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       I.   HAND PATTERNS

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With, thankfully, no money at stake you hold:

s-lg.gif (923 bytes) 9 6 5 2 h-lg.gif (916 bytes) 5 2 d-lg.gif (910 bytes) 9 8 4 c-lg.gif (940 bytes) J 8 6 4

Though poor in high cards, the hand has a wealth of attributes:

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Hand pattern: 4-4-3-2.
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Distribution: 4=2=3=4.
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Index of the hand pattern: three.
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Single suit: diamonds.
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Parity of the single suit: odd.

   Warning!  Definitions below. Cut to the chase.

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A hand pattern is an arrangement of thirteen cards in four suits that forms one hand of a bridge deal. The four suit lengths that make up a hand pattern do not correspond to specific suits.

All thirty-nine hand patterns are listed below in order of frequency. Each hand pattern contains one number that differs from the other three- one odd number and three even numbers; or one even number and three odds.


The 39 Hand Patterns by frequency

 
1. 4-4-3-2 11. 7-3-2-1 The top twenty hand patterns encompass more than 99% of all hands. The remaining nineteen (below) range from the infrequent to the improbable.

 

2. 5-3-3-2 12. 6-4-3-0
3. 5-4-3-1 13. 5-4-4-0
4. 5-4-2-2 14. 5-5-3-0
5. 4-3-3-3 15. 6-5-1-1
6. 6-3-2-2 16. 6-5-2-0
7. 6-4-2-1 17. 7-2-2-2
8. 6-3-3-1 18. 7-4-1-1
9. 5-5-2-1 19. 7-4-2-0
10. 4-4-4-1 20. 7-3-3-0

 

21. 8-2-2-1 31. 8-5-0-0 The most common of this second batch, 8-2-2-1, appears once in 500 hands.
22. 8-3-1-1 32. 10-2-1-0
23/ 8-3-2-0 33. 9-4-0-0
23. 7-5-1-0 34. 10-1-1-1
25. 6-6-1-0 35. 10-3-0-0
26. 8-4-1-0 36. 11-1-1-0
27. 9-2-1-1 37. 11-2-0-0
28. 9-3-1-0 38. 12-1-0-0
29. 9-2-2-0 39. 13-0-0-0
30. 7-6-0-0
The least frequent, 13-0-0-0, appears once every 158 billion hands. It is likely that, if you ever have held this rarest of birds, you've been had.

The distribution of a hand is a permutation of a hand pattern that specifies the length of spades=hearts=diamonds=clubs, respectively.

Consider the most common hand pattern: 4-4-3-2. Twelve permutations of the pattern are generated by having the suit lengths that make up the hand pattern correspond to spades=hearts=diamonds=clubs, respectively. The twelve distributions spawned by the 4-4-3-2 hand pattern are:

4=4=3=2 4=3=2=4 3=4=2=4
4=4=2=3 4=2=3=4 2=4=3=4
4=3=4=2 3=4=4=2 3=2=4=4
4=2=4=3 2=4=4=3 2=3=4=4

All 560 distributions are not listed above or below.


   The parity of a number is either odd or even. If a number is odd, its parity is odd. If a number is even, its parity is even. Zero is even.


The relative parity of two numbers is either equal- both odd or both even; or opposite- one odd and one even.


The index of a hand pattern is the the sole odd number, or the sole even number of the four numbers that represent the hand pattern. The index appears boldfaced in numeric representations of hand patterns.


The single suit in a distribution is the one suit with length different in parity from each of the other three suit lengths.



The Chase

A prism signal reveals that the index of declarer's hand pattern is six. Search the list of thirty-nine hand patterns for the index six. You will discover only two patterns with  that index: 6-3-3-1; and 6-5-1-1. The auction and play are sure to indicate declarer's one-suiter,  6-3-3-1; or two-suiter,  6-5-1-1.

Defenders who use prism signals focus on the index of declarer's hand pattern. To facilitate this task, hand patterns can be grouped according to index:

HAND PATTERNS with EVEN INDEXES
index zero two four six
  5-5-3-0 5-3-3-2 5-4-3-1 6-3-3-1
7-3-3-0 5-5-2-1 4-3-3-3 6-5-1-1
  7-3-2-1 7-4-1-1  

HAND PATTERNS with ODD INDEXES

index one three five seven
  6-4-2-1 4-4-3-2 5-4-2-2 7-2-2-2
4-4-4-1 6-3-2-2 5-4-4-0 7-4-2-0
8-2-2-1 6-4-3-0 6-5-2-0  
Declarer will hold one of the listed hand patterns 99.5% of the time.

In roughly three out of four deals declarer will hold a highlighted pattern.


When a defender discovers the index of declarer's hand pattern, the task of exacting declarer's distribution is dramatically eased. Superficially similar hand patterns, such as  5-4-2-2 and 5-4-3-1, should not be confused. If declarer holds a five, then 2=4=5=2 is possible; and 3=4=5=1 ( four) is not.


How best to get a peek at declarer's single suit and index? Laws ban reflecting mirrors, but refracting prisms serve.

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