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 The estimated value of long suits in NT dummy hands Feb 26 20177

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PostSubject: The estimated value of long suits in NT dummy hands Feb 26 20177   Sat Feb 11, 2017 3:42 pm

Brief summary: for long suits that can be set up in a NT dummy hand
With a 5 card suit, add 2 points.
With a 6 card suit, add 5 points.
With a 7 card suit, add 8 points.
2 points for the 5th card, then 3 points for 6th and 7th card.

Long suits (5 cards and over) opposite a notrump opener can generate tricks from length in the long suit in addition to high card tricks. The question addressed here is how many tricks? This translates into the question of how many points do you add when valuing your dummy hand with long suits in NT contracts?

First, for long suits in dummy to have value, they need  to be  semi-solid suit or have outside entries which will allow declarer to set up the suit. A semi-solid suit is one that can be run without losing the lead more than 1 time, which means the suit is missing only 1 of the top 4 honor cards. Declarer should have at least 2 cards in the suit, so 2 entries. With outside entries, you can have fewer honors.

What follows is an estimate of the point count value of  5, 6 and 7 card  suits in a NT dummy hand. I have provided an estimate for average worth in points and for worst-case-senario (WCS) worth in points. The WCS means the long suit is opposite a 2 card suit in the NT opener's hand (minimum balanced hand suit) and there is a bad split in opponent's cards, not considering those bad splits with less than a 10% probability.

Value of long suits in NT dummy hands

A 5 card suit in a NT dummy hand is worth on average 6 points. WCS is no points.
This value is based on the following estimates
If NT opener has 2 cards (20% chance of this) the suit is worth
  1 trick 84% of the time and  2 tricks 36% of the time    Avg= 1 trick
If NT opener has 3 cards (50% chance of this) the suit is worth
  2 tricks 68% of the time and 1 trick 96% of the time     Avg = 1 2/3 trick
If NT opener has 4 cards (36% chance of this) the suit is worth
  3 tricks 40% of the time, and 2 tricks 90% of the time    Avg is 2.3 trick
Overall average is 2 tricks = 6 points

A 6 card suit opposite a notrump opener is worth on average 9 points.
WCS is at least 3 points 96% of the time.

A 7 card suit opposite a notrump opener is worth on average 12 points.
WCS is at least 9 points.
This means that a 7 card suit in a NT dummy hand (that can be setup) should always be worth at least 3 extra tricks (9 points) and on average is worth 4 extra tricks (12 points).

Given the above estimates,  a conservative value for long suits would be
With a 5 card suit in a NT dummy hand, add 3 points.
With a 6 card suit in a NT dummy hand, add 6 points.
With a 7 card suit in a NT dummy hand, add 9 points.

How many tricks a long suit in a NT dummy hand can take with spot cards is determined by how many rounds of the suit are required to remove all cards outside the suit. This latter is determined by how the outside cards split in opponent's hands and how frequently the dummy's long suit is opposite 2,3 or 4 cards in the NT declarer.

A NT declarer will have 2 cards roughly 20% of the time.  
A NT declarer will have 3 cards roughly 50% of the time.  
A NT declarer will have 4 cards roughly 36% of the time.
A NT declarer will have 5 cards only about 4% of the time so 5 cards in declarer is not included.

Example of calculations for 5 card suits
with a 5 card suits suit in a NT dummy,
if declarer  has 2 cards in suit (there is a 20% chance of this)
the 5 card suit  (7 card fit) is worth 2 tricks (3-3 split) 36% of the time and 1 trick (4-2 split) 24% of the time and 0 (no) tricks (5-1 or 6-0 split)  40% of the time
so this 5 card suit is worth at least 1 trick 54% of the time, average worth =1 trick,  
WCS= no tricks

if declarer has 3 cards in suit (there is a 50% chance of this)
the 5 card suit (8 card fit)  is worth 2 tricks (3-2 split) 68% of the time and 1 trick (4-1 split) 28% of the time. The 5-0 split is not included since it has a very low 4% frequency.
so this 5 card suit is worth at least 1 trick  96% of the time,  average worth = 1 2/3 trick,  
I would consider the WCS= 1 trick

if declarer has 4  cards in suit  (there is a 36% chance of this)
the 5  card suit (9 card fit) is worth 3 tricks (2-2)  40% of the time, and 2 tricks (3-1) 50% of the time and 1 trick (4-0) 10% of the time    
so this 5 card suit is worth at least 2 tricks  90% of the time,  average worth = 1 2/3 trick,  
WCS=1 trick
avg is 2.3 trick

Similar calculations were run for 6 and 7 card suits in dummy to get above estimates.
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