A109754 - J32

Lesson for Al's Billies

Get used in calculating the odds of different lines of play with MCC
You (South) hold A109754 opposite J32 (North) and need 5 tricks from this suit.
Other things being equal. How do you play this suit?

a. What are the possible lines?

b. Type in HHxx or KQxx or KQ86 in the missing cards calculator.
and look up the sums of percentages for every line.

c. Which line is the best?

These are the possible lines of play

1) Play the A to the first trick and small to J at second.

2) Finesse the 10 (if East plays no honour) and play the A at the second round.

3) Finesse the 10 (if EAST plays no honour) and finesse a second time, if the first finesse lost.
So called "double finesse".

At the table, you must make a fast decision and will calculate by head using the few important probabilities you learned by heart.:

1) A first wins, if the suit is 2/2 (40%) or anyone has a singleton honour(50% of the 3/1 distributions = 50% from 50%=25%) That sums up to 65%.

Here is the solution to this exercise:

To calculate exactly and get an overview over all possible distribution of the missing cards between EAST and WEST we type in the MissingCard:Calculator (MCC) KQ86 and get 16 rows:

Missing cards : KQ86

You get the same information with only 9 rows, if you type "HHxx" in MCC:

Missing cards : HHxx

Rows 2 and 3 of the first sheet are subsumed in row #2 of the second sheet.
Rows 6,7,10 and 11 are subsumed in row5, and so one. It is easier to handle 9 rows, therefore we use the compressed (second) version.

The first line of play ( A first ) is assigned to of the clickable columns. The first line wins 5 tricks with any 2/2 and any singleton honour.
We check out rows 3, 4, 5, 6, 7 and find 65,566% for this line of play 1. (A first)

Selected distributions' sum: % % %

The second line of play ( Finesse and lay down the Ain the second round , after the finesse lost to WEST) wins 5 tricks, if EAST has both honours oe the suit is divided 2/2.
We check out the rows 1, 2, 3, 5, 6, 7, and find 70,349% for this line of play.

Selected distributions' sum: % % %

The third line of play (double finesse) wins if EAST has at least one honour.
We check out lines 1, 2, 3, 4, 5, 6, and get 76,001% for this line of play.

Summary:

These are the possible lines of play and the odds to win

1) Play the A to the first trick and small to J at second.	66%
2) Finesse the 10 (if East plays no honour) and play the A at the second round.	70%
3) Finesse the 10 (if EAST plays no honour) and finesse a second time, if the first finesse lost. So called "double finesse".	76%

No	W	E	Probability
1	-	KQ86	4.783
2	6	KQ8	6.217
3	8	KQ6	6.217
4	86	KQ	6.783
5	Q	K86	6.217
6	Q6	K8	6.783
7	Q8	K6	6.783
8	Q86	K	6.217
9	K	Q86	6.217
10	K6	Q8	6.783
11	K8	Q6	6.783
12	K86	Q	6.217
13	KQ	86	6.783
14	KQ6	8	6.217
15	KQ8	6	6.217
16	KQ86	-	4.783

No	W	E	Probability	Times	Total
1	-	HHxx	4.783	1	4.783
2	x	HHx	6.217	2	12.435
3	xx	HH	6.783	1	6.783
4	H	Hxx	6.217	2	12.435
5	Hx	Hx	6.783	4	27.130
6	Hxx	H	6.217	2	12.435
7	HH	xx	6.783	1	6.783
8	HHx	x	6.217	2	12.435
9	HHxx	-	4.783	1	4.783

No	W	E	Probability	Times	Total
1	-	HHxx	4.783	1	4.783
2	x	HHx	6.217	2	12.435
3	xx	HH	6.783	1	6.783
4	H	Hxx	6.217	2	12.435
5	Hx	Hx	6.783	4	27.130
6	Hxx	H	6.217	2	12.435
7	HH	xx	6.783	1	6.783
8	HHx	x	6.217	2	12.435
9	HHxx	-	4.783	1	4.783

No	W	E	Probability	Times	Total
1	-	HHxx	4.783	1	4.783
2	x	HHx	6.217	2	12.435
3	xx	HH	6.783	1	6.783
4	H	Hxx	6.217	2	12.435
5	Hx	Hx	6.783	4	27.130
6	Hxx	H	6.217	2	12.435
7	HH	xx	6.783	1	6.783
8	HHx	x	6.217	2	12.435
9	HHxx	-	4.783	1	4.783