Page 0048

SO far in this series I have got away without giving

you lots of percentages. However you do need to

have some idea about how likely certain breaks are

because sometimes you have to choose between

lines of play that depend on breaks.

Missing 2 cards:

1-1 break = 52%; 2-0 break = 48%.

Missing 3 cards:

2-1 break = 78%; 3-0 break = 22%.

Missing 4 cards:

2-2 break = 40.7%; 3-1 break = 49.7%;

4-0 break = 9.6%.

Missing 5 cards:

3-2 break = 67.8%; 4-1 break = 28.3%;

5-0 break = 3.9%.

Missing 6 cards:

3-3 break = 35.5%; 4-2 break = 48.5%;

5-1 break = 14.5%; 6-0 break = 1.5%.

Missing 7 cards:

4-3 break = 62.2%; 5-2 break = 30.5%;

6-1 break = 6.8%; 7-0 break = 0.5%.

A word of warning here. These percentages assume

that the cards have been perfectly shuffled, as would

be the case if a duplimate machine is used. If players

shuffle and deal they rarely shuffle properly and the

good breaks become far more likely. Indeed research

done several years ago suggest that some players

shuffle so badly that at least at one club a 3-3 break

occurred more than 50% of the time. If you are

playing bridge where a 3-3 break is more likely than

a finesse the nature of bridge is fundamentally

altered. I cannot possibly know what happens at

your club; all I can do is write on the assumption

that your boards are duplimated.

HHHHH

It is worth noting at this stage that if you are missing

an odd number of cards in a suit the odds of the

best break are greater than a finesse, whereas if you

are missing an even number of cards the odds of the

best break are worse than a finesse (with the

marginal exception of the 1-1 break when missing

two cards).

On the deal below plan your play in 3NT by

South on the lead of the ´3.

Would your decision be different if you replaced

the t6 in dummy with the ®6?

Game All. Dealer South.

´ A 8

™ 8 7 3 2

t 7 6 5 4

® 7 5 4

´ 9 6

™ A K Q

t A Q 3 2

® A K Q 2

You have eight top tricks. Your ninth trick will have

to come from either the diamond finesse or a 3-3

club break. You would have liked to test the clubs

first, and fall back on the diamond finesse if clubs

broke unfavourably, but the opening lead has

removed your only entry to dummy so if you don't

take the diamond finesse now you will not have

another chance. So you must decide between the

two options. The diamond finesse is about 50%.

The 3-3 club break is 35.5%. So take the diamond

finesse at trick two.

If you had the ®6 in dummy instead of the t6,

you would be comparing the probability of a 3-2

club break (67.8%) against the 50% diamond

finesse. So now it would be incorrect to take the

diamond finesse.

Sadly life is not always so clearcut. On the next

deal you are in 6´. West leads the ™K, taken by your

™A. When you cash dummy's ´A, East follows with

48 English Bridge December 2015 www.ebu.co.uk

Combining Chances by Andrew Kambites

Suit Combinations

Suit Combinations

click

link

N

W E

S

Index

  1. Page 0001
  2. Page 0002
  3. Page 0003
  4. Page 0004
  5. Page 0005
  6. Page 0006
  7. Page 0007
  8. Page 0008
  9. Page 0009
  10. Page 0010
  11. Page 0011
  12. Page 0012
  13. Page 0013
  14. Page 0014
  15. Page 0015
  16. Page 0016
  17. Page 0017
  18. Page 0018
  19. Page 0019
  20. Page 0020
  21. Page 0021
  22. Page 0022
  23. Page 0023
  24. Page 0024
  25. Page 0025
  26. Page 0026
  27. Page 0027
  28. Page 0028
  29. Page 0029
  30. Page 0030
  31. Page 0031
  32. Page 0032
  33. Page 0033
  34. Page 0034
  35. Page 0035
  36. Page 0036
  37. Page 0037
  38. Page 0038
  39. Page 0039
  40. Page 0040
  41. Page 0041
  42. Page 0042
  43. Page 0043
  44. Page 0044
  45. Page 0045
  46. Page 0046
  47. Page 0047
  48. Page 0048
  49. Page 0049
  50. Page 0050
  51. Page 0051
  52. Page 0052
  53. Page 0053
  54. Page 0054
  55. Page 0055
  56. Page 0056
  57. Page 0057
  58. Page 0058
  59. Page 0059
  60. Page 0060
  61. Page 0061
  62. Page 0062
  63. Page 0063
  64. Page 0064
  65. Page 0065
  66. Page 0066
  67. Page 0067
  68. Page 0068
  69. Page 0069
  70. Page 0070