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Joint Pattern Pair
Each player's 13 card hand has a pattern for the ordered configuration of the four suits. The suits are ranked spades, hearts, diamonds, and clubs. The hand's pattern is described in order spades=hearts=diamonds=clubs. List the number of spades for spades, etc. 5=4=3=1 means 5 spades, 4 hearts, 3 diamonds and 1 club. The equal sign is used to denote a permutation in the order of spades, hearts, diamonds, and clubs. The hyphen will represent hand pattern without regard to suit order.
Pattern is a 4 dimensional independent random variable. Pattern is the second independent random variable for estimating tricks. Each of the four suits is interlocking dependent on the other three suits. Pattern is a four-dimensional vector in physical space. The sum of the initial length of this vector is 13 for 13 cards in each hand. There are 39 possible pattern combinations for each hand. 4-3-3-3 is the flattest pattern and generates the fewest tricks. 4-4-3-2 is the second flattest. 13-0-0-0 is the most skewed pattern and generates 13 tricks whenever the suit is trumps.
Pattern pair is the joint pattern of the partnership hands. The suit pattern pair or pattern fit is the pattern pairing of the two partners' hands. All 26 cards of the partnership are used to estimate the effects of pattern. This pattern pair is the second estimator used for estimating tricks for each partnership. On any given deal tricks is a discrete integer variable at each table. It is difficult to conceptualize the relationship between pattern and tricks. Subdivide pattern into its three main components.
The longest combined suit length is usually designated trumps. The trumps is the major component of pattern which is also linearly proportional to tricks. Therefore it is possible to express their relationship in a simple easy-to-use formula. The expected tricks is equal to the combined trumps of the partnership. With only this information the variance of this relationship is high.
E(tricks) = trumps
or
E(tricks) = trumps + e
where e is the error of the estimates.
The second component of pattern the shortness of the side suits. This is the shorter partnership holding in each of the short side suits. 4=3=2=4//4=2=3=4. In this example, hearts and diamonds are the short suits. Provided there are sufficient trumps, the maximum number of tricks which can be lost in each suit quickly is the shorter holding of the partnership. In this example for the hearts it is two and for the diamonds it is two.
E(tricks) = trumps + SST + e
SST is the short suit total adjustment. This adjustment can both increase and decrease tricks from the original estimates.
The third component of pattern is source of tricks(ST). This can come from long trumps in one hand or a long second suit, which is a source for extra tricks. Either the sum of two suits in one hand or the sum of two suits for the partnership.
E(tricks) = trumps + SST + ST + e
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Joint Pattern Pair Sum of two suits
#1
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Posted 2017-February-05, 09:43
#2
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Posted 2017-February-05, 10:58
I am not sure where you are going with this, the Joint Pattern Pair, but it gives me an excuse to put up an amusing hand from a recent club game.Perhaps applying your concepts to these hands would be illustrative. Everyone was in the auction so I won't bother to rotate.
It is not every day that I hold the W hand and hear rho come in with 2NT over 1S, but there we are. If N, on lead against 3NT, attacks my heart entry I will have problems but he started with a diamond after which nine tricks are easy and in fact I took eleven (not the best defense).
I found the hand amusing (no doubt getting a good result was part of the amusement) but it came to mind as I read your post about patterns.
I had thought a little about this after the game. N can assume they have 13 minor suit cards between them so it is then a matter of arithmetic that EW have 13 major suit cards between them. Quite likely ten with E, three with W, so he might have considered that knocking out the heart entry to the board was a priority, diamonds can wait. Whatever the merit of that thinking, he led the diamond.
It is not every day that I hold the W hand and hear rho come in with 2NT over 1S, but there we are. If N, on lead against 3NT, attacks my heart entry I will have problems but he started with a diamond after which nine tricks are easy and in fact I took eleven (not the best defense).
I found the hand amusing (no doubt getting a good result was part of the amusement) but it came to mind as I read your post about patterns.
I had thought a little about this after the game. N can assume they have 13 minor suit cards between them so it is then a matter of arithmetic that EW have 13 major suit cards between them. Quite likely ten with E, three with W, so he might have considered that knocking out the heart entry to the board was a priority, diamonds can wait. Whatever the merit of that thinking, he led the diamond.
Ken
#3
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Posted 2017-February-05, 19:56
Sum of two suits
The joint pattern pair of the partnership can be expressed as two 4-dimensional vectors or just sum the suits for the partnership and treated as one 4-dimensional vector of 26 cards. Using the one vector method, sum the two longest suits. The trick space for this sum would span from 14 to 26. There is a strong correlation between total tricks and the sum of two suits.
There are three combinations which total 14 cards. 7-7-6-6, 7-7-7-5, and 8-6-6-6. About 20.5% of the time the board will be one of these three patterns. These 14 cards sum depresses tricks. About 14.6% of the time the board will be 17+ cards in two suits. The higher this sum the higher the expected total tricks. But it is not a strict one to one correspondence. Also during the auction it is often difficult for either partner to properly access this sum of two suits. Playing jump fits in both contested and uncontested auctions helps the partners to make this accessment.
When the sum of two suits is high(17+), the source of tricks component plays a greater role in generating tricks.
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There is also sum of two suits for one hand. Ten cards in two suits in one hand often generates many extra tricks. Not so such for 5-5 hands. Think that pattern is overrated by the experts. 6-4 has been underrated. 11 cards in two suits is even better. When non-vul preempting with 7-4 can create many problems for opponents. Have few cards in the two side suits. Hands where most of the high card points are in the long suits tend to play 'lucky'.
The joint pattern pair of the partnership can be expressed as two 4-dimensional vectors or just sum the suits for the partnership and treated as one 4-dimensional vector of 26 cards. Using the one vector method, sum the two longest suits. The trick space for this sum would span from 14 to 26. There is a strong correlation between total tricks and the sum of two suits.
There are three combinations which total 14 cards. 7-7-6-6, 7-7-7-5, and 8-6-6-6. About 20.5% of the time the board will be one of these three patterns. These 14 cards sum depresses tricks. About 14.6% of the time the board will be 17+ cards in two suits. The higher this sum the higher the expected total tricks. But it is not a strict one to one correspondence. Also during the auction it is often difficult for either partner to properly access this sum of two suits. Playing jump fits in both contested and uncontested auctions helps the partners to make this accessment.
When the sum of two suits is high(17+), the source of tricks component plays a greater role in generating tricks.
------------
There is also sum of two suits for one hand. Ten cards in two suits in one hand often generates many extra tricks. Not so such for 5-5 hands. Think that pattern is overrated by the experts. 6-4 has been underrated. 11 cards in two suits is even better. When non-vul preempting with 7-4 can create many problems for opponents. Have few cards in the two side suits. Hands where most of the high card points are in the long suits tend to play 'lucky'.
#4
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Posted 2017-February-05, 20:10
kenberg, on 2017-February-05, 10:58, said:
I am not sure where you are going with this, the Joint Pattern Pair, but it gives me an excuse to put up an amusing hand from a recent club game.Perhaps applying your concepts to these hands would be illustrative. Everyone was in the auction so I won't bother to rotate.
It is not every day that I hold the W hand and hear rho come in with 2NT over 1S, but there we are. If N, on lead against 3NT, attacks my heart entry I will have problems but he started with a diamond after which nine tricks are easy and in fact I took eleven (not the best defense).
I found the hand amusing (no doubt getting a good result was part of the amusement) but it came to mind as I read your post about patterns.
I had thought a little about this after the game. N can assume they have 13 minor suit cards between them so it is then a matter of arithmetic that EW have 13 major suit cards between them. Quite likely ten with E, three with W, so he might have considered that knocking out the heart entry to the board was a priority, diamonds can wait. Whatever the merit of that thinking, he led the diamond.
It is not every day that I hold the W hand and hear rho come in with 2NT over 1S, but there we are. If N, on lead against 3NT, attacks my heart entry I will have problems but he started with a diamond after which nine tricks are easy and in fact I took eleven (not the best defense).
I found the hand amusing (no doubt getting a good result was part of the amusement) but it came to mind as I read your post about patterns.
I had thought a little about this after the game. N can assume they have 13 minor suit cards between them so it is then a matter of arithmetic that EW have 13 major suit cards between them. Quite likely ten with E, three with W, so he might have considered that knocking out the heart entry to the board was a priority, diamonds can wait. Whatever the merit of that thinking, he led the diamond.
Mainly I'm claiming flat patterns are unlucky and skewed patterns are lucky. On this board N-S is 7=6=7=6 and E-W is 6=7=6=7. I tend to prefer to defend with this pattern.
But pure suits like ♠ KQJ92 tend to be lucky. North holding 5 spades is unlucky to not hold the ten spot.
There are many parameters which affects our tricks. Usually during the auction we cannot properly access the value of all the parameters. This thread is saying try to access our tricks as best we can from what we know about our(partnership) points and pattern. Knowing that there are other parameters which also affect our tricks.
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