	NORTH KJ76 AJ97 AQ KQ4
Q842 52 J743 872		T KT843 KT85 T65
	A953 Q6 962 AJ93

Dealer: North Vul: NS MP Scoring

West

Pass
Pass
Pass
Pass
Pass
Pass

North
2N
32
3
4
4N
6

East
Pass
Pass
Pass
Pass
Pass
Pass

South
31
33
4
4
54
Pass

Slam Choices

1 Puppet Stayman: Asks for Five Card or Four Card Majors
2 Shows at least one four card major
3 Artificial, shows 4 spades
4 Two keycards in spades (two of

East led the singleton

T.
Declarer North judged that the opening leader would not lead away from the trump

Q and won the

A.
The

9 was passed and when East showed out, North counted 4 spades, 1 heart, 1 diamond and 4 clubs.
A heart might be developed, a heart ruffed in dummy, or a diamond finessed.
East followed to the 2nd round of trumps with the

8.
Declarer North asked of the defensive signals and was told 'high encourages'.
The

J was won and a heart played towards dummy.
East won, returned a heart won in dummy, and declarer pulled the last trump.
There were 4 clubs, 3 hearts, 4 spades and 1 diamond.

Rather than risk a heart ruff, Declarer could have pulled the fourth round of trumps earlier, giving up the idea of ruffing a third heart in dummy.
If the

K had been with West and a diamond returned, Declarer could have either fallen back on a diamond finesse or won the

A, run winners ending in dummy and eventually finessed the

Before considering the effect of the 4:1 spade division, the odds of West having fewer than 3 hearts can be calculated:

Cards Missing Break %

7
4-3 62.2

5-2 30.5

6-1 6.8

7-0 0.5

North would succeed on 4:3 divisions of the suit (62.2%) plus HALF of the other divisions of the suit (where East is the short suited: 37.8x.5), in total 81.1% in theory, much better than a finesse.

Given West having 4 spades and East only 1, the odds shift in favour of West being the shorter of the two defenders in hearts.

from: http://www.rpbridge.net/xcc1.htm , entering the North South holdings and 12 unknown for Left Hand Opponent and 9 for RHO:

# A B C D West East Ways Ratio Percent

1 KT8xxxx — 1 154 0.68
2 KT8xxx x 4 924 4.09
3 KT8xx xx 6 1584 7.01
4 KT8x xxx 4 924 4.09
5 KT8 xxxx 1 154 0.68
6 KTxxxx 8 1 231 1.02
7 KTxxx 8x 4 1056 4.67
8 KTxx 8xx 6 1386 6.13
9 KTx 8xxx 4 616 2.72
10 KT 8xxxx 1 77 0.34
11 K8xxxx T 1 231 1.02
12 K8xxx Tx 4 1056 4.67
13 K8xx Txx 6 1386 6.13
14 K8x Txxx 4 616 2.72
15 K8 Txxxx 1 77 0.34
16 Kxxxx T8 1 264 1.17
17 Kxxx T8x 4 924 4.09
18 Kxx T8xx 6 924 4.09
19 Kx T8xxx 4 308 1.36
20 K T8xxxx 1 28 0.12
21 T8xxxx K 1 231 1.02
22 T8xxx Kx 4 1056 4.67
23 T8xx Kxx 6 1386 6.13
24 T8x Kxxx 4 616 2.72
25 T8 Kxxxx 1 77 0.34
26 Txxxx K8 1 264 1.17
27 Txxx K8x 4 924 4.09
28 Txx K8xx 6 924 4.09
29 Tx K8xxx 4 308 1.36
30 T K8xxxx 1 28 0.12
31 8xxxx KT 1 264 1.17
32 8xxx KTx 4 924 4.09
33 8xx KTxx 6 924 4.09
34 8x KTxxx 4 308 1.36
35 8 KTxxxx 1 28 0.12
36 xxxx KT8 1 231 1.02
37 xxx KT8x 4 616 2.72
38 xx KT8xx 6 462 2.04
39 x KT8xxx 4 112 0.50
40 — KT8xxxx 1 7 0.03
Groups and Totals 128 22610 100.00
A 20 64 15400 68.11
B 20 64 12920 57.14
C 0 0 0 0.00
D 0 0 0 0.00
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from which LHO having 5 or more cards in the suit combinations can be summed:

#	West	East	Ways	Ratio	Percent
1	KT8xxxx	—	1	154	0.68
2	KT8xxx	x	4	924	4.09
3	KT8xx	xx	6	1584	7.01
6	KTxxxx	8	1	231	1.02
7	KTxxx	8x	4	1056	4.67
11	K8xxxx	T	1	231	1.02
12	K8xxx	Tx	4	1056	4.67
16	Kxxxx	T8	1	264	1.17
21	T8xxxx	K	1	231	1.02
22	T8xxx	Kx	4	1056	4.67
26	Txxxx	K8	1	264	1.17
31	8xxxx	KT	1	264	1.17
Groups and Totals					66 270 2900 32.36

If the odds of LHO having greater than 4 hearts are 32.36%, the odds of RHO having at least 3 hearts are inversely 67.62%