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Tuesday, 28 August 2012

Suit Combination: AKQ9 v x(x) and AK9x v Qx

The video below talks about using computers to reduce the amount of calculation in maths. An example of where this is useful would be teaching standard deviation. The formulae are imposing to students and the difference between sample standard deviation and population standard deviation is less important than getting a feel for how standard deviation works.


Still sometimes it is important to understand how the gears work.

I was looking through the Suit Combinations missing 1 point on Bridge Guy's and felt that some of their answers were off so I decided to check them myself.

I ran the first example by hand before turning it over to Richard Pavlicek's Card-Combination Analyzer.

AKQ9 v x

BridgeGuys: Finesse the 9 which works 6% of the time.

Drop:
  • JTx: 5-3 split is 47.1, 12/112 comb -> 5.05%
  • JT: 6-2 split is 17.1, 2/56 comb -> 0.61
  • Total: 5.66%
Finesse: theoretically 0%  and JT onside in any combination is obviously 24% ( 1/2*12/25).
  • JT onside: 0.3%
  • JTx onside: 2.52%
  • JTxx onside: 32.7 * 15/70 -> 7.01%
  • JTxxx onside: 41.7 * 20/112 -> 8.41%
  • JTxxxx onside: 17.1 * 15/56 -> 4.58%
  • JTxxxxx onside: 2.9 * 6/16 -> 1.09%
  • JTxxxxxx onside: 0.08 but 0% if AKQ9 in dummy
  • Total: 23.99%

Card Combination Analysis

North:  AKQ9
South:  x

Case  Group   West     East   Ways   Ratio  Percent
1      B      JTxxxxxx    -      1     252     0.08
2      B      JTxxxxx     x      6    3276     1.07
3      B      JTxxxx     xx     15   14040     4.59
4      B      JTxxx     xxx     20   25740     8.41
5      B      JTxx     xxxx     15   21450     7.01
6     AB      JTx     xxxxx      6    7722     2.52
7     AB      JT     xxxxxx      1     936     0.31
8             Jxxxxxx     T      1     546     0.18
9             Jxxxxx     Tx      6    5616     1.84
10            Jxxxx     Txx     15   19305     6.31
11            Jxxx     Txxx     20   28600     9.35
12            Jxx     Txxxx     15   19305     6.31
13            Jx     Txxxxx      6    5616     1.84
14            J     Txxxxxx      1     546     0.18
15            Txxxxxx     J      1     546     0.18
16            Txxxxx     Jx      6    5616     1.84
17            Txxxx     Jxx     15   19305     6.31
18            Txxx     Jxxx     20   28600     9.35
19            Txx     Jxxxx     15   19305     6.31
20            Tx     Jxxxxx      6    5616     1.84
21            T     Jxxxxxx      1     546     0.18
22    A       xxxxxx     JT      1     936     0.31
23    A       xxxxx     JTx      6    7722     2.52
24            xxxx     JTxx     15   21450     7.01
25            xxx     JTxxx     20   25740     8.41
26            xx     JTxxxx     15   14040     4.59
27            x     JTxxxxx      6    3276     1.07
28            -    JTxxxxxx      1     252     0.08

Groups and Totals          28  256  305900   100.00
A Drop                      4   14   17316     5.66
B Finesse                   7   64   73416    24.00
C                           0    0       0     0.00
D                           0    0       0     0.00

[This e-mail was generated automatically]

Software created by Richard Pavlicek
Web site: http://www.rpbridge.net


Conclusion: unless you have splintered it is very difficult for LHO to know to split when you lead towards the AKQ9 so the 3/1 odds are very favourable. When you lead from dummy it is clearer for RHO to split but is it as high as 75% of the time?

AKQ9 v xx:

BridgeGuys: drop the JT which will work 24% of the time

North:  AKQ9
South:  xx

Case  Group   West     East   Ways   Ratio  Percent
1      B      JTxxxxx     -      1      42     0.26
2      B      JTxxxx      x      5     390     2.42
3      B      JTxxx      xx     10    1170     7.27
4      B      JTxx      xxx     10    1430     8.88
5     AB      JTx      xxxx      5     715     4.44
6     AB      JT      xxxxx      1     117     0.73
7             Jxxxxx      T      1      78     0.48
8             Jxxxx      Tx      5     585     3.63
9             Jxxx      Txx     10    1430     8.88
10            Jxx      Txxx     10    1430     8.88
11            Jx      Txxxx      5     585     3.63
12            J      Txxxxx      1      78     0.48
13            Txxxxx      J      1      78     0.48
14            Txxxx      Jx      5     585     3.63
15            Txxx      Jxx     10    1430     8.88
16            Txx      Jxxx     10    1430     8.88
17            Tx      Jxxxx      5     585     3.63
18            T      Jxxxxx      1      78     0.48
19    A       xxxxx      JT      1     117     0.73
20    A       xxxx      JTx      5     715     4.44
21            xxx      JTxx     10    1430     8.88
22            xx      JTxxx     10    1170     7.27
23            x      JTxxxx      5     390     2.42
24            -     JTxxxxx      1      42     0.26

Groups and Totals          24  128   16100   100.00
A Drop                      4   12    1664    10.34
B Finesse                   6   32    3864    24.00

Conclusion: This may just have been a typo as it is the double finesse that works 24% of the time.

AK9x v Qx

BridgeGuys: Drop JT which will work 10% of the time

This is the same calculation as above.

Conclusion: If the opponents give count the most somnolent opponent will split JT so the drop is the best chance.

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