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari
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### #14jogs

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Posted 2014-March-10, 14:06

I've never understood why most systems attempt to evaluate every variable in terms of points. Why aren't they attempting to estimate partnership tricks? Don't they know all estimates are dynamic and not static? The estimates can change dramatically with each piece of new information.
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### #15nige1

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Posted 2014-March-10, 14:47

gszes, on 2014-March-09, 09:41, said:

When do I get to start downgrading those posters that rag on the poster? They think of the poster as spamming them and I view their jaundiced opinion as spam to me. IE adding absolutely nothing of worth to the conversation at hand and wasting my time with irrelevancies over how they feel disrespected at having to even view such simplistic questions.

mikeh, on 2014-March-10, 08:57, said:

Your advice about ignoring a post doesn't work until one has read the post. One cannot (usually) tell that a post in the expert forum is a non-expert issue until one has read it. The very notion that one uses an arithmetical approach to hand evaluation, adding or subtracting points or half points, as you say you do, is inappropriate for the expert forum, if we are talking about real experts rather than self-proclaimed BBO experts. I'd be interested in hearing from the real experts here as to how many of them use an arithmetical formula for distributional points at the table. I haven't done so in so many years that I can't recall when I stopped. Hand evaluation can be discussed at the expert level, but it is far too subtle a concept, at that level, to be reduced to a number. That approach, useful tho it will be for the advancing player, is far too simplistic, no matter how one fine-tunes the formula, for expert usage.
I agree that BBO self-rating is unreliable; but no matter what the skill level of the OP, he is likely to appreciate expert-opinion. To reduce the time wasted on status-snobbery, it might be better to condense Bridge-related discussions to
• Declarer play
• Defence
• Uncontested Auction
• Contested Auction and
• Reviews (books etc).
(BTW, there's little point in a separate Non-natural system forum, when members post queries about artificial conventions like Bergen, Lebensohl, and so on to the "Natural" bidding forum).

jogs, on 2014-March-10, 14:06, said:

I've never understood why most systems attempt to evaluate every variable in terms of points. Why aren't they attempting to estimate partnership tricks? Don't they know all estimates are dynamic and not static? The estimates can change dramatically with each piece of new information.
Winners (and the almost equivalent LTC) attempt to estimate tricks, dynamically. BBO critics (and other world-class players) may regard such rules-of thumb as beneath contempt but during every auction, even they must (consciously or subconsciously) use some method to assess and re-assess the trick-taking potential of their side. Manifestly, some Olympians are better at this than others.
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### #16ggwhiz

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Posted 2014-March-10, 14:58

We need a separate forum for those who think reading such a post is below them.

I vote for a seperate planet where the horrors of wasting 10 seconds of my time is a capital offence. That or remedial speed reading lessons.
When Ghandi was asked what he thought about western civilization he said: I think it would be a good idea.
If two people always agree one of them is unnecessary - Carol Frank
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### #17diana_eva

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Posted 2014-March-10, 17:08

The OP was spam ... did you guys even check poster's history at all? She came, plugged a link to some website that probably is supposed to provide a revolutionary formula to calculate distribution points, and that was all. It's not about expert topics or seeking expert advice, it's just plain regular spam IMO.

### #18nige1

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Posted 2014-March-10, 17:44

diana_eva, on 2014-March-10, 17:08, said:

The OP was spam ... did you guys even check poster's history at all? She came, plugged a link to some website that probably is supposed to provide a revolutionary formula to calculate distribution points, and that was all. It's not about expert topics or seeking expert advice, it's just plain regular spam IMO.
Thanks Diana
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### #19Cyberyeti

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Posted 2014-March-10, 17:46

ggwhiz, on 2014-March-10, 14:58, said:

We need a separate forum for those who think reading such a post is below them.

I vote for a seperate planet where the horrors of wasting 10 seconds of my time is a capital offence. That or remedial speed reading lessons.

Actually this is stupid, a one line meaningless post and a link that wouldn't load for several of us is just spam, I was begining to wonder whether it was in fact downloading malware.
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### #20gergana85

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Posted 2014-March-15, 05:23

see post #1
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