8Z28 rpbridge.net Main

Singleton against 3 NT?

by Richard Pavlicek

If your opponents reach 3 NT without showing a specific suit, and without pursuing a major-suit contract, could a minor-suit singleton be the best opening lead in theory? This seems highly unlikely to me, so I was surprised to discover that another bridge site had determined a diamond lead to be best with the following hand:

E-W vul West North East South
Q 9 7 2 Table 1 NT
K 6 3 2 Pass 3 NT Pass Pass
7 Pass
K J 7 2
3 NT

My routine choice would be to lead the 2, but their contention was that the 7 was 0.2 IMPs per board better. Wow! The obvious downside of a spade lead is the potential loss of a trick, but in my view this is more than compensated by its attacking ability and tempo gain. I could certainly be wrong, so it begged for a simulation. For completeness, I also included the 2 and 2 leads — though surely inferior in anyone’s view — and the scenario with declarer vulnerable as well.

For a simulation I created 10,000 random deals with West fixed and the other hands constrained to fit the auction. South: 15-17 HCP; balanced (5-card major allowed if the doubleton is J-x or better). North: 8-14 HCP; 10-14 revalued points; no 5+ major; no 7+ minor unless 7-2-2-2; no 4-card major unless 4-3-3-3. East: no 8+ card suit; no 7-card suit unless less than 6.5 playing tricks; else less than 7.5 playing tricks or freakness less than 6 (i.e., to bid without a 7-card suit East would need 7.5+ playing tricks and extreme shape).

Results are tabulated below. Set Percent shows how often the contract is defeated, and Hold Percent how often it is made exactly (no overtrick). Trick Average shows the average number of tricks won by the defense. The second table shows a scoring comparison for each lead against each other lead, with the better lead at IMPs leftmost. Win Percent shows the verdict at matchpoints or board-a-match (above 50.00 wins). Net Score shows the cumulative gain if scoring is by total points, and IMP/bd shows the average gain per board at IMP scoring. Net Score and IMP/bd are calculated twice, first with declarer nonvul (green) then with declarer vul (red). Win Percent is not affected by vulnerability.

Results for 10,000 Deals
3 NT South Set Percent Hold Percent Trick Average
2 lead 14.86 26.60 3.1696
2 lead 14.72 24.33 3.1197
7 lead 14.50 24.66 3.1729
2 lead 11.24 24.48 3.0145

Results for 10,000 Deals
3 NT South	Set Percent	Hold Percent	Trick Average
2 lead	14.86	26.60	3.1696
2 lead	14.72	24.33	3.1197
7 lead	14.50	24.66	3.1729
2 lead	11.24	24.48	3.0145

Comparison Win Percent Net Score NV IMP/bd NV Net Score Vul IMP/bd Vul
2 vs 7 48.21 +15510 +0.0186 +27960 +0.0294
2 vs 2 51.98 +21910 +0.0615 +28060 +0.0685
2 vs 2 56.40 +201610 +0.4757 +299710 +0.5600
7 vs 2 53.89 +6400 +0.0417 +100 +0.0372
7 vs 2 58.71 +186100 +0.4616 +271750 +0.5349
2 vs 2 54.39 +179700 +0.4139 +271650 +0.4912

Comparison	Win Percent	Net Score NV	IMP/bd NV	Net Score Vul	IMP/bd Vul
2 vs 7	48.21	+15510	+0.0186	+27960	+0.0294
2 vs 2	51.98	+21910	+0.0615	+28060	+0.0685
2 vs 2	56.40	+201610	+0.4757	+299710	+0.5600
7 vs 2	53.89	+6400	+0.0417	+100	+0.0372
7 vs 2	58.71	+186100	+0.4616	+271750	+0.5349
2 vs 2	54.39	+179700	+0.4139	+271650	+0.4912

I am relieved to see my beliefs are upheld. While the 7 shows a slight gain at matchpoints, the 2 is superior at IMPs — not by a great margin but clearly a favorite. To be sure, claiming the 7 is 0.2 IMPs per board better than the 2 is off base. Or perhaps they were up all night partying and figured an opening-lead beer card would help them get sober. Whatever. No doubt a hand could be constructed where a minor-suit singleton is the best lead, but I won’t be looking for it.

8Z28 rpbridge.net Main Top Singleton against 3 NT?

Sample 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 3 NT by South.

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

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

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

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

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

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

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

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

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

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

8Z28 rpbridge.net Main Top Singleton against 3 NT?

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

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

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

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

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

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

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

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

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

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

8Z28 rpbridge.net Main Top Singleton against 3 NT?

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

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

187. 8 6 4
9 8 4
A Q 9 8 6
A 6
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 5
J 10 7 5
K 10 4 3
9 5 3
2 → 4
2 → 4
7 → 5
2 → 3 A K J 3
A Q
J 5 2
Q 10 8 4

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

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

330. 8 6 5
J 9
A Q J 5 4 3
10 9
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 4
A Q 10 8 4
10 9 8
Q 6 4
2 → 3
2 → 5
7 → 4
2 → 4 A K J 3
7 5
K 6 2
A 8 5 3

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

422. 10 6 5
Q 7
K Q 8 4 3 2
Q 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 4
9 5 4
J 6
A 9 8 5 3
2 → 4
2 → 3
7 → 4
2 → 5 A K 3
A J 10 8
A 10 9 5
10 6

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

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

8Z28 rpbridge.net Main Top Singleton against 3 NT?

616. 10 5 3
A 9 4
Q 10 8
A 10 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 6
J 10 8 7
A 9 5 4 2
9 3
2 → 3
2 → 4
7 → 5
2 → 3 A K J 4
Q 5
K J 6 3
Q 8 6

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

735. 10 8
Q 4
A J 8 6 5 2
Q 10 8
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K J 5 4
10 9 7
K 10 9
9 4 3
2 → 5
2 → 3
7 → 4
2 → 3 A 6 3
A J 8 5
Q 4 3
A 6 5

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

972. 5 3
5
A K 10 6 3
Q 9 6 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 6
J 10 7 4
Q J 9 8 2
8
2 → 4
2 → 4
7 → 5
2 → 4 A J 8 4
A Q 9 8
5 4
A 10 5

1005. K 3
J 9
A J 10 9 5 4 3
10 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 6 5 4
10 8 7 4
K 8 6
A 9
2 → 4
2 → 4
7 → 4
2 → 5 A J 10
A Q 5
Q 2
Q 8 6 5 4

1026. J 8
10 5
K Q J 10 8 5
Q 10 8
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 6
9 8 7
6 3 2
A 6 5 3
2 → 5
2 → 3
7 → 3
2 → 4 A 5 4 3
A Q J 4
A 9 4
9 4

1080. J 8 6
Q 4
A J 10 6 5 2
9 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 5 4
A 10 9 8 5
3
Q 10 8 3
2 → 3
2 → 5
7 → 4
2 → 4 A K 3
J 7
K Q 9 8 4
A 6 4

1113. K 5 4
J 8 7
K 8 4 2
A 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 3
10 9 5
A 10 6 3
10 9 5
2 → 4
2 → 4
7 → 5
2 → 4 A 10 6
A Q 4
Q J 9 5
Q 8 6

1207. J 4 3
5 4
Q J 10 9 6 4
A 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table A 10 5
Q 10 9 8
2
Q 10 9 6 3
2 → 4
2 → 4
7 → 4
2 → 5 K 8 6
A J 7
A K 8 5 3
8 5

8Z28 rpbridge.net Main Top Singleton against 3 NT?

1260. K 6 4
Q 9
J 9 5 4 2
A 8 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table A J 10
10 8 4
10 8 3
10 9 6 5
2 → 6
2 → 4
7 → 4
2 → 4 8 5 3
A J 7 5
A K Q 6
Q 4

1384. A 10 4
J 10
J 10 3 2
A 10 8 6
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 6
Q 9 7 5 4
Q 9 8 5 4
Q 5
2 → 3
2 → 5
7 → 4
2 → 4 K J 8 5 3
A 8
A K 6
9 4 3

1773. K 8 5 3
10 5 4
Q 8 2
A Q 9
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 6 4
J 9 8
K J 10 6 5 3
10 4
2 → 4
2 → 4
7 → 5
2 → 4 A J 10
A Q 7
A 9 4
8 6 5 3

1936. K 4 3
9 5 4
K J 10 5 4
A 9
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 5
10 8
Q 9 8 6
Q 10 8 5 3
2 → 3
2 → 3
7 → 4
2 → 5 A J 8 6
A Q J 7
A 3 2
6 4

1965. 10
9 8 5
A J 10 8 4
A 10 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table A 8 6 5 4
10 4
Q 3 2
9 8 6
2 → 5
2 → 3
7 → 3
2 → 3 K J 3
A Q J 7
K 9 6 5
Q 3

1989. 6 5 4
4
A Q J 9
A 10 9 8 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 3
Q J 10 8 5
10 8 5 4
5 4
2 → 2
2 → 5
7 → 2
2 → 2 A K 10 8
A 9 7
K 6 3 2
Q 6

2025. 8 6 5
Q 9 5
K J 10 9 4
A 8
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 3
J 10
A 8 3 2
10 9 6 4 3
2 → 3
2 → 4
7 → 5
2 → 4 A K 10 4
A 8 7 4
Q 6 5
Q 5

2163. A 5 4
Q 10 9
K 9 4 3 2
8 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 6
7 4
J 6 5
Q 10 9 6 5
2 → 4
2 → 3
7 → 3
2 → 5 J 8 3
A J 8 5
A Q 10 8
A 4

2175. A
Q J 8
Q J 9 8 5
Q 9 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 8 6 4
9 7 5 4
6 4 2
6
2 → 5
2 → 2
7 → 3
2 → 3 J 5 3
A 10
A K 10 3
A 10 8 3

2220. 5 4
Q J
A J 8 6 4
Q 8 6 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 3
10 9 7 5 4
Q 10 3 2
10 5
2 → 4
2 → 5
7 → 4
2 → 4 A J 10 8 6
A 8
K 9 5
A 9 3

8Z28 rpbridge.net Main Top Singleton against 3 NT?

2562. 10 5
9 7 5
A K 5 4
A 8 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 6
10 8 4
J 10 9 8 2
9 6 3
2 → 4
2 → 4
7 → 5
2 → 4 A J 8 4 3
A Q J
Q 6 3
Q 10

2581. A 5 3
J 9
K J 9 5 4 2
5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 6
Q 10 7 4
6
A 10 9 8 6
2 → 4
2 → 4
7 → 4
2 → 5 K 10 4
A 8 5
A Q 10 8 3
Q 3

2589. A 10 3
Q 10 9 8
K 9 4
Q 5 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K J 6
7 4
J 10 8 2
9 8 6 4
2 → 5
2 → 4
7 → 4
2 → 4 8 5 4
A J 5
A Q 6 5 3
A 10

2661. K 6 3
A 10
A 5 3 2
8 6 5 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 4
J 9 8 5 4
Q J 10 8 6
9
2 → 4
2 → 5
7 → 4
2 → 3 A J 10 5
Q 7
K 9 4
A Q 10 4

2858. K J 4
8 5 4
A J 8 5
Q 8 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 6
10 9 7
K Q 10 9 6
10 9 6
2 → 4
2 → 4
7 → 5
2 → 4 A 10 5 3
A Q J
4 3 2
A 4 3

2866. K J 4
8 4
A Q 9 6 5 2
8 6
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 5
J 10 9 7
J 10
A 10 9 5 4
2 → 3
2 → 2
7 → 3
2 → 5 A 8 6 3
A Q 5
K 8 4 3
Q 3

2870. A 5 4
Q 7 5 4
8 4 3
A 8 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 6 3
9 8
A J 9 6 5
9 5
2 → 5
2 → 4
7 → 4
2 → 3 K 10
A J 10
K Q 10 2
Q 10 6 4

2872. A K 4
J 8
K J 8 6 4 3
10 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 3
A 10 9 7 4
10 5 2
9 6 3
2 → 3
2 → 5
7 → 3
2 → 2 J 10 6 5
Q 5
A Q 9
A Q 8 5

2882. K 6 3
10 9 4
K 9 4
A 8 6 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 5 4
5
A Q 8 6 3 2
10 4 3
2 → 4
2 → 4
7 → 5
2 → 4 A J 10
A Q J 8 7
J 10 5
Q 9

2925. J 5
Q J
K J 8 6 4 3 2
A 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 4
10 9 8 4
Q 10 9
Q 8 5 3
2 → 2
2 → 2
7 → 2
2 → 5 A K 10 6 3
A 7 5
A 5
10 9 6

8Z28 rpbridge.net Main Top Singleton against 3 NT?

2947. A 4
Q 9 5
Q 10 6 5
Q 6 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8
10 8 4
A J 9 8 4 3
9 8
2 → 5
2 → 4
7 → 4
2 → 4 K 10 6 5 3
A J 7
K 2
A 10 3

2951. 10 6 4
Q 10
A K 10 6 4 2
6 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 5 3
A 9 8 7 5
J 8 3
Q 4
2 → 3
2 → 5
7 → 4
2 → 4 A K J
J 4
Q 9 5
A 10 9 8 5

3102. 10 5 4
A 9 8
A Q 4
10 9 8 6
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 6 3
J 7 5
K J 9 8 5 2
5 3
2 → 4
2 → 4
7 → 5
2 → 4 A K J 8
Q 10 4
10 6 3
A Q 4

3121. K 4
9 8 4
K Q 10 8 4 2
10 9
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 5 3
7
A 6 3
Q 8 6 4 3
2 → 4
2 → 3
7 → 4
2 → 5 A 10 6
A Q J 10 5
J 9 5
A 5

3122. —
J 9 7
A 10 9 8 6
A 10 9 8 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table A 10 6 5 4 3
4
J 5 4 2
6 3
2 → 6
2 → 3
7 → 3
2 → 2 K J 8
A Q 10 8 5
K Q 3
Q 5

3156. 8 5
5 4
K Q 9 5 4 2
A 9 8
Q 9 7 2
K 6 3 2
7
K J 7 2 Table A J 3
Q 10 9 7
10 8 6 3
6 5
2 → 4
2 → 5
7 → 3
2 → 3 K 10 6 4
A J 8
A J
Q 10 4 3

3364. 6 5
Q J 7
A J 9 6
Q 10 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 10 8 3
5 4
K Q 4 3 2
8 3
2 → 4
2 → 4
7 → 5
2 → 4 A K 4
A 10 9 8
10 8 5
A 9 6

3660. A 3
Q 10
Q 10 9 6 4 3 2
5 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 8
J 9 5
8 5
A 10 9 6 4
2 → 4
2 → 3
7 → 4
2 → 5 J 6 5 4
A 8 7 4
A K J
Q 8

3686. K
A Q 8
K 5 4 3
10 8 6 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 10 8 5 4
7 5
Q J 10 6 2
9
2 → 5
2 → 3
7 → 3
2 → 3 A 6 3
J 10 9 4
A 9 8
A Q 5

3709. K 8
J 9
Q 10 9 5 2
A 10 9 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 5
Q 10 7 5
K 8 6 4 3
8 6
2 → 4
2 → 5
7 → 4
2 → 3 A J 6 4 3
A 8 4
A J
Q 4 3

8Z28 rpbridge.net Main Top Singleton against 3 NT?

3830. J 10 3
A J 5
A J 4 3
8 6 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 8 4
10 9
Q 10 9 8 6
10 4 3
2 → 4
2 → 4
7 → 5
2 → 4 A 6 5
Q 8 7 4
K 5 2
A Q 9

3847. A 4 3
10 5 4
A J 10 6 5
6 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 10 8 5
J 9 7
Q 9 3
A 10 9 3
2 → 4
2 → 4
7 → 4
2 → 5 K J 6
A Q 8
K 8 4 2
Q 8 4

3915. A 8
J 10 8
A J 9 5 3
10 9 8
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 4 3
Q 9 7 5
10 8 6 4
3
2 → 5
2 → 4
7 → 4
2 → 3 J 6 5
A 4
K Q 2
A Q 6 5 4

4009. 8 4 3
A Q
A Q 6 5 4
10 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10
J 10 7 5
10 9 8 3 2
8 6
2 → 4
2 → 5
7 → 4
2 → 3 A J 6 5
9 8 4
K J
A Q 9 3

4111. A 5 4
Q 4
K J 9 5 3
10 5 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table J 8 3
J 10 9 7 5
A 8 6 4
4
2 → 4
2 → 4
7 → 5
2 → 3 K 10 6
A 8
Q 10 2
A Q 9 8 6

4117. A K 10
Q 9 7
J 8 6 3
9 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 6 4 3
J 10 8
K 10 9 2
Q 10 3
2 → 4
2 → 4
7 → 4
2 → 5 J 8 5
A 5 4
A Q 5 4
A 8 6

4181. 6 5
Q J 9
K Q J 3
A 8 6 5
Q 9 7 2
K 6 3 2
7
K J 7 2 Table K 10 8 4 3
10 7 4
9 6 5 4 2
—
2 → 5
2 → 2
7 → 3
2 → 3 A J
A 8 5
A 10 8
Q 10 9 4 3

4182. J 4
9 7
K J 9 8 2
A Q 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 8 6 5 3
A J 10 8 4
5 4 3
6
2 → 2
2 → 5
7 → 2
2 → 2 A K 10
Q 5
A Q 10 6
10 9 8 5

4367. J 6 5
A 5 4
A J 5 2
6 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 4 3
Q 9 8
K 10 9 4 3
10 8 5
2 → 4
2 → 4
7 → 5
2 → 4 A K 10 8
J 10 7
Q 8 6
A Q 9

4464. K J
10 9 4
K Q J 8 2
9 5 4
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 5 4
8 7 5
A 9 6 3
Q 10 8 6
2 → 3
2 → 2
7 → 3
2 → 5 A 10 8 6 3
A Q J
10 5 4
A 3

8Z28 rpbridge.net Main Top Singleton against 3 NT?

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

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

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

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

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

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

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

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

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

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

8Z28 rpbridge.net Main Top Singleton against 3 NT?

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

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

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

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

9995. A 10
9 4
A K J 6 4 3
6 4 3
Q 9 7 2
K 6 3 2
7
K J 7 2 Table 6 4 3
Q 10 7 5
8 5 2
10 9 5
2 → 1
2 → 1
7 → 1
2 → 1 K J 8 5
A J 8
Q 10 9
A Q 8

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

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

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

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

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

8Z28 rpbridge.net Main Top Singleton against 3 NT?

	E-W vul	West	`North`	East	`South`
Q 9 7 2					1 NT
K 6 3 2		Pass	3 NT	Pass	Pass
7		Pass
K J 7 2
	3 NT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

187.	8 6 4 9 8 4 A Q 9 8 6 A 6
Q 9 7 2 K 6 3 2 7 K J 7 2		10 5 J 10 7 5 K 10 4 3 9 5 3
2 → 4 2 → 4 7 → 5 2 → 3	A K J 3 A Q J 5 2 Q 10 8 4

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

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

330.	8 6 5 J 9 A Q J 5 4 3 10 9
Q 9 7 2 K 6 3 2 7 K J 7 2		10 4 A Q 10 8 4 10 9 8 Q 6 4
2 → 3 2 → 5 7 → 4 2 → 4	A K J 3 7 5 K 6 2 A 8 5 3

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

422.	10 6 5 Q 7 K Q 8 4 3 2 Q 4
Q 9 7 2 K 6 3 2 7 K J 7 2		J 8 4 9 5 4 J 6 A 9 8 5 3
2 → 4 2 → 3 7 → 4 2 → 5	A K 3 A J 10 8 A 10 9 5 10 6

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