Simulation 8Z30 Main

Lead against Two Hearts

by Richard Pavlicek

Kelvin Ng of Singapore inquired about West’s opening lead against 2 on the auction below. Scoring was IMPs.

N-S vul West North East South
9 8 6 4 Table Pass 1 Dbl 1
4 2 Pass 1 NT Pass 2
6 4 Pass Pass Pass
K J 9 7 5
2

Kelvin felt the doubleton diamond was best, and I agree, as besides being safe it expedites the chance of a ruff. Nonetheless, I thought a simulation would be interesting to compare the leads of each suit. The specific cards chosen would rarely matter, so I’ll assume standard methods and compare leads of the 4, 2, 6 and 7. Chances of defeating 2 seem pretty slim, especially with partner advertising where the strength and trumps are, so this is probably just a matter of overtricks, but let’s give it a whirl.

For a simulation I created 10,000 random deals with the West hand fixed and these constraints: North, a natural 1 opening and a balanced 12-14 HCP with no four-card major; East, a takeout double of 1 with at most 15 HCP and 13-18 points (per my evaluation method); South, 7-11 points with six hearts, or an unbalanced hand with five hearts and fewer than four clubs. Results were determined with perfect play by both sides after the opening lead. While this would usually not occur in practice, differences tend to even out, as my studies show a close correlation between actual play and double-dummy.

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. Hold Percent shows how often the contract is made exactly, i.e., without an overtrick. The second table compares the leads per form of scoring, with the superior lead shown first (leftmost). Win Percent delivers the verdict for matchpoints or board-a-match. Net Score and Net IMPs are calculated first with declarer nonvul (green) then with declarer vul (red) but only the latter applies to the actual case. Signed numbers indicate the net gain or loss over 10,000 deals.

As I anticipated, we’re dealing with peanuts here. The contract is rarely set with any lead, but as Kelvin and I expected, the 6 is a clear winner. At matchpoints or board-a-match the advantage would be significant, but at the actual IMP scoring… well,… pass me some peanuts.

Results for 10,000 Deals
2 South Trick Average Set Percent Hold Percent
6 lead 3.9139 4.07 21.69
4 lead 3.7822 1.88 16.67
2 lead 3.6838 1.22 13.68
7 lead 3.4699 0.50 8.45

Results for 10,000 Deals
2 South	Trick Average	Set Percent	Hold Percent
6 lead	3.9139	4.07	21.69
4 lead	3.7822	1.88	16.67
2 lead	3.6838	1.22	13.68
7 lead	3.4699	0.50	8.45

Scoring Comparison Win Percent NV Net Score NV Net IMPs Vul Net Score Vul Net IMPs
6 lead vs 4 56.27 +68460 +1992 +80610 +2235
6 lead vs 2 60.69 +106620 +3176 +122220 +3488
6 lead vs 7 69.45 +180230 +5515 +199630 +5903
4 lead vs 2 54.76 +38160 +1184 +41610 +1253
4 lead vs 7 64.62 +111770 +3539 +119020 +3684
2 lead vs 7 60.20 +73610 +2357 +77410 +2433

Scoring Comparison	Win Percent	NV Net Score	NV Net IMPs	Vul Net Score	Vul Net IMPs
6 lead vs 4	56.27	+68460	+1992	+80610	+2235
6 lead vs 2	60.69	+106620	+3176	+122220	+3488
6 lead vs 7	69.45	+180230	+5515	+199630	+5903
4 lead vs 2	54.76	+38160	+1184	+41610	+1253
4 lead vs 7	64.62	+111770	+3539	+119020	+3684
2 lead vs 7	60.20	+73610	+2357	+77410	+2433

Note: Removing the decimal point in averages or percents shows the number of occurrences.
For example, the set percent of 4.07 translates to 407 sets in 10,000 deals.

Simulation 8Z30 Main Top Lead against Two Hearts

Actual Deals

Below are 100 of the 10,000 deals, including the first 20 and last 20. The 60 selected deals in between cycle through optimal gains for each lead. Numbers show tricks won by the defense with double-dummy play after that opening lead. Contract is always 2 by South.

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

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

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

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

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

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

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

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

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

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

Simulation 8Z30 Main Top Lead against Two Hearts

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

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

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

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

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

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

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

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

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

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

Simulation 8Z30 Main Top Lead against Two Hearts

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

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

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

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

667. 3 2
Q 8 5
A Q 7 3
A Q 10 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 10 5
A J 7
K 9 2
6 3 2
6 → 4
4 → 3
2 → 3
7 → 3 A J 7
K 10 9 6 3
J 10 8 5
8

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

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

1329. A Q 5
K 10 8
A J 8
10 8 6 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table J 10 3 2
Q 5 3
K Q 7 2
A 2
6 → 3
4 → 3
2 → 3
7 → 4 K 7
A J 9 7 6
10 9 5 3
Q 3

1330. A K 7
9 8
J 10 9 3
A Q 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table 5 3 2
A K Q 10
K Q 2
10 8 6
6 → 5
4 → 4
2 → 4
7 → 4 Q J 10
J 7 6 5 3
A 8 7 5
4

1343. K 3 2
Q J 3
10 9
A Q 10 8 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 10 5
K 10 9
K Q 7 5 2
2
6 → 3
4 → 4
2 → 3
7 → 3 J 7
A 8 7 6 5
A J 8 3
6 3

Simulation 8Z30 Main Top Lead against Two Hearts

1353. 7 3 2
K 7 5
K 7
A Q 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K 10 5
A Q 8
Q 10 9 3
8 2
6 → 3
4 → 4
2 → 5
7 → 3 Q J
J 10 9 6 3
A J 8 5 2
10

2665. K Q J
K 3
J 5 3
A 10 8 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A 10 7 3
A 10 6
K Q 10 8 2
Q
6 → 4
4 → 4
2 → 4
7 → 5 5 2
Q J 9 8 7 5
A 9 7
6 2

2673. 10 3 2
K 10
A Q J
A 10 8 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q J 7
A 8 6
K 10 9 7 5
4
6 → 5
4 → 4
2 → 4
7 → 3 A 5
Q J 9 7 5 3
8 3 2
Q 2

2692. Q 3 2
8 7 3
A Q
A Q 10 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 10 7
A J 10
K J 10 5 3
6
6 → 3
4 → 4
2 → 3
7 → 3 A 5
K Q 9 6 5
9 8 7 2
8 2

2696. A 10 2
K 10 3
J 8
A Q 10 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 5
J 7 5
A K Q 5 3
8 4
6 → 3
4 → 3
2 → 4
7 → 3 Q 7 3
A Q 9 8 6
10 9 7 2
2

3079. A 10 2
A Q 10
K 10 7
10 8 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q 7 5 3
K 7 3
Q J 3
A Q 4
6 → 2
4 → 2
2 → 2
7 → 3 K J
J 9 8 6 5
A 9 8 5 2
3

3085. J 5 2
K 6
A Q 8
A 10 8 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 10 7
A J 9
K J 9 7 5
3
6 → 5
4 → 4
2 → 4
7 → 3 A 3
Q 10 8 7 5 3
10 3 2
Q 4

3089. A 7 3
Q 7 6
A J 2
Q 8 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 10 2
A K 8
Q 9 7 3
10 2
6 → 3
4 → 4
2 → 3
7 → 3 Q 5
J 10 9 5 3
K 10 8 5
A 4

3136. J 5 2
Q 8
A 9 5 2
A Q 6 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 7
A K 10 5
Q 8 7
10 8 2
6 → 3
4 → 3
2 → 4
7 → 3 A 10 3
J 9 7 6 3
K J 10 3
3

3186. A Q 10
K 9 5
A J 3
6 4 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table J 7 3 2
Q 10 8
K Q 9 7
A 8
6 → 3
4 → 3
2 → 3
7 → 4 K 5
A J 7 6 3
10 8 5 2
Q 10

Simulation 8Z30 Main Top Lead against Two Hearts

3190. A Q 10
K 3
Q 10 7
Q 10 8 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K 5 3 2
Q J 10
A K 9 8 3
4
6 → 5
4 → 4
2 → 4
7 → 4 J 7
A 9 8 7 6 5
J 5 2
A 2

3192. A 7 5
K 6 5
J 10 7
A Q 10 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 10 2
A J 9
K 9 8 5
8 3
6 → 1
4 → 2
2 → 1
7 → 1 Q 3
Q 10 8 7 3
A Q 3 2
6 4

3198. Q 10 5
K 10 8
J 9
A Q 10 8 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K J 7
Q 9 3
K Q 10 7 2
6
6 → 3
4 → 3
2 → 4
7 → 3 3 2
A J 7 6 5
A 8 5 3
4 2

4380. Q 10
Q J 8
K 9 7
A Q 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A J 7 3
K 9 7
A J 8 2
10 3
6 → 2
4 → 2
2 → 2
7 → 3 K 5 2
A 10 6 5 3
Q 10 5 3
8

4387. A J 2
Q 7
9 8 5 3
A Q 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q 10 3
A 9 3
A K J 10 7
10 8
6 → 4
4 → 3
2 → 3
7 → 3 K 7 5
K J 10 8 6 5
Q 2
4 3

4428. K J 7
10 3
A 8 5
A 8 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 10 2
K Q J 9
K 10 9 2
10
6 → 6
4 → 7
2 → 6
7 → 6 5 3
A 8 7 6 5
Q J 7 3
Q 2

4438. J 10
J 9 8
A 10 3
A Q 10 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table 7 5 2
A K Q
K Q J 8 2
8 4
6 → 3
4 → 3
2 → 4
7 → 3 A K Q 3
10 7 6 5 3
9 7 5
6

4596. A Q 5
Q 7 3
A 7 3
Q 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table 10 7 3 2
A 9 8
K J 10 8
A 2
6 → 4
4 → 4
2 → 4
7 → 5 K J
K J 10 6 5
Q 9 5 2
10 8

4608. A J 2
8 5
K 10 9
A Q 8 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 5 3
Q J 9 6
A Q 8 7
6
6 → 5
4 → 4
2 → 4
7 → 3 10 7
A K 10 7 3
J 5 3 2
10 2

4617. A K 3
A 8
J 5 2
Q 10 6 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q 7 5 2
K Q J 9
Q 10 9 7
A
6 → 5
4 → 6
2 → 5
7 → 5 J 10
10 7 6 5 3
A K 8 3
8 4

Simulation 8Z30 Main Top Lead against Two Hearts

4695. A Q 10
A 9 3
9 3
A 8 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table J 7 3
K 7 5
A K Q J 10
10 2
6 → 3
4 → 3
2 → 5
7 → 3 K 5 2
Q J 10 8 6
8 7 5 2
Q

4838. A K 3
K 9 7
A 10 2
8 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table J 10 5 2
Q J 3
K Q 3
A 10 3
6 → 3
4 → 3
2 → 3
7 → 4 Q 7
A 10 8 6 5
J 9 8 7 5
Q

4861. 10 7
K Q 7
K 10 8
A Q 10 8 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 3
A J 6
A Q 5 3 2
6 4
6 → 5
4 → 4
2 → 4
7 → 4 A Q 5 2
10 9 8 5 3
J 9 7
2

4877. K Q 7
Q J 10
Q 7 2
A 10 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A J 3 2
K 5 3
K J 10 9
Q 8
6 → 4
4 → 5
2 → 4
7 → 4 10 5
A 9 8 7 6
A 8 5 3
4 3

4884. A 7
K 10 7
10 7 5 2
A Q 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 10
A 8 3
A J 9 3
8 6 2
6 → 3
4 → 3
2 → 4
7 → 3 J 5 3 2
Q J 9 6 5
K Q 8
10

5190. A 5 2
K 8
Q 10 7
A 8 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q J 7
A Q 10 7
K 5 3 2
Q 3
6 → 3
4 → 3
2 → 3
7 → 4 K 10 3
J 9 6 5 3
A J 9 8
10

5191. J 10 5
A Q 3
8 5 2
A Q 10 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 2
K J 7
K Q 9 7
8 6 3
6 → 5
4 → 4
2 → 4
7 → 4 K 7 3
10 9 8 6 5
A J 10 3
2

5220. 10 7 2
A 3
K 7 3
A Q 8 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q J 3
Q 9 7 5
A J 9 2
10
6 → 3
4 → 4
2 → 3
7 → 3 K 5
K J 10 8 6
Q 10 8 5
4 3

5319. 10 7
K Q 6
A J 2
A 10 8 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K Q 3
J 7 5
Q 10 8 5
Q 4
6 → 3
4 → 3
2 → 4
7 → 3 J 5 2
A 10 9 8 3
K 9 7 3
2

5455. A K 10
A Q 7
J 8 2
10 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table 7 5 3 2
K 5 3
K Q 7 3
A 8
6 → 3
4 → 3
2 → 3
7 → 4 Q J
J 10 9 8 6
A 10 9 5
Q 3

Simulation 8Z30 Main Top Lead against Two Hearts

5458. K 10 2
K 7
A 7 2
A 8 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q J 5 3
A J 9 3
K Q 9 5
10
6 → 5
4 → 4
2 → 4
7 → 4 A 7
Q 10 8 6 5
J 10 8 3
Q 3

5488. 10 7 5
A 3
K 10 9
A Q 10 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K J 2
K 10 8 5
Q 7 5 3
3
6 → 3
4 → 4
2 → 3
7 → 3 Q 3
Q J 9 7 6
A J 8 2
8 6

5496. K 3
K 9 6
A Q 9
Q 6 4 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q 10 7 5
A 5 3
K J 2
A 10 8
6 → 2
4 → 2
2 → 3
7 → 2 A J 2
Q J 10 8 7
10 8 7 5 3
—

6266. A Q 2
A J
J 9 8
Q 8 4 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 3
10 9 6 5
A Q 3
A 10 6
6 → 3
4 → 3
2 → 3
7 → 4 10 7 5
K Q 8 7 3
K 10 7 5 2
—

6267. K J
K 5 3
J 8 7 3
A Q 10 6
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q 5 3
Q 10 6
A K Q 10 2
4 2
6 → 2
4 → 1
2 → 1
7 → 1 A 10 7 2
A J 9 8 7
9 5
8 3

6288. K 10 5
K J
8 7 5 3
A Q 10 6
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q J 7
A 10 5 3
K J 10
3 2
6 → 3
4 → 4
2 → 3
7 → 3 3 2
Q 9 8 7 6
A Q 9 2
8 4

6294. 10 7 3
A Q 8
A 2
A 8 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 5
K 6 5
Q J 9 8 7
Q 2
6 → 2
4 → 2
2 → 3
7 → 2 K J 2
J 10 9 7 3
K 10 5 3
10

6751. K 10 7
A 10
8 7 5
A Q 10 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A J 3
K J 9 3
A Q 10 9
6 4
6 → 4
4 → 4
2 → 4
7 → 5 Q 5 2
Q 8 7 6 5
K J 3 2
8

6755. K 3 2
K J 9
A 9 3
Q 8 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 7 5
A 10 8
K J 8 7
10 6
6 → 6
4 → 5
2 → 5
7 → 4 J 10
Q 7 6 5 3
Q 10 5 2
A 4

6773. Q J 5
Q 8 3
A J 10
A 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K 10
A J 9
8 7 3 2
10 8 3
6 → 3
4 → 4
2 → 3
7 → 3 7 3 2
K 10 7 6 5
K Q 9 5
Q

Simulation 8Z30 Main Top Lead against Two Hearts

6800. K 5 2
A Q 9
A 10 5
8 4 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A 10 3
J 10 8
K J 9 2
A 10 6
6 → 3
4 → 3
2 → 4
7 → 3 Q J 7
K 7 6 5 3
Q 8 7 3
Q

6819. Q 3 2
9 6
A K 7
A 10 8 6 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table A K 10 5
Q J 10 5
Q 3 2
Q 2
6 → 4
4 → 4
2 → 4
7 → 5 J 7
A K 8 7 3
J 10 9 8 5
4

6822. A Q 7
Q 10 7
A 9 7
Q 8 6 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table K J 5 3
A J 3
K J 10 3
4 3
6 → 5
4 → 4
2 → 3
7 → 3 10 2
K 9 8 6 5
Q 8 5 2
A 10

6840. A K 3
J 6
Q J 3
Q 8 6 4 3
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q J 5
A 9 8 5
K 10 9 2
A 10
6 → 4
4 → 5
2 → 4
7 → 4 10 7 2
K Q 10 7 3
A 8 7 5
2

6864. K 10
A 9 5
A J 5 2
Q 10 8 4
9 8 6 4
4 2
6 4
K J 9 7 5 Table A J 2
K 8 6
K Q 10 7 3
6 3
6 → 4
4 → 4
2 → 5
7 → 3 Q 7 5 3
Q J 10 7 3
9 8
A 2

7258. A K
10 9 3
Q 10 7
A 10 6 4 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table Q J 10 2
A Q 8
K 8 5 2
Q 3
6 → 1
4 → 1
2 → 1
7 → 2 7 5 3
K J 7 6 5
A J 9 3
8

7259. Q 2
A Q 8
A 10 9 5
Q 10 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table K 5 3
K 9 7
K J 8 3
A 8 6
6 → 4
4 → 3
2 → 3
7 → 3 A J 10 7
J 10 6 5 3
Q 7 2
4

7290. A J 5
5 3
K 10 5
A Q 10 8 6
9 8 6 4
4 2
6 4
K J 9 7 5 Table K Q 7
A Q 9 8
Q J 3 2
4 3
6 → 3
4 → 4
2 → 3
7 → 3 10 3 2
K J 10 7 6
A 9 8 7
2

7407. Q 7 5
A Q 5
J 5
A 10 4 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A J 10 2
K 9 8
A Q 10 8 3
6
6 → 4
4 → 4
2 → 5
7 → 4 K 3
J 10 7 6 3
K 9 7 2
Q 8

7414. J 7 5
K Q
A 8 2
A 8 6 3 2
9 8 6 4
4 2
6 4
K J 9 7 5 Table A Q 10
A 6 5 3
Q 7 3
Q 10 4
6 → 2
4 → 2
2 → 2
7 → 3 K 3 2
J 10 9 8 7
K J 10 9 5
—

Simulation 8Z30 Main Top Lead against Two Hearts

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

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

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

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

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

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

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

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

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

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

Simulation 8Z30 Main Top Lead against Two Hearts

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

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

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

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

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

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

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

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

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

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

Simulation 8Z30 Main Top Lead against Two Hearts

	N-S vul	`West`	North	`East`	South
9 8 6 4		Pass	1	Dbl	1
4 2		Pass	1 NT	Pass	2
6 4		Pass	Pass	Pass
K J 9 7 5
	2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

667.	3 2 Q 8 5 A Q 7 3 A Q 10 4
9 8 6 4 4 2 6 4 K J 9 7 5		K Q 10 5 A J 7 K 9 2 6 3 2
6 → 4 4 → 3 2 → 3 7 → 3	A J 7 K 10 9 6 3 J 10 8 5 8

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

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

1329.	A Q 5 K 10 8 A J 8 10 8 6 4
9 8 6 4 4 2 6 4 K J 9 7 5		J 10 3 2 Q 5 3 K Q 7 2 A 2
6 → 3 4 → 3 2 → 3 7 → 4	K 7 A J 9 7 6 10 9 5 3 Q 3

1330.	A K 7 9 8 J 10 9 3 A Q 3 2
9 8 6 4 4 2 6 4 K J 9 7 5		5 3 2 A K Q 10 K Q 2 10 8 6
6 → 5 4 → 4 2 → 4 7 → 4	Q J 10 J 7 6 5 3 A 8 7 5 4