Simulation 8Z24 Main

Four or Five-Card Major?

by Richard Pavlicek

Which card would you lead against 3 NT on this auction:

Any vul West North East South
Q 9 6 5 Table 1 Pass 3 NT¹
A 8 7 6 2 Pass Pass Pass
10 4
6 2 1. 12-14 balanced, no 4+ major
3 NT

A heart seems the obvious choice (longest suit), but another consideration is that the Q would then have little or no significance toward a successful defense. In contrast, a spade lead will bring both of your assets ( Q and A) into play. I thought it would interesting to compare the two lead options ( 5 or 6) with a simulation. How close is it? Place your bets as I spin the wheel.

For a simulation I created 10,000 random deals with the West hand fixed and the other hands constrained to fit the auction. North: minimum-range 1 opening (longer or better minor, could be 3). South: 12-14 HCP; balanced; no 4-card major. East: no appropriate action (bid or double) over 1 .

Results are shown below. Trick Average shows the average number of tricks won by the defense. Set Percent shows how often the contract is defeated, and Hold Percent how often it is made without an overtrick. The second table compares the leads for bridge scoring, with the better choice leftmost. Net W-L (matchpoints or board-a-match verdict) counts +1 for a win and -1 for a loss. Net Score and Net IMPs are calculated twice, first with declarer nonvul (green) then with declarer vul (red). Plus values show the net gain over 10,000 deals.

Interesting indeed: a split decision. The heart lead wins comfortably at total points or IMPs, while the spade lead wins narrowly at matchpoints or board-a-match.

Results for 10,000 Deals
Lead Trick Average Set Percent Hold Percent
5 3.4752 22.42 23.35
6 3.4597 26.36 19.73

Results for 10,000 Deals
Lead	Trick Average	Set Percent	Hold Percent
5	3.4752	22.42	23.35
6	3.4597	26.36	19.73

Comparison Net W-L NV Net Score NV Net IMPs Vul Net Score Vul Net IMPs
6 vs. 5 -371 +154,790 +2936 +238,190 +3574

Comparison	Net W-L	NV Net Score	NV Net IMPs	Vul Net Score	Vul Net IMPs
6 vs. 5	-371	+154,790	+2936	+238,190	+3574

Actual Deals

Below are 100 of the 10,000 deals, including the first 20, last 20, and 60 in-between with the greatest IMP gains (30 for each lead). Numbers after each lead show the tricks won by the defense with double-dummy play by both sides.

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

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

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

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

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

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

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

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

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

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

Simulation 8Z24 Main Top Four or Five-Card Major?

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

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

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

14. A K 7 3
9
A 8 6 2
K 10 9 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 10
Q J 10 5 3
9 3
Q 7 5 4
5 → 2
6 → 1 8 4 2
K 4
K Q J 7 5
A J 3

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

16. 8 2
5
A Q J 9 5 2
Q J 9 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 10 7 4
Q 9 4 3
K 8
A 10 4
5 → 5
6 → 4 A K 3
K J 10
7 6 3
K 7 5 3

17. 7 2
Q 4 3
K Q J 8 3
A 10 9
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 4 3
10 9
7 2
Q J 8 4 3
5 → 4
6 → 3 K 10 8
K J 5
A 9 6 5
K 7 5

18. 4 2
K 10
K Q 8 7 3 2
A 8 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A 8 7 3
J 5 4
J 6 5
K 7 3
5 → 4
6 → 3 K J 10
Q 9 3
A 9
Q J 10 9 4

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

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

Simulation 8Z24 Main Top Four or Five-Card Major?

77. A K
J
K 9 8 6 5 2
Q 9 7 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 7 4 2
K 10 9 4 3
J 3
K 5
5 → 0
6 → 5 J 8 3
Q 5
A Q 7
A J 10 8 3

102. 8 4 3
4
A K J 9 3
K 10 9 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K 10 7 2
K Q 10 5
7 5 2
J 8
5 → 2
6 → 5 A J
J 9 3
Q 8 6
A Q 7 4 3

260. 4 3
9
A J 9 6 3
K Q J 8 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 7
Q J 10 5 4
8 7
10 7
5 → 9
6 → 2 10 8 2
K 3
K Q 5 2
A 9 4 3

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

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

881. 7
J 5 3
K 8 7 5 2
A Q J 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 4 3
Q 10
A 9
8 7 4
5 → 7
6 → 3 K 2
K 9 4
Q J 6 3
K 10 9 3

999. —
K 10 3
K Q 9 8 7 6 3
Q 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 8 7 3
J 5
5 2
K 7 4
5 → 7
6 → 0 10 4 2
Q 9 4
A J
A J 10 9 8

1338. 10
9 5
A J 9 7 6 5
A K J 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K J 3 2
K Q 4
8 3
10 7 5 3
5 → 2
6 → 5 A 8 7 4
J 10 3
K Q 2
Q 9 4

1575. A K 3
4
K 9 7 5 2
J 10 8 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 8 4
K Q 9 5
8 6 3
K 4 3
5 → 2
6 → 5 10 7 2
J 10 3
A Q J
A Q 9 7

2061. 2
K J 10 3
A K J 5 3
10 8 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 4 3
5
8 6
A J 9 5
5 → 7
6 → 3 K 7
Q 9 4
Q 9 7 2
K Q 7 4

Simulation 8Z24 Main Top Four or Five-Card Major?

2522. K J
4
A Q J 9 7 5 3 2
9 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A 8 7 3
Q J 10 5
8
Q J 8 3
5 → 6
6 → 0 10 4 2
K 9 3
K 6
A K 10 7 5

2643. A K 4
J 4 3
A J 5 2
10 8 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 8 7
Q 10 5
K 7 6 3
A 9 4
5 → 4
6 → 6 J 3 2
K 9
Q 9 8
K Q J 5 3

2657. A 4 2
Q
K J 9 6 5 2
K 9 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 7 3
K 10 9 5
Q
Q J 7 4 3
5 → 2
6 → 5 K J 8
J 4 3
A 8 7 3
A 10 8

2710. J 10 4
J
K Q J 7 6 5
A Q J
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 3 2
K Q 10 9
9 2
10 9 8 5
5 → 0
6 → 5 A K 7
5 4 3
A 8 3
K 7 4 3

3004. K 3 2
J 9
A Q J 9 7 2
A 10
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 8 7 4
K Q 5
6 5
Q 8 5 4
5 → 1
6 → 5 A J
10 4 3
K 8 3
K J 9 7 3

3033. A 10 7 4
10 5
9 8 3 2
A K 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 3 2
K 9 4 3
A Q J 5
10 5 4
5 → 4
6 → 6 K J 8
Q J
K 7 6
Q J 9 8 3

3221. A 10 7 4
4
A Q J 6 5
9 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 3
K J 10 5
7 2
A K 10 8 4
5 → 4
6 → 7 K J 2
Q 9 3
K 9 8 3
Q J 7

3224. K 10 3
10 9
A Q 9 2
Q J 5 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 7
Q J 4 3
J 7 3
9 7 3
5 → 7
6 → 4 8 4 2
K 5
K 8 6 5
A K 10 8

3388. K 4
K 4
K J 7 6 2
Q 10 8 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 7 3 2
Q J 9
A 8
J 9 5 4
5 → 2
6 → 5 A J 10
10 5 3
Q 9 5 3
A K 3

3401. 2
Q 10 9 5
A K J 7
Q 9 7 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 4 3
3
9 6
A J 4 3
5 → 7
6 → 3 K 7
K J 4
Q 8 5 3 2
K 10 8

Simulation 8Z24 Main Top Four or Five-Card Major?

3562. —
9 5
K J 9 7 6 3 2
A Q 8 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 10 8 2
Q J 10
8 5
J 10
5 → 11
6 → 0 7 4 3
K 4 3
A Q
K 9 7 5 4

3675. K 10 8 2
9
K 8 5 3 2
A Q 10
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 4 3
K Q J 4
J 6
J 7 5 3
5 → 1
6 → 5 A 7
10 5 3
A Q 9 7
K 9 8 4

4054. —
Q J 5 3
J 8 6 3 2
A Q J 9
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 7 2
4
A 9 7 5
10 8
5 → 7
6 → 4 K 4 3
K 10 9
K Q
K 7 5 4 3

4121. 4
4
Q J 9 7 6 5 2
A K Q 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K 10 8 7 3
K Q J 10
3
10 8 3
5 → 1
6 → 5 A J 2
9 5 3
A K 8
J 9 7 5

4422. 10
9 4
A K 9 5 3 2
A 8 5 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 7 2
Q J 5 3
8 6
7 3
5 → 10
6 → 1 8 4 3
K 10
Q J 7
K Q J 10 9

4726. A 8 3 2
Q 4
A Q 9 6 3
5 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 7 4
K J 5
J 8 2
A J 10 8 3
5 → 4
6 → 6 K J 10
10 9 3
K 7 5
K Q 9 7

4873. A J 10 3 2
4
K J 9 7 5 2
5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 4
K Q 9 3
8
A K J 8 7 3
5 → 4
6 → 7 K 7
J 10 5
A Q 6 3
Q 10 9 4

4905. A 10 3 2
4 3
A 8 6 3 2
K 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 7
K Q 9
Q 9 7 5
Q 10 5 3
5 → 2
6 → 5 K J 4
J 10 5
K J
A J 9 8 4

4994. —
K 5 3
A K J 9 7 6 3
9 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 8 3 2
J 9
5
Q 10 8 7
5 → 7
6 → 2 10 7 4
Q 10 4
Q 8 2
A K J 4

5043. 4 3
Q 9
A Q J 8 3
K J 4 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8
K J 5
6 2
10 8 7 5
5 → 4
6 → 6 K 7 2
10 4 3
K 9 7 5
A Q 9

Simulation 8Z24 Main Top Four or Five-Card Major?

5305. —
J 10 5
A Q J 9 8 7 3 2
A 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 10 8 7 4
9 4
5
K 10 9 8
5 → 7
6 → 3 J 3 2
K Q 3
K 6
Q J 7 5 3

5364. 8 7
4
A K J 8 6
Q 10 8 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 4 3
Q J 9 5 3
9 2
7 4
5 → 9
6 → 2 J 10 2
K 10
Q 7 5 3
A K J 9

5422. —
Q J 10 4
Q 8 6 5 3
A Q 9 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 7 4 3
3
A 7
10 7 5 3
5 → 7
6 → 3 K 8 2
K 9 5
K J 9 2
K J 8

5481. A 4 2
J
K 7 6 5 3
K Q 7 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K 10 7
K 10 9 5 4
Q 9 2
J 8
5 → 2
6 → 5 J 8 3
Q 3
A J 8
A 10 9 5 3

5861. A 8 7
K 10
8 7 6 5 3
K Q 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 4 3
Q 9 3
Q J 9
A J 9 3
5 → 4
6 → 6 K J 2
J 5 4
A K 2
10 7 5 4

5882. A 10 2
10 9
A K 9 8 5 2
J 10
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 7 4
K J 3
J 7 6
K 5 4 3
5 → 1
6 → 5 K J 3
Q 5 4
Q 3
A Q 9 8 7

5993. J 3 2
—
A K J 7 6 5 2
Q 9 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 8
Q J 10 5 4
9 3
J 7 3
5 → 9
6 → 0 10 7 4
K 9 3
Q 8
A K 10 8 4

6366. 10 8
5
K Q 8 5 3 2
A J 10 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 4 2
Q J 10 4 3
J 7
7 4
5 → 9
6 → 1 J 7 3
K 9
A 9 6
K Q 9 5 3

6497. K 10 2
5
Q 9 7 6 5
A Q 7 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 4
Q J 9 4 3
K 2
9 8 5
5 → 7
6 → 3 8 7 3
K 10
A J 8 3
K J 10 4

7179. 10
K J 10 9
A K 7 5
10 9 8 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 8 7 3 2
4
J 9 6 2
A J
5 → 7
6 → 4 K 4
Q 5 3
Q 8 3
K Q 7 4 3

Simulation 8Z24 Main Top Four or Five-Card Major?

7210. K 7
9 5
A 8 7 3 2
A 7 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 4 2
Q J 10
Q 9 6
J 10 9
5 → 9
6 → 3 10 8 3
K 4 3
K J 5
K Q 8 4

7608. 10 8
Q
A J 9 8 6 3
K Q 8 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K J 4 3
K 10 9 5
5 2
J 10 3
5 → 2
6 → 5 A 7 2
J 4 3
K Q 7
A 9 7 5

7633. A J 3
5
K Q J 7 6 3 2
9 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 7 4
K Q 9 4
9 8
A Q 10 4
5 → 3
6 → 6 K 8 2
J 10 3
A 5
K J 7 5 3

7842. —
Q 10 9 5
A K J 9 5
Q 10 8 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 7 4 2
4
8 2
A J 7
5 → 7
6 → 3 K 3
K J 3
Q 7 6 3
K 9 5 3

7882. 8
K Q 5 4
K Q J 9 5 3
5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K J 7 4 3 2
9
A 8
Q J 10 7
5 → 7
6 → 4 A 10
J 10 3
7 6 2
A K 9 8 4

8021. 4
Q 10 9 3
A K J 9 2
J 4 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table K 10 8 7 2
J 5
8 6 3
A K 8
5 → 7
6 → 4 A J 3
K 4
Q 7 5
Q 10 9 7 5

8201. 8
10 9
A Q 8 5 3
A 10 7 4 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 10 3 2
Q J 5 4
7 6
Q 9
5 → 10
6 → 2 J 7 4
K 3
K J 9 2
K J 8 5

8315. K J 8
5
A K Q 9 5 2
10 8 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 3 2
K Q 9 3
8 3
Q 9 7 5
5 → 1
6 → 5 A 7 4
J 10 4
J 7 6
A K J 4

8637. K 10 7 3
10
A Q J 5 3
J 10 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 8
Q 9 5 4 3
9 8 2
A Q 3
5 → 2
6 → 5 A 4 2
K J
K 7 6
K 9 8 7 4

8643. 10 8
10 4
A K Q J 9
J 8 4 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K 7 4
Q J 9 5
8 7 6
10 7
5 → 9
6 → 2 J 3 2
K 3
5 3 2
A K Q 9 5

Simulation 8Z24 Main Top Four or Five-Card Major?

8701. K J 7 2
10 3
K Q 5 2
K 10 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A 4
J 9 4
9 8 7 6 3
A 7 5
5 → 3
6 → 6 10 8 3
K Q 5
A J
Q J 9 8 4

8800. K
K 4 3
A K 9 8 7 5 2
J 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 8 7
9 5
J 3
10 9 5 4
5 → 6
6 → 0 4 3 2
Q J 10
Q 6
A K Q 8 7

8832. K 8 4 2
5
A K J 8 6 5
Q 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 3
K Q J 9
7 3
K 10 9 7 4
5 → 2
6 → 5 A J 7
10 4 3
Q 9 2
A J 5 3

8882. K J 4
9
A K 6 5 2
K 10 5 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 8 3
K Q 5 3
J 8
J 9 8 7
5 → 2
6 → 5 A 7 2
J 10 4
Q 9 7 3
A Q 3

9069. K J 3
9
K Q 8 7 3 2
K J 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 4 2
K 10 5 4 3
6
A Q 9 3
5 → 4
6 → 7 A 8 7
Q J
A J 9 5
10 8 5 4

9547. —
Q J 9 5
K Q J 8 6
Q 8 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A K J 10 8 7
10
7 3
J 10 9 7
5 → 7
6 → 4 4 3 2
K 4 3
A 9 5 2
A K 4

9562. K 2
9
K 8 7 6 5 2
A J 8 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 7
Q J 10 4 3
J 9
5 3
5 → 9
6 → 1 8 4 3
K 5
A Q 3
K Q 10 9 7

9702. —
K 10 3
Q J 7 6 5 3
A 9 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 7 3 2
J 4
A 2
Q 10 8
5 → 7
6 → 3 K 8 4
Q 9 5
K 9 8
K J 7 4

9924. A 4
K
K Q J 9 6
J 10 9 7 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 10 8 7 2
J 10 9 4
A 7 3
Q
5 → 2
6 → 5 K 3
Q 5 3
8 5 2
A K 8 5 3

9967. 10 7 4
Q
A K Q 6 5 2
K 8 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 3 2
K J 9 3
9
A 10 7 4 3
5 → 4
6 → 6 A K J
10 5 4
J 8 7 3
Q J 9

Simulation 8Z24 Main Top Four or Five-Card Major?

9981. 7 2
5 4 3
K Q 9 7 2
A K 9
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 4 3
K 10
J 5
J 8 5 4 3
5 → 4
6 → 4 K 10 8
Q J 9
A 8 6 3
Q 10 7

9982. 8 4
K J 9 5
A K 6 3
J 10 7
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 7 3 2
10 4
Q J 8 5
A 8 4
5 → 3
6 → 2 A K 10
Q 3
9 7 2
K Q 9 5 3

9983. K J 7 3
Q J 5
A Q 6 5 2
9
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A 10
9 4 3
J 9 3
Q J 7 4 3
5 → 3
6 → 3 8 4 2
K 10
K 8 7
A K 10 8 5

9984. 3
K Q 3
Q J 9 7 5
A 9 5 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A 10 7 4 2
9 4
K 8 2
K 8 7
5 → 5
6 → 3 K J 8
J 10 5
A 6 3
Q J 10 3

9985. A K 8 2
5
Q J 9 8 2
K J 4
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 7
J 10 9 3
5 3
A Q 8 7 5
5 → 4
6 → 5 10 4 3
K Q 4
A K 7 6
10 9 3

9986. 7 3 2
—
A K J 8 6 5 2
K Q 8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table A J 10 4
J 9 5 4 3
3
J 9 4
5 → 2
6 → 0 K 8
K Q 10
Q 9 7
A 10 7 5 3

9987. A 10
K 3
K Q 9 7 2
Q 9 5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 8 3 2
Q 10 4
J 8
K J 7 4
5 → 3
6 → 4 K 7 4
J 9 5
A 6 5 3
A 10 8

9988. A
4 3
A Q J 7 5 3
J 10 9 5
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table J 10 7 4 2
Q 10 5
8 6
A Q 7
5 → 2
6 → 2 K 8 3
K J 9
K 9 2
K 8 4 3

9989. A 8 4
J 10 5
A K Q 9 6 3
8
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 10 7 3
9 4
J 7
K Q 10 7 5 3
5 → 1
6 → 2 K J 2
K Q 3
8 5 2
A J 9 4

9990. A 10 2
J 5
A K J 9 3 2
5 3
Q 9 6 5
A 8 7 6 2
10 4
6 2 Table 8 7 4
K Q 9
6
Q 10 9 8 7 4
5 → 1
6 → 5 K J 3
10 4 3
Q 8 7 5
A K J

Simulation 8Z24 Main Top Four or Five-Card Major?

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

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

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

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

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

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

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

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

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

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

Simulation 8Z24 Main Top Four or Five-Card Major?

	Any vul	West	North	East	South
Q 9 6 5			1	Pass	3 NT¹
A 8 7 6 2		Pass	Pass	Pass
10 4
6 2		1. 12-14 balanced, no 4+ major
	3 NT

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

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

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

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

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

6.	K 10 7 3 J 9 5 3 A K Q J 3
Q 9 6 5 A 8 7 6 2 10 4 6 2		8 4 2 Q 9 7 6 5 K J 10 5 4
5 → 1 6 → 1	A J K 10 4 8 3 2 A Q 9 8 7

7.	3 Q 9 3 A K Q 6 5 Q J 10 9
Q 9 6 5 A 8 7 6 2 10 4 6 2		K 10 8 7 4 5 4 9 8 2 K 7 3
5 → 2 6 → 1	A J 2 K J 10 J 7 3 A 8 5 4

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

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

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

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

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

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

14.	A K 7 3 9 A 8 6 2 K 10 9 8
Q 9 6 5 A 8 7 6 2 10 4 6 2		J 10 Q J 10 5 3 9 3 Q 7 5 4
5 → 2 6 → 1	8 4 2 K 4 K Q J 7 5 A J 3

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

16.	8 2 5 A Q J 9 5 2 Q J 9 8
Q 9 6 5 A 8 7 6 2 10 4 6 2		J 10 7 4 Q 9 4 3 K 8 A 10 4
5 → 5 6 → 4	A K 3 K J 10 7 6 3 K 7 5 3

17.	7 2 Q 4 3 K Q J 8 3 A 10 9
Q 9 6 5 A 8 7 6 2 10 4 6 2		A J 4 3 10 9 7 2 Q J 8 4 3
5 → 4 6 → 3	K 10 8 K J 5 A 9 6 5 K 7 5

18.	4 2 K 10 K Q 8 7 3 2 A 8 5
Q 9 6 5 A 8 7 6 2 10 4 6 2		A 8 7 3 J 5 4 J 6 5 K 7 3
5 → 4 6 → 3	K J 10 Q 9 3 A 9 Q J 10 9 4

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

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

77.	A K J K 9 8 6 5 2 Q 9 7 4
Q 9 6 5 A 8 7 6 2 10 4 6 2		10 7 4 2 K 10 9 4 3 J 3 K 5
5 → 0 6 → 5	J 8 3 Q 5 A Q 7 A J 10 8 3

102.	8 4 3 4 A K J 9 3 K 10 9 5
Q 9 6 5 A 8 7 6 2 10 4 6 2		K 10 7 2 K Q 10 5 7 5 2 J 8
5 → 2 6 → 5	A J J 9 3 Q 8 6 A Q 7 4 3

260.	4 3 9 A J 9 6 3 K Q J 8 5
Q 9 6 5 A 8 7 6 2 10 4 6 2		A K J 7 Q J 10 5 4 8 7 10 7
5 → 9 6 → 2	10 8 2 K 3 K Q 5 2 A 9 4 3

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

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

881.	7 J 5 3 K 8 7 5 2 A Q J 5
Q 9 6 5 A 8 7 6 2 10 4 6 2		A J 10 8 4 3 Q 10 A 9 8 7 4
5 → 7 6 → 3	K 2 K 9 4 Q J 6 3 K 10 9 3

999.	— K 10 3 K Q 9 8 7 6 3 Q 5 3
Q 9 6 5 A 8 7 6 2 10 4 6 2		A K J 8 7 3 J 5 5 2 K 7 4
5 → 7 6 → 0	10 4 2 Q 9 4 A J A J 10 9 8

1338.	10 9 5 A J 9 7 6 5 A K J 8
Q 9 6 5 A 8 7 6 2 10 4 6 2		K J 3 2 K Q 4 8 3 10 7 5 3
5 → 2 6 → 5	A 8 7 4 J 10 3 K Q 2 Q 9 4

1575.	A K 3 4 K 9 7 5 2 J 10 8 5
Q 9 6 5 A 8 7 6 2 10 4 6 2		J 8 4 K Q 9 5 8 6 3 K 4 3
5 → 2 6 → 5	10 7 2 J 10 3 A Q J A Q 9 7