Simulation 8Z08 Main

Four Hearts Lead II

by Richard Pavlicek

Next I ran the same simulation with West’s spades slightly stronger: A-J-9-2 instead of A-J-3-2. Would this change the outcome?

A J 9 2
3 2
J 3 2
J 4 3 2 Table

West

Pass
Pass North

1 NT¹
4 East

Pass
All Pass South
1
2

1. forcing

Should West lead the 2, 2 or 2?

To determine the best lead I created 10,000 random layouts with the West hand fixed, and the North-South hands constrained to fit the bidding: South points 13-16, spades 5+, hearts 4+, spades longer or equal to hearts; North points 11-13, hearts 4-5, not 4+ spades. Further, to exclude deals where East would bid or double: East longest suit less than 7, longest suit less than 6 or playing half-tricks less than 12, longest suit less than 5 or playing half-tricks less than 14, longest suit less than 5 or half-tricks in that suit less than 8, points less than 13 or hearts less than 3 or spades 3+.

A complete turnaround. Adding the nine-spot in spades makes a trump lead best at any form of scoring. Leading from the longer jack now gets second place. Intermediate cards in declarer’s first suit are clearly a key factor. For another follow-up see Part III.

Results for 10,000 Deals
Lead Trick Avg Make Pct Matchpoints Nonvul TPs Nonvul IMPs Vul TPs Vul IMPs
2 10.112 74.86 18662 46.66 306100 33.45 6945 33.43 306100 33.45 6945 33.43
2 10.196 78.15 21068 52.67 557800 60.96 12701 61.13 557800 60.96 12701 61.13
2 10.166 77.57 20270 50.68 508640 55.59 11520 55.45 508640 55.59 11520 55.45

Results for 10,000 Deals
Lead	Trick Avg	Make Pct	Matchpoints	Nonvul TPs	Nonvul IMPs	Vul TPs	Vul IMPs
2	10.112	74.86	18662 46.66	306100 33.45	6945 33.43	306100 33.45	6945 33.43
2	10.196	78.15	21068 52.67	557800 60.96	12701 61.13	557800 60.96	12701 61.13
2	10.166	77.57	20270 50.68	508640 55.59	11520 55.45	508640 55.59	11520 55.45

Trick Avg shows the average number of tricks won by declarer. Make Pct shows the percent of time the contract is made. Matchpoints shows the raw total (European style: 2 for a win, 1 for a tie) and effective scoring percent. Total Points and IMPs are shown similarly as raw totals and percents, with separate accountings for N-S nonvulnerable and N-S vulnerable. (Vulnerability does not affect matchpoints.) All numbers are relative to declarer, so lower values indicate better for the defense.

Below are 100 of the 10,000 deals, including the first 10 and last 10, and selected deals in-between where the lead made a significant difference. The number of tricks won by declarer is shown for each lead, assuming double-dummy play by both sides thereafter.

Seed 99D488B3 10000

1. —
K 9 8 7 6
K Q 9 7 4
10 9 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 5 4
Q 5
10 8 5
A K Q 7
2 12
2 12
2 11 K 8 7 6 3
A J 10 4
A 6
8 6

2. 5
A J 5 4
A 10 6 5 4
10 9 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 4 3
Q 10 9
K 9 8 7
Q 6 5
2 10
2 10
2 10 K 10 8 7 6
K 8 7 6
Q
A K 8

3. —
10 8 7 4
A Q 10 5 4
K 10 9 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 10 8 4
A K 6
K 8 6
8 7 5
2 10
2 11
2 11 Q 7 6 5 3
Q J 9 5
9 7
A Q

4. K 10
K J 5 4
9 6
K 10 9 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 7
A Q 10
K 10 8 7 5
Q 8 7
2 9
2 9
2 9 Q 6 5 4 3
9 8 7 6
A Q 4
A

5. 5
A J 9 5
A 9 8 5
9 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 7
8 7 6
K Q 10 7 6
K Q
2 8
2 9
2 9 K 10 6 4 3
K Q 10 4
4
A 10 5

6. —
A Q 7 6 5
K 10 9 7 6
10 9 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 7 5
K 10
A Q 8 4
Q 7 6
2 10
2 11
2 11 K 8 6 4 3
J 9 8 4
5
A K 5

7. 4
K 10 9 5
K 10 8 7 5
A 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 8 7
8 7
A 6 4
Q 10 9 8 7
2 11
2 11
2 11 Q 10 6 5 3
A Q J 6 4
Q 9
K

8. 8 5
10 9 7 4
A K Q 8 4
10 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 3
K 6 5
10 9 6 5
K Q 8 6
2 10
2 10
2 10 Q 10 7 6 4
A Q J 8
7
A 7 5

9. —
Q 8 5 4
A 10 8 6
K 8 7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 8 3
J 7 6
K Q 9 7 4
A 9
2 9
2 9
2 10 Q 10 7 6 5 4
A K 10 9
5
Q 10

10. 7 4
K Q 8 5
A 10 9 5 4
8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 6 5
J 10 7
K 8 6
A Q 9 7 6
2 10
2 10
2 10 K Q 10 8 3
A 9 6 4
Q 7
K 10

Simulation 8Z08 Main Top Four Hearts Lead II

19. 5
A Q J 9
K 9 8 6 5
10 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 8 7
K 6 4
A 4
K Q 9 8 5
2 10
2 9
2 10 K Q 6 4 3
10 8 7 5
Q 10 7
A

21. K 8
J 8 6 4
Q 10 8 5
K Q 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 4
A Q 7
9 7 4
A 9 8 6 5
2 10
2 10
2 9 Q 10 7 6 3
K 10 9 5
A K 6
10

36. K
Q 10 8 5
K Q 7 6 5
K 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 7 6
A 7 4
A 10 9 4
10 9 6
2 9
2 10
2 10 Q 8 5 4 3
K J 9 6
8
A Q 8

55. Q 5
K J 9 5
8 4
A Q 8 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 7
Q 10 6
K Q 10 9
K 10 9 6
2 9
2 10
2 10 K 8 6 4 3
A 8 7 4
A 7 6 5
—

65. 4
J 10 8 6
K 10 4
A K 8 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 5
A K 9
9 8 6 5
Q 10 9
2 9
2 10
2 10 K 10 7 6 3
Q 7 5 4
A Q 7
7

68. 5
A J 10 4
8 6
K 10 8 7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 7 3
Q 9 8
K Q 9 7 5
A 9
2 10
2 9
2 10 K Q 10 6 4
K 7 6 5
A 10 4
Q

77. 4
9 6 5 4
Q 7 5 4
A K 10 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 7 3
A J 7
K 9 8 6
8 7 6
2 9
2 10
2 10 Q 10 8 6 5
K Q 10 8
A 10
Q 5

84. Q
K Q 7 6 5
Q 5 4
K 9 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 5 4
9 4
A K 10 7
Q 10 8 5
2 10
2 9
2 10 K 10 8 6 3
A J 10 8
9 8 6
A

87. 7 3
10 8 7 6 4
A Q 9
K Q 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 6
K
10 8 7 5 4
A 10 9 6 5
2 11
2 11
2 9 K 10 8 5 4
A Q J 9 5
K 6
8

96. 10 7
K 10 6 5
A 10 8 7
A 10 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 4
Q J 7
K 9 6 5 4
9 6 5
2 9
2 10
2 10 Q 8 6 5 3
A 9 8 4
Q
K Q 8

Simulation 8Z08 Main Top Four Hearts Lead II

103. 6
K 10 7 4
A 8 7 6 4
Q 10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 10 5
9 6 5
Q 10 9
A K 9 6
2 9
2 10
2 10 Q 8 7 4 3
A Q J 8
K 5
7 5

105. 10 5
A J 7 5
K Q 8 6 5
Q 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 3
Q 9 6
A 10 9 7 4
K 10 5
2 10
2 10
2 9 K Q 8 6 4
K 10 8 4
—
A 9 8 6

106. 10 7
J 8 7 5
A K Q 10 7
10 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 4
K 10 6
9 8 6
A Q 9 8 5
2 10
2 10
2 9 K 8 6 5 3
A Q 9 4
5 4
K 6

147. 8 5
A K 10 8
K Q 9 6
9 8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 6
Q 5
10 8 7 5 4
A Q 10 6
2 10
2 10
2 9 Q 10 7 4 3
J 9 7 6 4
A
K 7

159. 7
Q 10 6 4
K 8 6
A 10 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 6
9 8 5
A 9 7 5
K 9 5
2 9
2 10
2 10 K 8 5 4 3
A K J 7
Q 10 4
Q

194. 5
Q J 5 4
K 10 8 5
A 10 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 7 3
A 10 7
7 4
K Q 9 6 5
2 9
2 10
2 10 Q 10 8 6 4
K 9 8 6
A Q 9 6
—

225. 8
A K J 7
9 8 4
Q 10 9 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 5 3
10 8 4
Q 10 7 5
A K 6
2 9
2 10
2 10 K 10 7 6 4
Q 9 6 5
A K 6
5

228. 8
A Q 8 5
8 6 4
K Q 10 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 4 3
9 7 6
A Q 9 7
A 9 6
2 10
2 9
2 10 K Q 7 6 5
K J 10 4
K 10 5
5

234. 6 4
Q 10 6 4
K Q 10 7 6
A 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8
K 9 8
A 8 5
Q 10 9 8 5
2 10
2 9
2 10 K 10 7 5 3
A J 7 5
9 4
K 7

236. 7
Q J 8 6
K 9 8 5
A 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 4 3
9 5 4
A Q 7
K 10 9 5
2 9
2 10
2 10 K Q 10 8 6
A K 10 7
10 6 4
Q

Simulation 8Z08 Main Top Four Hearts Lead II

249. 6 5
10 7 5 4
A K Q 10 9
8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 4
K J 6
7 5 4
A 10 9 6 5
2 10
2 10
2 9 K 10 8 7 3
A Q 9 8
8 6
K Q

259. 4
Q 8 6 5
Q 10 8 6
K Q 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 7 5
J 10 7
A 7
A 10 9 8 7
2 10
2 9
2 10 Q 10 8 6 3
A K 9 4
K 9 5 4
—

267. 3
A 10 7 5
7 6 5 4
A Q 8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 7
K 9 6
Q 8
K 10 9 7 6
2 9
2 10
2 10 K 10 6 5 4
Q J 8 4
A K 10 9
—

289. 8 7
K Q J 5
10 9 7
A 10 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 5
10 8 7
A Q 8 4
K Q 8 7
2 9
2 10
2 10 K Q 6 4 3
A 9 6 4
K 6 5
9

317. Q
Q J 5 4
K 10 9 8 7 4
A 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 8 5
A 10 7
A Q 6
8 7 6 5
2 9
2 10
2 10 K 7 6 4 3
K 9 8 6
5
K Q 10

322. 7 5 3
K 9 8 7
A 9 6
A Q 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 4
A J 4
10 7 5 4
K 10 8 6 5
2 10
2 10
2 9 K Q 10 8 6
Q 10 6 5
K Q 8
9

327. 10
Q J 9 7
Q 6 5 4
A Q 10 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 7 5
10 6 5
A K 8 7
9 8 6
2 9
2 10
2 10 K 8 6 4 3
A K 8 4
10 9
K 7

337. 4
A Q 6 4
K Q 10 4
10 7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 5
K 9 5
9 8 7 5
A Q 9
2 9
2 10
2 10 K 8 7 6 3
J 10 8 7
A 6
K 8

349. 3
Q 10 9 8
A 10 7 6
K 10 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 5 4
K J 5
Q 9 8 4
A 9 5
2 9
2 10
2 10 K Q 10 7 6
A 7 6 4
K 5
Q 6

353. 5
K Q 8 4
Q 9 8 7 5 4
K 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 4 3
J 6 5
A K 6
A 8 7 5
2 9
2 10
2 10 K Q 8 7 6
A 10 9 7
10
Q 10 9

Simulation 8Z08 Main Top Four Hearts Lead II

356. Q 6
K Q 9 6
K 9 6 5
Q 9 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 5
A 8 7
10 7 4
K 10 8 6 5
2 9
2 10
2 10 10 8 7 4 3
J 10 5 4
A Q 8
A

369. 10 8
A Q 10 9
A 10 9 7 4
10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 6
J 7 5
K Q 6 5
Q 7 6 5
2 9
2 10
2 10 Q 7 5 4 3
K 8 6 4
8
A K 9

399. 4 3
A J 8 7
Q 10 9 7
K Q 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8
10 5 4
K 8 5 4
A 9 6 5
2 9
2 10
2 10 K 10 7 6 5
K Q 9 6
A 6
10 7

477. 7 4
Q 7 6 4
K 10 9 5
A Q 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 5
A K 5
Q 8 7 6 4
9 7 5
2 9
2 10
2 10 K Q 8 6 3
J 10 9 8
A
K 10 6

512. K 10
J 8 7 4
9 8 7 4
A Q 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 6
10 9 6
A K 5
K 10 9 8 6
2 10
2 10
2 9 Q 7 5 4 3
A K Q 5
Q 10 6
7

540. —
A Q 10 6
Q 9 7 5 4
Q 9 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 6 4
J 5 4
K 8 6
A K 8 5
2 9
2 10
2 10 Q 10 8 7 5 3
K 9 8 7
A 10
10

553. 3
A J 8 4
9 7 4
A Q 10 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 7 4
6 5
A K Q 6
K 9 8 6
2 10
2 9
2 11 K Q 8 6 5
K Q 10 9 7
10 8 5
—

556. Q
10 7 6 4
A K Q 6
10 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 5 3
Q 8 5
9 8 5 4
A K Q
2 10
2 11
2 9 K 10 7 6 4
A K J 9
10 7
9 5

568. 5 4
A Q 7 4
K 8 4
Q 8 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 3
K 10 6
Q 9 7 6 5
A 10 7
2 9
2 10
2 10 K Q 10 7 6
J 9 8 5
A 10
K 9

579. 8 7
K Q 9 8 4
A 8 7 5 4
8
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 4
J 6
K Q 10 9 6
A Q 9 7
2 9
2 10
2 10 Q 10 6 5 3
A 10 7 5
—
K 10 6 5

Simulation 8Z08 Main Top Four Hearts Lead II

583. 8
10 8 7 5
A K 6 5
Q 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 5 3
K Q 4
10 9 8 7
A 10 5
2 9
2 10
2 10 Q 10 7 6 4
A J 9 6
Q 4
K 9

586. 6
A J 9 6
Q 10 9 8 5
Q 8 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 8 5
10 5 4
A K
K 10 9 7 5
2 10
2 9
2 10 Q 10 7 4 3
K Q 8 7
7 6 4
A

587. —
9 8 7 5
A Q 7 6 4
K 10 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 7 4
A J 10
10 8 5
A Q 8
2 10
2 9
2 10 K 8 6 5 3
K Q 6 4
K 9
9 6

604. 10 4
A J 8 5 4
Q 7 5
K 10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table K
9 6
K 10 8 6 4
A 9 7 6 5
2 10
2 9
2 10 Q 8 7 6 5 3
K Q 10 7
A 9
Q

605. —
A Q 10 5
Q 9 8 7 5 4
10 9 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K Q 7
J 8 7
A K 10 6
Q 8 5
2 9
2 10
2 10 10 8 6 5 4 3
K 9 6 4
—
A K 6

679. —
K 9 6 5
K Q 9 8 7 6
Q 8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 6 3
10 8 7
A 10 5 4
A K 6
2 9
2 10
2 10 K Q 10 8 5 4
A Q J 4
—
10 9 7

680. 10 6
A J 9 8
10 7 5
K Q 9 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 4
7 6 4
A Q 8 6 4
A 10 7
2 9
2 10
2 10 K Q 8 7 3
K Q 10 5
K 9
6 5

709. 8 6
K J 6 4
Q 9 5
A 9 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 7
A 8 5
K 10 8 7 4
Q 10 6
2 9
2 10
2 10 K Q 5 4 3
Q 10 9 7
A 6
K 8

723. 10 8
K Q 10 9 6
A 10 7
8 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 7
J 4
K 9 6 5 4
K Q 9 7
2 10
2 10
2 9 Q 6 5 4 3
A 8 7 5
Q 8
A 10

732. 7
A 10 9 7
K 7 5
Q 10 8 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 10 5
K Q 8
10 9 6 4
K 9 6
2 9
2 10
2 10 Q 8 6 4 3
J 6 5 4
A Q 8
A

Simulation 8Z08 Main Top Four Hearts Lead II

748. 7 6
A J 8 5
A 6 5
K 10 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 5
10 7 4
K Q 9 8 4
Q 6 5
2 9
2 10
2 10 Q 10 8 4 3
K Q 9 6
10 7
A 9

756. 8 5
A 8 5 4
K Q 10 6 4
9 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10
K 10 6
8 7 5
K Q 10 8 6
2 10
2 10
2 9 K 7 6 4 3
Q J 9 7
A 9
A 7

807. —
10 6 5 4
K Q 8 7 4
K 9 8 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 8 5 4
Q J 9
A 10 6 5
A 5
2 9
2 10
2 10 Q 10 7 6 3
A K 8 7
9
Q 10 7

854. —
K Q 7 4
Q 10 8 7
K 10 9 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 6 5
A 8 6
K 6 4
A Q 6 5
2 9
2 10
2 10 K Q 10 8 4 3
J 10 9 5
A 9 5
—

860. Q 3
A K 10 4
Q 9 7
10 9 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 4
8 7 6
K 8 6 5 4
K 8 6
2 9
2 11
2 10 10 8 7 6 5
Q J 9 5
A 10
A Q

897. 3
K J 9 7 4
K Q 7 6
8 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 6 5
Q 5
A 10 9 8 4
K Q 6
2 10
2 10
2 9 K Q 10 7 4
A 10 8 6
5
A 10 9

901. 8
9 8 7 6 5
A 8 7 5 4
A 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 7 4
Q 4
K Q 10 9 6
K Q 6
2 9
2 10
2 10 Q 10 6 5 3
A K J 10
—
10 9 8 5

918. 10
K Q J 8
10 7 5
K Q 9 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 6 5 4
10 9 5
A 8 6 4
A 10 6
2 9
2 10
2 10 K Q 8 7 3
A 7 6 4
K Q 9
5

932. K
Q 8 6 5 4
A 7 6
Q 9 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 6 5 3
9 7
K Q 9 5
A 10 8 7
2 10
2 9
2 10 Q 10 8 7 4
A K J 10
10 8 4
K

942. —
K 9 8 6
A 10 9 7 5
K 7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 4 3
A Q 5
K 8 6 4
9 8
2 9
2 10
2 10 K 10 7 6 5
J 10 7 4
Q
A Q 10

Simulation 8Z08 Main Top Four Hearts Lead II

950. 7
A K 5 4
K 9 8 5 4
9 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 3
9 8 6
Q 7 6
A K 8 6
2 9
2 10
2 10 K 10 6 5 4
Q J 10 7
A 10
Q 10

952. 8 3
10 9 8 7 6
A Q 9 5
A 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 5
J 4
K 7 6 4
K 10 8 6 5
2 10
2 10
2 9 Q 10 7 6 4
A K Q 5
10 8
Q 7

962. 8 5
A Q 10 6
9 8 5
A 10 9 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 3
9 8 5
A Q 10 4
K 8 7 5
2 9
2 10
2 10 K Q 10 6 4
K J 7 4
K 7 6
Q

995. 8
K 10 6 4
K Q 9 7
K 9 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 5 4
Q J 5
A 10 8 6 5
Q 8
2 9
2 10
2 10 K 10 7 6 3
A 9 8 7
4
A 10 5

999. 6
10 8 5 4
Q 8 6
A K Q 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 8 5
K 9 6
A K 10 7
10 9 6
2 10
2 9
2 10 K Q 7 4 3
A Q J 7
9 5 4
5

1007. 3
K Q 9 7 5
7 6 4
K Q 10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 5
A 6
Q 9 8 5
A 9 7 5
2 10
2 9
2 10 K 8 7 6 4
J 10 8 4
A K 10
6

1010. 10 6 3
A J 10 9
A 10 9
K 10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table 4
K 8 6
K Q 8 7 4
9 7 6 5
2 10
2 9
2 10 K Q 8 7 5
Q 7 5 4
6 5
A Q

1029. 10 5
9 7 6 4
A K Q 8 7
10 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 4
A 10 5
10 9 4
A Q 9 8 6
2 10
2 10
2 9 K Q 7 6 3
K Q J 8
6 5
K 5

1051. 10
A 10 9 8 6
A Q 6 4
7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 5 3
K 5
10 9 8 7
A K 10 8
2 10
2 10
2 9 K Q 7 6 4
Q J 7 4
K 5
Q 9

1056. 8
Q 10 8 7
K 9 8
K Q 9 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 10 3
K J 5
A 10 7 5 4
10 7
2 9
2 10
2 10 K 7 6 5 4
A 9 6 4
Q 6
A 8

Simulation 8Z08 Main Top Four Hearts Lead II

1069. 8 5
K 10 7 4
K 10 7 5
A 10 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 6
A J 8
A 9 8 6 4
9 6 5
2 10
2 9
2 10 K Q 10 4 3
Q 9 6 5
Q
K Q 7

1086. K Q
Q 10 9 5
K 9 7 6 4
Q 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 3
K J 4
A 10 8 5
10 9 8 7
2 9
2 10
2 10 8 7 6 5 4
A 8 7 6
Q
A K 5

1122. 8
9 7 6 5
A 8 5
K Q 10 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 6 3
Q 10 8
K 9 7 6
A 8 7
2 9
2 10
2 10 Q 10 7 5 4
A K J 4
Q 10 4
9

1161. 10 7
K Q 8 6
8 4
A 10 9 8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 8
J 10 7
Q 10 9 6 5
K Q 7
2 9
2 10
2 10 Q 6 5 4 3
A 9 5 4
A K 7
6

1162. 4
A Q 9 8
K 10 9 6
9 8 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 7 5
K 5 4
Q 8 4
K Q 10 6
2 9
2 10
2 10 K 10 8 6 3
J 10 7 6
A 7 5
A

1190. 7
A J 10 5
9 7 6 5 4
A Q 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 10 3
9 8 7
K Q 10
K 10 9 7
2 9
2 10
2 10 Q 8 6 5 4
K Q 6 4
A 8
8 5

1214. —
K J 8 5
Q 10 8 7 4
A 10 9 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 8 4
Q 9 6
A K 9 5
Q 6 5
2 10
2 9
2 11 K 10 7 6 5 3
A 10 7 4
6
K 8

1215. 8 3
Q J 9 4
A 6 5
K Q 10 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 4
A 7 5
Q 9 7 4
A 7 6 5
2 9
2 10
2 10 K Q 10 7 6
K 10 8 6
K 10 8
8

1226. 10 8
9 8 6 4
A K Q 7
Q 9 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 3
A Q 5
10 9 8 6
A 8 7 5
2 10
2 10
2 9 K Q 7 6 4
K J 10 7
5 4
K 10

1227. Q
Q J 9 8
Q 8
A Q 9 8 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 7 6
K 10 4
K 10 9 6 4
K 5
2 10
2 9
2 10 K 8 5 4 3
A 7 6 5
A 7 5
10

Simulation 8Z08 Main Top Four Hearts Lead II

9991. 6 3
J 10 8 4
A 10 6
A 7 6 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table Q 4
Q 9 7
Q 9 8 7 5 4
Q 9
2 10
2 10
2 10 K 10 8 7 5
A K 6 5
K
K 10 8

9992. 5
9 7 6 4
A K 6
A 9 8 7 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 3
Q 10 8
Q 10 9 7 4
K Q 10
2 11
2 11
2 11 K Q 10 8 6 4
A K J 5
8 5
6

9993. K 8
9 8 7 5
Q 6
K Q 9 8 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 6
K 10 6
K 10 9 8 7
A 10 5
2 10
2 9
2 9 Q 10 5 4 3
A Q J 4
A 5 4
6

9994. 10 6
A Q 9 7
10 7 4
K Q 8 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 7 4
8 6 5
A Q 9 8 6
A 10 9
2 9
2 10
2 10 K Q 8 5 3
K J 10 4
K 5
7 6

9995. —
K 9 8 6 4
9 7 5 4
A K 9 8
A J 9 2
3 2
J 3 2
J 4 3 2 Table K 6 4
Q 10
K Q 10 8 6
Q 7 6
2 12
2 12
2 12 Q 10 8 7 5 3
A J 7 5
A
10 5

9996. 8 7
A Q 7 6
K 10 5
Q 10 9 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 4 3
J 8 5
A Q 8 7
K 8 7 5
2 9
2 9
2 9 K Q 10 6 5
K 10 9 4
9 6 4
A

9997. 6
9 6 5 4
10 8 5
A K Q 10 7
A J 9 2
3 2
J 3 2
J 4 3 2 Table 5 4 3
K Q
A Q 9 6 4
8 6 5
2 11
2 10
2 11 K Q 10 8 7
A J 10 8 7
K 7
9

9998. 5
A J 8 4
10 8 7 5 4
A 10 9
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 8 6
K 7 6
Q 6
K 8 7 6 5
2 10
2 10
2 10 K Q 7 4 3
Q 10 9 5
A K 9
Q

9999. 10 6
K J 9 8
A 8 5 4
Q 7 6
A J 9 2
3 2
J 3 2
J 4 3 2 Table 8 5
A 10 5
K Q 9 7 6
10 9 5
2 10
2 10
2 10 K Q 7 4 3
Q 7 6 4
10
A K 8

10000. K 4
K J 10 5
K 8 7 5 4
10 5
A J 9 2
3 2
J 3 2
J 4 3 2 Table 10 3
9 6 4
A Q 9 6
K 9 8 6
2 10
2 10
2 10 Q 8 7 6 5
A Q 8 7
10
A Q 7

Simulation 8Z08 Main

Top Four Hearts Lead II

1.	— K 9 8 7 6 K Q 9 7 4 10 9 5
A J 9 2 3 2 J 3 2 J 4 3 2		Q 10 5 4 Q 5 10 8 5 A K Q 7
2 12 2 12 2 11	K 8 7 6 3 A J 10 4 A 6 8 6

2.	5 A J 5 4 A 10 6 5 4 10 9 7
A J 9 2 3 2 J 3 2 J 4 3 2		Q 4 3 Q 10 9 K 9 8 7 Q 6 5
2 10 2 10 2 10	K 10 8 7 6 K 8 7 6 Q A K 8

3.	— 10 8 7 4 A Q 10 5 4 K 10 9 6
A J 9 2 3 2 J 3 2 J 4 3 2		K 10 8 4 A K 6 K 8 6 8 7 5
2 10 2 11 2 11	Q 7 6 5 3 Q J 9 5 9 7 A Q

4.	K 10 K J 5 4 9 6 K 10 9 6 5
A J 9 2 3 2 J 3 2 J 4 3 2		8 7 A Q 10 K 10 8 7 5 Q 8 7
2 9 2 9 2 9	Q 6 5 4 3 9 8 7 6 A Q 4 A

5.	5 A J 9 5 A 9 8 5 9 8 7 6
A J 9 2 3 2 J 3 2 J 4 3 2		Q 8 7 8 7 6 K Q 10 7 6 K Q
2 8 2 9 2 9	K 10 6 4 3 K Q 10 4 4 A 10 5

6.	— A Q 7 6 5 K 10 9 7 6 10 9 8
A J 9 2 3 2 J 3 2 J 4 3 2		Q 10 7 5 K 10 A Q 8 4 Q 7 6
2 10 2 11 2 11	K 8 6 4 3 J 9 8 4 5 A K 5

7.	4 K 10 9 5 K 10 8 7 5 A 6 5
A J 9 2 3 2 J 3 2 J 4 3 2		K 8 7 8 7 A 6 4 Q 10 9 8 7
2 11 2 11 2 11	Q 10 6 5 3 A Q J 6 4 Q 9 K

8.	8 5 10 9 7 4 A K Q 8 4 10 9
A J 9 2 3 2 J 3 2 J 4 3 2		K 3 K 6 5 10 9 6 5 K Q 8 6
2 10 2 10 2 10	Q 10 7 6 4 A Q J 8 7 A 7 5

9.	— Q 8 5 4 A 10 8 6 K 8 7 6 5
A J 9 2 3 2 J 3 2 J 4 3 2		K 8 3 J 7 6 K Q 9 7 4 A 9
2 9 2 9 2 10	Q 10 7 6 5 4 A K 10 9 5 Q 10

10.	7 4 K Q 8 5 A 10 9 5 4 8 5
A J 9 2 3 2 J 3 2 J 4 3 2		6 5 J 10 7 K 8 6 A Q 9 7 6
2 10 2 10 2 10	K Q 10 8 3 A 9 6 4 Q 7 K 10

19.	5 A Q J 9 K 9 8 6 5 10 7 6
A J 9 2 3 2 J 3 2 J 4 3 2		10 8 7 K 6 4 A 4 K Q 9 8 5
2 10 2 9 2 10	K Q 6 4 3 10 8 7 5 Q 10 7 A

21.	K 8 J 8 6 4 Q 10 8 5 K Q 7
A J 9 2 3 2 J 3 2 J 4 3 2		5 4 A Q 7 9 7 4 A 9 8 6 5
2 10 2 10 2 9	Q 10 7 6 3 K 10 9 5 A K 6 10

36.	K Q 10 8 5 K Q 7 6 5 K 7 5
A J 9 2 3 2 J 3 2 J 4 3 2		10 7 6 A 7 4 A 10 9 4 10 9 6
2 9 2 10 2 10	Q 8 5 4 3 K J 9 6 8 A Q 8

55.	Q 5 K J 9 5 8 4 A Q 8 7 5
A J 9 2 3 2 J 3 2 J 4 3 2		10 7 Q 10 6 K Q 10 9 K 10 9 6
2 9 2 10 2 10	K 8 6 4 3 A 8 7 4 A 7 6 5 —

65.	4 J 10 8 6 K 10 4 A K 8 6 5
A J 9 2 3 2 J 3 2 J 4 3 2		Q 8 5 A K 9 9 8 6 5 Q 10 9
2 9 2 10 2 10	K 10 7 6 3 Q 7 5 4 A Q 7 7

68.	5 A J 10 4 8 6 K 10 8 7 6 5
A J 9 2 3 2 J 3 2 J 4 3 2		8 7 3 Q 9 8 K Q 9 7 5 A 9
2 10 2 9 2 10	K Q 10 6 4 K 7 6 5 A 10 4 Q

77.	4 9 6 5 4 Q 7 5 4 A K 10 9
A J 9 2 3 2 J 3 2 J 4 3 2		K 7 3 A J 7 K 9 8 6 8 7 6
2 9 2 10 2 10	Q 10 8 6 5 K Q 10 8 A 10 Q 5

84.	Q K Q 7 6 5 Q 5 4 K 9 7 6
A J 9 2 3 2 J 3 2 J 4 3 2		7 5 4 9 4 A K 10 7 Q 10 8 5
2 10 2 9 2 10	K 10 8 6 3 A J 10 8 9 8 6 A

87.	7 3 10 8 7 6 4 A Q 9 K Q 7
A J 9 2 3 2 J 3 2 J 4 3 2		Q 6 K 10 8 7 5 4 A 10 9 6 5
2 11 2 11 2 9	K 10 8 5 4 A Q J 9 5 K 6 8

96.	10 7 K 10 6 5 A 10 8 7 A 10 7
A J 9 2 3 2 J 3 2 J 4 3 2		K 4 Q J 7 K 9 6 5 4 9 6 5
2 9 2 10 2 10	Q 8 6 5 3 A 9 8 4 Q K Q 8

103.	6 K 10 7 4 A 8 7 6 4 Q 10 8
A J 9 2 3 2 J 3 2 J 4 3 2		K 10 5 9 6 5 Q 10 9 A K 9 6
2 9 2 10 2 10	Q 8 7 4 3 A Q J 8 K 5 7 5

105.	10 5 A J 7 5 K Q 8 6 5 Q 7
A J 9 2 3 2 J 3 2 J 4 3 2		7 3 Q 9 6 A 10 9 7 4 K 10 5
2 10 2 10 2 9	K Q 8 6 4 K 10 8 4 — A 9 8 6

106.	10 7 J 8 7 5 A K Q 10 7 10 7
A J 9 2 3 2 J 3 2 J 4 3 2		Q 4 K 10 6 9 8 6 A Q 9 8 5
2 10 2 10 2 9	K 8 6 5 3 A Q 9 4 5 4 K 6

147.	8 5 A K 10 8 K Q 9 6 9 8 5
A J 9 2 3 2 J 3 2 J 4 3 2		K 6 Q 5 10 8 7 5 4 A Q 10 6
2 10 2 10 2 9	Q 10 7 4 3 J 9 7 6 4 A K 7

159.	7 Q 10 6 4 K 8 6 A 10 8 7 6
A J 9 2 3 2 J 3 2 J 4 3 2		Q 10 6 9 8 5 A 9 7 5 K 9 5
2 9 2 10 2 10	K 8 5 4 3 A K J 7 Q 10 4 Q

194.	5 Q J 5 4 K 10 8 5 A 10 8 7
A J 9 2 3 2 J 3 2 J 4 3 2		K 7 3 A 10 7 7 4 K Q 9 6 5
2 9 2 10 2 10	Q 10 8 6 4 K 9 8 6 A Q 9 6 —

225.	8 A K J 7 9 8 4 Q 10 9 8 7
A J 9 2 3 2 J 3 2 J 4 3 2		Q 5 3 10 8 4 Q 10 7 5 A K 6
2 9 2 10 2 10	K 10 7 6 4 Q 9 6 5 A K 6 5

228.	8 A Q 8 5 8 6 4 K Q 10 8 7
A J 9 2 3 2 J 3 2 J 4 3 2		10 4 3 9 7 6 A Q 9 7 A 9 6
2 10 2 9 2 10	K Q 7 6 5 K J 10 4 K 10 5 5

234.	6 4 Q 10 6 4 K Q 10 7 6 A 6
A J 9 2 3 2 J 3 2 J 4 3 2		Q 8 K 9 8 A 8 5 Q 10 9 8 5
2 10 2 9 2 10	K 10 7 5 3 A J 7 5 9 4 K 7

236.	7 Q J 8 6 K 9 8 5 A 8 7 6
A J 9 2 3 2 J 3 2 J 4 3 2		5 4 3 9 5 4 A Q 7 K 10 9 5
2 9 2 10 2 10	K Q 10 8 6 A K 10 7 10 6 4 Q